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Page 1
Pinnacle Day: 84th - 86th Average
Average
Key Points:
1) An average or arithmetic mean of
given data is the sum of the given
observations divided by the number of
observations.
For example : If we have to ?nd out the
average of 10, 15, 25 and 30, then
required average will be equal to:
= 20
10 + 15 + 25 + 30
4
=
80
4
Therefore, we can say, Average (A) =
?????? ???? ??h?? ?????????? ???????????????????????? ( ?? )
???????????? ???? ???????????????????????? ( ?? )
2) If all the numbers increase by ‘a’ then
the average of the numbers will also
increase by ‘a’.
3) If all the numbers decrease by ‘a’ then
the average of the numbers will also
decrease by ‘a’.
4) If all the numbers are multiplied by ‘a’
then their average must also be
multiplied by ‘a’.
5) If all the numbers are divided by ‘a’
then their average must also be divided
by ‘a’.
6) Average of ?rst n natural numbers
=
?? + 1
2
( )
7) Average of ?rst n even numbers
= ( ?? + 1 )
8) Average of ?rst n odd numbers = ??
9) Average of consecutive numbers
=
?????????? ???????????? + ???????? ????????????
2
10) Average of 1 to n odd numbers
=
???????? ?????? ???????????? + 1
2
11) Average of 1 to n even numbers
=
???????? ???????? ???????????? + 2
2
12) Average of squares of ?rst n natural
numbers =
( ?? + 1 )( 2 ?? + 1 )
6
13) Average of cubes of ?rst n natural
numbers =
?? ( ?? + 1 )
2
4
14) Average of n multiples of any number
=
???????????? × ( ?? + 1 )
2
15) Combined mean or combined
average :
If the mean of and observations are ??
1
??
2
and respectively then, ??
1
??
2
Combined mean =
??
1
??
1
+ ??
2
??
2
??
1
+ ??
2
Ex : If the average marks of 30 boys is 50
and 40 girls is 60, then ?nd the combined
average marks of the whole class.
Soln : Combined average marks of whole
class = =
30 × 50 + 40 × 60
30 + 40
= = 55.71 marks
1500 + 2400
70
3900
70
16) Basically the term Run Rate means
how many runs have been scored in one
over of a cricket match. Higher run rate is
good for batsmen.
Run rate =
?????????? ???????? ????????????
???????????? ???? ?????????? ????????????
Ex : If the batsman has scored 225 runs
in 9 overs, ?nd his run rate.
Soln : Run rate = = 25 runs/over
225
9
17) Bowling Average
=
?????????? ???????? ??????????????
?????????? ???????????? ???? ?????????????? ??????????
Lower Bowling average is good for
bowlers.
Ex : If the bowler has taken 3 wickets
allowing 120 runs, ?nd his bowling
average.
Bowling Average = = 40
120
3
runs/wicket
18) If the average is x and a number
having value greater than x is added then
the new average will be greater than x.
Similarly, if a number having value less
than x is added then the new average will
be less than x.
Ex 1. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
adding 6.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 6 is greater than the old
average, the new average is going to be
greater than the old average.
So, new average = = = 3.5
15 + 6
5 + 1
21
6
which is greater than 3.
Ex 2. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
adding 2.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 2 is less than the old average,
the new average is going to be less than
the old average.
So, new average = = = 2.83
15 + 2
5 + 1
17
6
which is less than 3.
19) If the average is x and a number
having value less than x is removed then
the new average will be greater than x.
Similarly, if a number having value
greater than x is removed then the new
average will be less than x.
Ex 1. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
removing 2.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 2 is less than the old average,
the new average is going to be greater
than the old average.
So, new average = = = 3.25
15 - 2
5 - 1
13
4
which is greater than 3.
Ex 2. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
removing 4.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 4 is greater than the old
average, the new average is going to be
less than the old average.
So, new average = = = 2.75
15 - 4
5 - 1
11
4
which is less than 3.
Variety Questions
Q.1. Rajender is working as a delivery
boy in a multinational company. The
company is paying him ?90 per delivery.
In a fortnight comprising 15 consecutive
working days, his average earnings per
day was ?540. If his average earnings of
the ?rst 7 days was ?519 per day and
that of the last 7 days was ?546 per day,
then at was his earning on the 8th day of
the fortnight?
SSC CHSL 07/08/2023 (3rd Shift)
(a) ?571 (b) ?681 (c) ?661 (d) ?645
Q.2. The average weight of a group of 12
children is 66 kg. If 2 children, X and Y,
replace A and B, the new average weight
becomes 65 kg. The weight of A= weight
of B and the weight of X = weight of Y.
Another child, C, is included in the group,
and the new average weight remains 65
kg. Weight of C= weight of X. Find the
weight of A.
SSC CHSL 04/08/2023 (3rd Shift)
(a) 69 kg (b) 72 kg (c) 71 kg (d) 67 kg
Q.3. Sudesh is the owner of a
multipurpose shop. For a speci?c month,
his pro?ts are detailed below.
Category Pro?t earned in ?
Groceries 50,000
Cosmetics 20,000
Ladies' dresses 10,000
In order to estimate the expected pro?t
www.ssccglpinnacle.com Download Pinnacle Exam Preparation App 610
Page 2
Pinnacle Day: 84th - 86th Average
Average
Key Points:
1) An average or arithmetic mean of
given data is the sum of the given
observations divided by the number of
observations.
For example : If we have to ?nd out the
average of 10, 15, 25 and 30, then
required average will be equal to:
= 20
10 + 15 + 25 + 30
4
=
80
4
Therefore, we can say, Average (A) =
?????? ???? ??h?? ?????????? ???????????????????????? ( ?? )
???????????? ???? ???????????????????????? ( ?? )
2) If all the numbers increase by ‘a’ then
the average of the numbers will also
increase by ‘a’.
3) If all the numbers decrease by ‘a’ then
the average of the numbers will also
decrease by ‘a’.
4) If all the numbers are multiplied by ‘a’
then their average must also be
multiplied by ‘a’.
5) If all the numbers are divided by ‘a’
then their average must also be divided
by ‘a’.
6) Average of ?rst n natural numbers
=
?? + 1
2
( )
7) Average of ?rst n even numbers
= ( ?? + 1 )
8) Average of ?rst n odd numbers = ??
9) Average of consecutive numbers
=
?????????? ???????????? + ???????? ????????????
2
10) Average of 1 to n odd numbers
=
???????? ?????? ???????????? + 1
2
11) Average of 1 to n even numbers
=
???????? ???????? ???????????? + 2
2
12) Average of squares of ?rst n natural
numbers =
( ?? + 1 )( 2 ?? + 1 )
6
13) Average of cubes of ?rst n natural
numbers =
?? ( ?? + 1 )
2
4
14) Average of n multiples of any number
=
???????????? × ( ?? + 1 )
2
15) Combined mean or combined
average :
If the mean of and observations are ??
1
??
2
and respectively then, ??
1
??
2
Combined mean =
??
1
??
1
+ ??
2
??
2
??
1
+ ??
2
Ex : If the average marks of 30 boys is 50
and 40 girls is 60, then ?nd the combined
average marks of the whole class.
Soln : Combined average marks of whole
class = =
30 × 50 + 40 × 60
30 + 40
= = 55.71 marks
1500 + 2400
70
3900
70
16) Basically the term Run Rate means
how many runs have been scored in one
over of a cricket match. Higher run rate is
good for batsmen.
Run rate =
?????????? ???????? ????????????
???????????? ???? ?????????? ????????????
Ex : If the batsman has scored 225 runs
in 9 overs, ?nd his run rate.
Soln : Run rate = = 25 runs/over
225
9
17) Bowling Average
=
?????????? ???????? ??????????????
?????????? ???????????? ???? ?????????????? ??????????
Lower Bowling average is good for
bowlers.
Ex : If the bowler has taken 3 wickets
allowing 120 runs, ?nd his bowling
average.
Bowling Average = = 40
120
3
runs/wicket
18) If the average is x and a number
having value greater than x is added then
the new average will be greater than x.
Similarly, if a number having value less
than x is added then the new average will
be less than x.
Ex 1. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
adding 6.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 6 is greater than the old
average, the new average is going to be
greater than the old average.
So, new average = = = 3.5
15 + 6
5 + 1
21
6
which is greater than 3.
Ex 2. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
adding 2.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 2 is less than the old average,
the new average is going to be less than
the old average.
So, new average = = = 2.83
15 + 2
5 + 1
17
6
which is less than 3.
19) If the average is x and a number
having value less than x is removed then
the new average will be greater than x.
Similarly, if a number having value
greater than x is removed then the new
average will be less than x.
Ex 1. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
removing 2.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 2 is less than the old average,
the new average is going to be greater
than the old average.
So, new average = = = 3.25
15 - 2
5 - 1
13
4
which is greater than 3.
Ex 2. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
removing 4.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 4 is greater than the old
average, the new average is going to be
less than the old average.
So, new average = = = 2.75
15 - 4
5 - 1
11
4
which is less than 3.
Variety Questions
Q.1. Rajender is working as a delivery
boy in a multinational company. The
company is paying him ?90 per delivery.
In a fortnight comprising 15 consecutive
working days, his average earnings per
day was ?540. If his average earnings of
the ?rst 7 days was ?519 per day and
that of the last 7 days was ?546 per day,
then at was his earning on the 8th day of
the fortnight?
SSC CHSL 07/08/2023 (3rd Shift)
(a) ?571 (b) ?681 (c) ?661 (d) ?645
Q.2. The average weight of a group of 12
children is 66 kg. If 2 children, X and Y,
replace A and B, the new average weight
becomes 65 kg. The weight of A= weight
of B and the weight of X = weight of Y.
Another child, C, is included in the group,
and the new average weight remains 65
kg. Weight of C= weight of X. Find the
weight of A.
SSC CHSL 04/08/2023 (3rd Shift)
(a) 69 kg (b) 72 kg (c) 71 kg (d) 67 kg
Q.3. Sudesh is the owner of a
multipurpose shop. For a speci?c month,
his pro?ts are detailed below.
Category Pro?t earned in ?
Groceries 50,000
Cosmetics 20,000
Ladies' dresses 10,000
In order to estimate the expected pro?t
www.ssccglpinnacle.com Download Pinnacle Exam Preparation App 610
Pinnacle Day: 84th - 86th Average
for the next month, he assigns the
weights of 6, 5 and 8 to the different
categories in the same order. What will
be the weighted average of his pro?ts?
SSC CHSL 03/08/2023 (2nd Shift)
(a) 25,265.18 (nearly) ?
(b) 24,863.16 (nearly) ?
(c) 25,163.16 (nearly) ?
(d) 25,263.16 (nearly) ?
Q.4. During a school excursion each
student of junior school was charged
?325 and each student of senior school
was charged ?400. If there were 80
students from junior school and the
combined average amount charged per
student was ?352, then how many
students from senior school went for the
excursion?
SSC CGL 24/07/2023 (1st shift)
(a) 55 (b) 45 (c) 50 (d) 40
Q.5. In ?150, B buys 10 pens for ?8 each,
10 erasers for ?5 each and some
sharpeners for ?4 each. What is the
average price per item in ??
SSC CGL 19/07/2023 (3rd shift)
(a) 8 (b) 7 (c) 10 (d) 6
Q.6. 20 students of a college went to a
hotel. 19 of them spent ?175 each on
their meal and the 20
th
student spent ?19
more than the average of all the 20.
Find the total money spent by them.
SSC CGL 17/07/2023 (4th shift)
(a) ?3,490 (b) ?3,540
(c) ?3,520 (d) ?3,500
Q.7. The average score in a test for 50
students is 44. Out of the total students,
40% of the students are girls and the rest
are boys. The average score of boys is
20% less than that of girls. What is the
average score of girls?
Higher Secondary 27/06/2023 (Shift - 3)
(a) 50 (b) 54 (c) 48 (d) 52
Q.8. A is the average of 10 given
numbers. B is the average after 2 of the
numbers were replaced by 3 other
different numbers. The average of the
removed numbers is 48 and the average
of the newly included numbers is 56. If A
+ B = 438, then the value of A - B is:
Matriculation Level 27/06/2023 (Shift - 2)
(a) 21 (b) 14 (c) 12 (d) 26
Q.9. Average of 8 numbers is 44. The
average of ?rst three numbers is 50 and
the average of next two numbers is 52. If
the sixth number is 6 and 8 less than
seventh and eighth number respectively,
then what is the value of eighth number?
SSC MTS 16/05/2023 (Morning)
(a) 36 (b) 32 (c) 40 (d) 56
Q.10. Eleven friends spent Rs. 18 each
on a tour and the twelfth friend spent Rs.
11 less than the average expenditure of
all twelve of them. What is the total
money spent by twelve friends
SSC MTS 02/05/2023 (Afternoon)
(a) Rs.204 (b) Rs.215
(c) Rs.212 (d) Rs.208
Q.11. Sonali applied for a job of Science
teacher in a school. In the test for job,
she scored 8 in physics, 8 in chemistry, 6
in biology, and 6.5 in the interview. For
calculating the ?nal score, weightage of
2, 3, 3, and 4 were assigned to Physics,
Chemistry, Biology and interview,
respectively. What is the weighted
average score of Sonali ?
SSC CGL 06/12/2022 (1st Shift)
(a) 7 (b) 8.4 (c) 7.2 (d) 21
Q.12. The batting average for 27 innings
of a cricket player is 47 runs. His highest
score in an innings exceeds his lowest
score by 157 runs. If these two innings
are excluded, the average score of the
remaining 25 innings is 42 runs. Find his
highest score in an innings.
SSC CGL 01/12/2022 (1st Shift)
(a) 176 (b) 188 (c) 186 (d) 174
Q.13. In an o?ce, 80% workers are men
while 20% are women. The average age
of the men is 30 and the average age of
the women is 40. What is the average
age of all the workers in that o?ce?
Graduate Level 04/08/2022 (Shift - 2)
(a) 50 (b) 32 (c) 30 (d) 35
Q.14. The average age of a husband and
his wife 3 years ago was 39 years. The
average age of the husband, wife and
their child 2 years hence will be 34 years.
Find the present age of the child.
SSC MTS 11/07/2022 (Afternoon)
(a) 12 years (b) 16 years
(c) 15 years (d) 18 years
Q.15. In a family of six males and a few
females, the average monthly
consumption of grain head is 14.4 kg. If
the average monthly consumption per
head is 20 kg in the case of males and 6
kg in the case of females. Find the
number of females in the family?
SSC MTS 11/07/2022 (Morning)
(a) 8 (b) 4 (c) 6 (d) 7
Q.16. A is the average marks of a group
of 10 students in a class and A+8 is the
average of a group of 15 students which
includes the group of 10 students as
given. The total marks obtained by the
group of 10 students is X and the total
marks obtained by the group of 15
students is Y. If X : Y = 3 : 5, then the
value of A + X + Y is _________.
SSC CHSL 30/05/2022 (Afternoon)
(a) 1964 (b) 1845 (c) 2012 (d) 1992
Q.17. A retailer opens her outlet on all
seven days of the week. It is observed
that her average sales for Saturdays and
Sundays combined is 300, and 200 ? ?
for the remaining ?ve days combined.
For a month starting on saturday, it was
found that the total sales were 7,000. ?
Which among the following months it
could be
SSC MTS 05/10/2021 (Morning)
(a) March (b) April (c) Jan (d) Feb
Q.18. Consider ten consecutive odd
numbers starting from 5. Multiply each
of them, except the ?rst and the second,
with three. What will be the average of
the ten numbers so formed?
SSC MTS 5/10/2021 (Morning)
(a) 39.6 (b) 39 (c) 42 (d) 38.4
Q.19. What is the average of numbers
from 1 to 50 which are multiples of 2 or
5? (correct to one decimal place)
SSC CGL 24/8/2021 (Evening)
(a) 25.4 (b) 25.9 (c) 26.4 (d) 25.8
Q.20. The average weight of students of
section A and B having 40 students each
is 45.5 kg and 44.2 kg respectively. Two
students of section A having average
weight 48.75 kg were shifted to B and 2
students of section B were shifted to
section A, making the average weight of
both the sections equal. What is the
average weight (in kg) of the students
who were shifted from section B to
section A?
SSC CGL 23/8/2021 (Afternoon)
(a) 34.5 (b) 35 (c) 35.75 (d) 34.25
Q.21. In an examination, the average
score of a student was 67.6. If he would
have got 27 more marks in Mathematics,
10 more marks in Computer Science, 18
more marks in History and retained the
same marks in other subjects, then his
average score would have been 72.6.
How many papers were there in the
examination?
SSC CGL 23/8/2021 (Morning)
(a) 11 (b) 10 (c) 12 (d) 9
Q.22. The average monthly salary of 60
employees of a factory is Rs.29900. If
two o?cers are getting Rs.90,000 each
and the average salary of 8 supervisors
is Rs.65,000, then what is the average
salary (in Rs.) of the remaining
employees?
SSC CGL 20/8/2021 (Afternoon)
www.ssccglpinnacle.com Download Pinnacle Exam Preparation App 611
Page 3
Pinnacle Day: 84th - 86th Average
Average
Key Points:
1) An average or arithmetic mean of
given data is the sum of the given
observations divided by the number of
observations.
For example : If we have to ?nd out the
average of 10, 15, 25 and 30, then
required average will be equal to:
= 20
10 + 15 + 25 + 30
4
=
80
4
Therefore, we can say, Average (A) =
?????? ???? ??h?? ?????????? ???????????????????????? ( ?? )
???????????? ???? ???????????????????????? ( ?? )
2) If all the numbers increase by ‘a’ then
the average of the numbers will also
increase by ‘a’.
3) If all the numbers decrease by ‘a’ then
the average of the numbers will also
decrease by ‘a’.
4) If all the numbers are multiplied by ‘a’
then their average must also be
multiplied by ‘a’.
5) If all the numbers are divided by ‘a’
then their average must also be divided
by ‘a’.
6) Average of ?rst n natural numbers
=
?? + 1
2
( )
7) Average of ?rst n even numbers
= ( ?? + 1 )
8) Average of ?rst n odd numbers = ??
9) Average of consecutive numbers
=
?????????? ???????????? + ???????? ????????????
2
10) Average of 1 to n odd numbers
=
???????? ?????? ???????????? + 1
2
11) Average of 1 to n even numbers
=
???????? ???????? ???????????? + 2
2
12) Average of squares of ?rst n natural
numbers =
( ?? + 1 )( 2 ?? + 1 )
6
13) Average of cubes of ?rst n natural
numbers =
?? ( ?? + 1 )
2
4
14) Average of n multiples of any number
=
???????????? × ( ?? + 1 )
2
15) Combined mean or combined
average :
If the mean of and observations are ??
1
??
2
and respectively then, ??
1
??
2
Combined mean =
??
1
??
1
+ ??
2
??
2
??
1
+ ??
2
Ex : If the average marks of 30 boys is 50
and 40 girls is 60, then ?nd the combined
average marks of the whole class.
Soln : Combined average marks of whole
class = =
30 × 50 + 40 × 60
30 + 40
= = 55.71 marks
1500 + 2400
70
3900
70
16) Basically the term Run Rate means
how many runs have been scored in one
over of a cricket match. Higher run rate is
good for batsmen.
Run rate =
?????????? ???????? ????????????
???????????? ???? ?????????? ????????????
Ex : If the batsman has scored 225 runs
in 9 overs, ?nd his run rate.
Soln : Run rate = = 25 runs/over
225
9
17) Bowling Average
=
?????????? ???????? ??????????????
?????????? ???????????? ???? ?????????????? ??????????
Lower Bowling average is good for
bowlers.
Ex : If the bowler has taken 3 wickets
allowing 120 runs, ?nd his bowling
average.
Bowling Average = = 40
120
3
runs/wicket
18) If the average is x and a number
having value greater than x is added then
the new average will be greater than x.
Similarly, if a number having value less
than x is added then the new average will
be less than x.
Ex 1. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
adding 6.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 6 is greater than the old
average, the new average is going to be
greater than the old average.
So, new average = = = 3.5
15 + 6
5 + 1
21
6
which is greater than 3.
Ex 2. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
adding 2.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 2 is less than the old average,
the new average is going to be less than
the old average.
So, new average = = = 2.83
15 + 2
5 + 1
17
6
which is less than 3.
19) If the average is x and a number
having value less than x is removed then
the new average will be greater than x.
Similarly, if a number having value
greater than x is removed then the new
average will be less than x.
Ex 1. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
removing 2.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 2 is less than the old average,
the new average is going to be greater
than the old average.
So, new average = = = 3.25
15 - 2
5 - 1
13
4
which is greater than 3.
Ex 2. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
removing 4.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 4 is greater than the old
average, the new average is going to be
less than the old average.
So, new average = = = 2.75
15 - 4
5 - 1
11
4
which is less than 3.
Variety Questions
Q.1. Rajender is working as a delivery
boy in a multinational company. The
company is paying him ?90 per delivery.
In a fortnight comprising 15 consecutive
working days, his average earnings per
day was ?540. If his average earnings of
the ?rst 7 days was ?519 per day and
that of the last 7 days was ?546 per day,
then at was his earning on the 8th day of
the fortnight?
SSC CHSL 07/08/2023 (3rd Shift)
(a) ?571 (b) ?681 (c) ?661 (d) ?645
Q.2. The average weight of a group of 12
children is 66 kg. If 2 children, X and Y,
replace A and B, the new average weight
becomes 65 kg. The weight of A= weight
of B and the weight of X = weight of Y.
Another child, C, is included in the group,
and the new average weight remains 65
kg. Weight of C= weight of X. Find the
weight of A.
SSC CHSL 04/08/2023 (3rd Shift)
(a) 69 kg (b) 72 kg (c) 71 kg (d) 67 kg
Q.3. Sudesh is the owner of a
multipurpose shop. For a speci?c month,
his pro?ts are detailed below.
Category Pro?t earned in ?
Groceries 50,000
Cosmetics 20,000
Ladies' dresses 10,000
In order to estimate the expected pro?t
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Pinnacle Day: 84th - 86th Average
for the next month, he assigns the
weights of 6, 5 and 8 to the different
categories in the same order. What will
be the weighted average of his pro?ts?
SSC CHSL 03/08/2023 (2nd Shift)
(a) 25,265.18 (nearly) ?
(b) 24,863.16 (nearly) ?
(c) 25,163.16 (nearly) ?
(d) 25,263.16 (nearly) ?
Q.4. During a school excursion each
student of junior school was charged
?325 and each student of senior school
was charged ?400. If there were 80
students from junior school and the
combined average amount charged per
student was ?352, then how many
students from senior school went for the
excursion?
SSC CGL 24/07/2023 (1st shift)
(a) 55 (b) 45 (c) 50 (d) 40
Q.5. In ?150, B buys 10 pens for ?8 each,
10 erasers for ?5 each and some
sharpeners for ?4 each. What is the
average price per item in ??
SSC CGL 19/07/2023 (3rd shift)
(a) 8 (b) 7 (c) 10 (d) 6
Q.6. 20 students of a college went to a
hotel. 19 of them spent ?175 each on
their meal and the 20
th
student spent ?19
more than the average of all the 20.
Find the total money spent by them.
SSC CGL 17/07/2023 (4th shift)
(a) ?3,490 (b) ?3,540
(c) ?3,520 (d) ?3,500
Q.7. The average score in a test for 50
students is 44. Out of the total students,
40% of the students are girls and the rest
are boys. The average score of boys is
20% less than that of girls. What is the
average score of girls?
Higher Secondary 27/06/2023 (Shift - 3)
(a) 50 (b) 54 (c) 48 (d) 52
Q.8. A is the average of 10 given
numbers. B is the average after 2 of the
numbers were replaced by 3 other
different numbers. The average of the
removed numbers is 48 and the average
of the newly included numbers is 56. If A
+ B = 438, then the value of A - B is:
Matriculation Level 27/06/2023 (Shift - 2)
(a) 21 (b) 14 (c) 12 (d) 26
Q.9. Average of 8 numbers is 44. The
average of ?rst three numbers is 50 and
the average of next two numbers is 52. If
the sixth number is 6 and 8 less than
seventh and eighth number respectively,
then what is the value of eighth number?
SSC MTS 16/05/2023 (Morning)
(a) 36 (b) 32 (c) 40 (d) 56
Q.10. Eleven friends spent Rs. 18 each
on a tour and the twelfth friend spent Rs.
11 less than the average expenditure of
all twelve of them. What is the total
money spent by twelve friends
SSC MTS 02/05/2023 (Afternoon)
(a) Rs.204 (b) Rs.215
(c) Rs.212 (d) Rs.208
Q.11. Sonali applied for a job of Science
teacher in a school. In the test for job,
she scored 8 in physics, 8 in chemistry, 6
in biology, and 6.5 in the interview. For
calculating the ?nal score, weightage of
2, 3, 3, and 4 were assigned to Physics,
Chemistry, Biology and interview,
respectively. What is the weighted
average score of Sonali ?
SSC CGL 06/12/2022 (1st Shift)
(a) 7 (b) 8.4 (c) 7.2 (d) 21
Q.12. The batting average for 27 innings
of a cricket player is 47 runs. His highest
score in an innings exceeds his lowest
score by 157 runs. If these two innings
are excluded, the average score of the
remaining 25 innings is 42 runs. Find his
highest score in an innings.
SSC CGL 01/12/2022 (1st Shift)
(a) 176 (b) 188 (c) 186 (d) 174
Q.13. In an o?ce, 80% workers are men
while 20% are women. The average age
of the men is 30 and the average age of
the women is 40. What is the average
age of all the workers in that o?ce?
Graduate Level 04/08/2022 (Shift - 2)
(a) 50 (b) 32 (c) 30 (d) 35
Q.14. The average age of a husband and
his wife 3 years ago was 39 years. The
average age of the husband, wife and
their child 2 years hence will be 34 years.
Find the present age of the child.
SSC MTS 11/07/2022 (Afternoon)
(a) 12 years (b) 16 years
(c) 15 years (d) 18 years
Q.15. In a family of six males and a few
females, the average monthly
consumption of grain head is 14.4 kg. If
the average monthly consumption per
head is 20 kg in the case of males and 6
kg in the case of females. Find the
number of females in the family?
SSC MTS 11/07/2022 (Morning)
(a) 8 (b) 4 (c) 6 (d) 7
Q.16. A is the average marks of a group
of 10 students in a class and A+8 is the
average of a group of 15 students which
includes the group of 10 students as
given. The total marks obtained by the
group of 10 students is X and the total
marks obtained by the group of 15
students is Y. If X : Y = 3 : 5, then the
value of A + X + Y is _________.
SSC CHSL 30/05/2022 (Afternoon)
(a) 1964 (b) 1845 (c) 2012 (d) 1992
Q.17. A retailer opens her outlet on all
seven days of the week. It is observed
that her average sales for Saturdays and
Sundays combined is 300, and 200 ? ?
for the remaining ?ve days combined.
For a month starting on saturday, it was
found that the total sales were 7,000. ?
Which among the following months it
could be
SSC MTS 05/10/2021 (Morning)
(a) March (b) April (c) Jan (d) Feb
Q.18. Consider ten consecutive odd
numbers starting from 5. Multiply each
of them, except the ?rst and the second,
with three. What will be the average of
the ten numbers so formed?
SSC MTS 5/10/2021 (Morning)
(a) 39.6 (b) 39 (c) 42 (d) 38.4
Q.19. What is the average of numbers
from 1 to 50 which are multiples of 2 or
5? (correct to one decimal place)
SSC CGL 24/8/2021 (Evening)
(a) 25.4 (b) 25.9 (c) 26.4 (d) 25.8
Q.20. The average weight of students of
section A and B having 40 students each
is 45.5 kg and 44.2 kg respectively. Two
students of section A having average
weight 48.75 kg were shifted to B and 2
students of section B were shifted to
section A, making the average weight of
both the sections equal. What is the
average weight (in kg) of the students
who were shifted from section B to
section A?
SSC CGL 23/8/2021 (Afternoon)
(a) 34.5 (b) 35 (c) 35.75 (d) 34.25
Q.21. In an examination, the average
score of a student was 67.6. If he would
have got 27 more marks in Mathematics,
10 more marks in Computer Science, 18
more marks in History and retained the
same marks in other subjects, then his
average score would have been 72.6.
How many papers were there in the
examination?
SSC CGL 23/8/2021 (Morning)
(a) 11 (b) 10 (c) 12 (d) 9
Q.22. The average monthly salary of 60
employees of a factory is Rs.29900. If
two o?cers are getting Rs.90,000 each
and the average salary of 8 supervisors
is Rs.65,000, then what is the average
salary (in Rs.) of the remaining
employees?
SSC CGL 20/8/2021 (Afternoon)
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Pinnacle Day: 84th - 86th Average
(a) 21080 (b) 22680 (c) 29080 (d) 21880
Q.23. What is the ratio of the average of
?rst eight prime numbers to the average
of ?rst ten even natural numbers?
SSC CGL 16/8/2021 (Afternoon)
(a) 1 : 7 (b) 7 : 80 (c) 8 : 70 (d) 7 : 8
Q.24. x, y and z are three positive
numbers such that y is times of x and
4
5
z is times of y. If the average of
5
8
reciprocals of the numbers x, y and z is
, then the average of 3 times of x
17
240
and 5 times of y will be:
SSC CHSL 10/8/2021 (Afternoon)
(a) 70 (b) 60 (c) 40 (d) 45
Q.25. The numbers 2, 3, 4 and 5 occur (2
+ 5k), (5k - 7), (2k - 3) and (k + 2) times,
respectively. The average of the number
is 2.85. Later on, the number 2 was
replaced by 6 in all the places. What is
the average of the new numbers?
SSC CHSL 5/8/2021 (Evening)
(a) 2.4 (b) 5.25 (c) 3.85 (d) 4.75
Q.26. If the average of the 3-digit
numbers 335, 2x5, x35, 63x and 406 is
411, then what will be the average of (x -
1), (x - 3), (x + 3) and (x + 5) ?
SSC CHSL 16/4/2021 (Afternoon)
(a) 6 (b) 3 (c) 5 (d) 4
Q.27. The average of the numbers a, b, c
and d is 2d + 4, Also, the averages of the
numbers a and b, b and c, c and d are 8, 5
and 4, respectively. If e = a + d + 1, then
what is the average of the numbers d and
e ?
SSC CHSL 13/4/2021 (Evening)
(a) 8 (b) 8.5 (c) 3 (d) 7
Q.28. The average of four consecutive
odd natural numbers is eight less than
the average of three consecutive even
natural numbers. If the sum of these
even numbers is equal to the sum of
above four odd numbers, then the
average of four original odd numbers is:
SSC CHSL 20/10/2020 (Afternoon)
(a) 36 (b) 24 (c) 18 (d) 32
Q.29. The average of nine 2 digit
numbers is decreased by 6 when the
digits of one of the 2 digit numbers is
interchanged. Find the difference
between the digits of that number.
SSC CHSL 20/10/2020 (Morning)
(a) 6 (b) 4 (c) 2 (d) 8
Q.30. The numbers 24, 45, a, 35, 59, 83,
46, b, 29, 74 are serially numbered as
they appear in the sequence. When each
number is added to its serial number,
then the average of the new numbers
formed is 55. The average of the missing
numbers (a and b) is:
SSC CHSL 13/10/2020 (Afternoon)
(a) 38 (b) 58 (c) 62 (d) 50
Q.31. The average of 35 consecutive
natural numbers is N. Dropping the ?rst
10 numbers and including the next 10
numbers, the average is changed to M. If
the value of M - N = 600, then the
2 2
average of 3M and 5N is:
SSC CHSL 13/10/2020 (Morning)
(a) 90 (b) 120 (c) 100 (d) 115
Q.32. A batsman in his 11th innings
makes a score of 77 runs, thereby
increasing his average scores by 3. What
is his average score after the 11th
innings?
SSC CHSL 17/03/2020 (Morning )
(a) 46 (b) 49 (c) 47 (d) 48
Q.33. The average age of husband, wife
and child 7 years ago was 42 years and
that of wife and child 9 years ago was 36
years. The present age of the husband is:
SSC CPO 12/12/2019(Evening)
(a) 50 (b) 55 (c) 48 (d) 57
Q.34. A batsman scores 92 runs in the
15th innings and thus increases his
average by 4. What is his average after
the 15th innings?
SSC CPO 12/12/2019(Evening)
(a) 40 (b) 32 (c) 35 (d) 36
Q.35. The average age of 120 students in
a group is 13.56 years, 35% of the
number of students are girls and the rest
are boys. If the ratio of the average age
of boys and girls is 6:5, then what is the
average age (in years) of the girls?
SSC CGL Tier II (13/09/2019)
(a) 12 (b) 11.6 (c) 10 (d) 14.4
Q.36. The average of 18 numbers is 37.5.
If six numbers of average x are added to
them, then the average of all the
numbers increases by one. The value of x
is : :
SSC CGL Tier II (13/09/2019)
(a) 40 (b) 41.5 (c) 42 (d) 38.5
Q.37. The average weight of a certain
number of students in a group is 72 kg. If
10 students having an average weight of
78 kg leave and 4 students having an
average weight of 80 kg join the group,
the average weight of the students in the
group decreases by 0.7 kg. The number
of students initially in the group is :
SSC CGL Tier II (12/09/2019)
(a) 56 (b) 46 (c) 44 (d) 54
Q.38. The average of 33 numbers is 74.
The average of the ?rst 17 numbers is
72.8 and that of the last 17 numbers is
77.2. If the 17th number is excluded, then
what will be the average of the remaining
numbers (correct to one decimal place)?
SSC CGL Tier II (12/09/2019)
(a) 72.9 (b) 73.4 (c) 71.6 (d) 70.8
Q.39. The number of students in a class
is 75, out of which 33 % are boys and
1
3
the rest are girls. The average score in
mathematics of the boys is 66 % more
2
3
than that of the girls. If the average score
of all the students is 66, then the average
score of the girls is:
SSC CGL Tier II (11/09/2019)
(a) 52 (b) 55 (c) 54 (d) 58
Q.40. The owner of a bike buys petrol at
the rate of Rs. 64, Rs. 80 and Rs. 320 per
litre for three consecutive years. If he
spends Rs. 32000 on petrol every year,
then what is the average price (Rs.) of
petrol per litre ?
SSC MTS 16/08/2019 (Evening)
(a) 120 (b) 84 (c) 108 (d) 96
Q.41. An art exhibition was held in the
month of november. The numbers of
visitors on weekdays and on weekends
were 450 and 750 respectively. If the ?rst
day of the month was Monday, then what
was the average number of visitors in the
month ?
SSC MTS 16/08/2019 (Evening)
(a) 520 (b) 530 (c) 510 (d) 540
Q.42. A person was asked to guess his
own weight. He estimated his weight to
be over 70 kg but less than 80 kg. His
friend estimated his weight to be more
than 74 kg but less than 84 kg. His
mother said that his weight is less than
78 kg. Assuming that the weights are a
whole number and that the three had
correctly guessed, then what is the
average of the possible weights(in Kg)?
SSC MTS 14/08/2019 (Morning)
(a) 76.5 (b) 76 (c) 77 (d) 75
Q.43. A party was held for 50 people on
their own expenses. Out of them, 48
people paid Rs. 950 each and the other
two persons paid Rs. 1200 more than the
average expenses of the group. The total
amount spent was :
SSC MTS 14/08/2019 (Morning)
(a) Rs 75,000 (b) Rs 40,000
(c) Rs 25,000 (d) Rs 50,000
Q.44. Out of four numbers the average of
the ?rst three is 16 and that of the last
three is 15. If the last number is 21 then
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Page 4
Pinnacle Day: 84th - 86th Average
Average
Key Points:
1) An average or arithmetic mean of
given data is the sum of the given
observations divided by the number of
observations.
For example : If we have to ?nd out the
average of 10, 15, 25 and 30, then
required average will be equal to:
= 20
10 + 15 + 25 + 30
4
=
80
4
Therefore, we can say, Average (A) =
?????? ???? ??h?? ?????????? ???????????????????????? ( ?? )
???????????? ???? ???????????????????????? ( ?? )
2) If all the numbers increase by ‘a’ then
the average of the numbers will also
increase by ‘a’.
3) If all the numbers decrease by ‘a’ then
the average of the numbers will also
decrease by ‘a’.
4) If all the numbers are multiplied by ‘a’
then their average must also be
multiplied by ‘a’.
5) If all the numbers are divided by ‘a’
then their average must also be divided
by ‘a’.
6) Average of ?rst n natural numbers
=
?? + 1
2
( )
7) Average of ?rst n even numbers
= ( ?? + 1 )
8) Average of ?rst n odd numbers = ??
9) Average of consecutive numbers
=
?????????? ???????????? + ???????? ????????????
2
10) Average of 1 to n odd numbers
=
???????? ?????? ???????????? + 1
2
11) Average of 1 to n even numbers
=
???????? ???????? ???????????? + 2
2
12) Average of squares of ?rst n natural
numbers =
( ?? + 1 )( 2 ?? + 1 )
6
13) Average of cubes of ?rst n natural
numbers =
?? ( ?? + 1 )
2
4
14) Average of n multiples of any number
=
???????????? × ( ?? + 1 )
2
15) Combined mean or combined
average :
If the mean of and observations are ??
1
??
2
and respectively then, ??
1
??
2
Combined mean =
??
1
??
1
+ ??
2
??
2
??
1
+ ??
2
Ex : If the average marks of 30 boys is 50
and 40 girls is 60, then ?nd the combined
average marks of the whole class.
Soln : Combined average marks of whole
class = =
30 × 50 + 40 × 60
30 + 40
= = 55.71 marks
1500 + 2400
70
3900
70
16) Basically the term Run Rate means
how many runs have been scored in one
over of a cricket match. Higher run rate is
good for batsmen.
Run rate =
?????????? ???????? ????????????
???????????? ???? ?????????? ????????????
Ex : If the batsman has scored 225 runs
in 9 overs, ?nd his run rate.
Soln : Run rate = = 25 runs/over
225
9
17) Bowling Average
=
?????????? ???????? ??????????????
?????????? ???????????? ???? ?????????????? ??????????
Lower Bowling average is good for
bowlers.
Ex : If the bowler has taken 3 wickets
allowing 120 runs, ?nd his bowling
average.
Bowling Average = = 40
120
3
runs/wicket
18) If the average is x and a number
having value greater than x is added then
the new average will be greater than x.
Similarly, if a number having value less
than x is added then the new average will
be less than x.
Ex 1. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
adding 6.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 6 is greater than the old
average, the new average is going to be
greater than the old average.
So, new average = = = 3.5
15 + 6
5 + 1
21
6
which is greater than 3.
Ex 2. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
adding 2.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 2 is less than the old average,
the new average is going to be less than
the old average.
So, new average = = = 2.83
15 + 2
5 + 1
17
6
which is less than 3.
19) If the average is x and a number
having value less than x is removed then
the new average will be greater than x.
Similarly, if a number having value
greater than x is removed then the new
average will be less than x.
Ex 1. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
removing 2.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 2 is less than the old average,
the new average is going to be greater
than the old average.
So, new average = = = 3.25
15 - 2
5 - 1
13
4
which is greater than 3.
Ex 2. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
removing 4.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 4 is greater than the old
average, the new average is going to be
less than the old average.
So, new average = = = 2.75
15 - 4
5 - 1
11
4
which is less than 3.
Variety Questions
Q.1. Rajender is working as a delivery
boy in a multinational company. The
company is paying him ?90 per delivery.
In a fortnight comprising 15 consecutive
working days, his average earnings per
day was ?540. If his average earnings of
the ?rst 7 days was ?519 per day and
that of the last 7 days was ?546 per day,
then at was his earning on the 8th day of
the fortnight?
SSC CHSL 07/08/2023 (3rd Shift)
(a) ?571 (b) ?681 (c) ?661 (d) ?645
Q.2. The average weight of a group of 12
children is 66 kg. If 2 children, X and Y,
replace A and B, the new average weight
becomes 65 kg. The weight of A= weight
of B and the weight of X = weight of Y.
Another child, C, is included in the group,
and the new average weight remains 65
kg. Weight of C= weight of X. Find the
weight of A.
SSC CHSL 04/08/2023 (3rd Shift)
(a) 69 kg (b) 72 kg (c) 71 kg (d) 67 kg
Q.3. Sudesh is the owner of a
multipurpose shop. For a speci?c month,
his pro?ts are detailed below.
Category Pro?t earned in ?
Groceries 50,000
Cosmetics 20,000
Ladies' dresses 10,000
In order to estimate the expected pro?t
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Pinnacle Day: 84th - 86th Average
for the next month, he assigns the
weights of 6, 5 and 8 to the different
categories in the same order. What will
be the weighted average of his pro?ts?
SSC CHSL 03/08/2023 (2nd Shift)
(a) 25,265.18 (nearly) ?
(b) 24,863.16 (nearly) ?
(c) 25,163.16 (nearly) ?
(d) 25,263.16 (nearly) ?
Q.4. During a school excursion each
student of junior school was charged
?325 and each student of senior school
was charged ?400. If there were 80
students from junior school and the
combined average amount charged per
student was ?352, then how many
students from senior school went for the
excursion?
SSC CGL 24/07/2023 (1st shift)
(a) 55 (b) 45 (c) 50 (d) 40
Q.5. In ?150, B buys 10 pens for ?8 each,
10 erasers for ?5 each and some
sharpeners for ?4 each. What is the
average price per item in ??
SSC CGL 19/07/2023 (3rd shift)
(a) 8 (b) 7 (c) 10 (d) 6
Q.6. 20 students of a college went to a
hotel. 19 of them spent ?175 each on
their meal and the 20
th
student spent ?19
more than the average of all the 20.
Find the total money spent by them.
SSC CGL 17/07/2023 (4th shift)
(a) ?3,490 (b) ?3,540
(c) ?3,520 (d) ?3,500
Q.7. The average score in a test for 50
students is 44. Out of the total students,
40% of the students are girls and the rest
are boys. The average score of boys is
20% less than that of girls. What is the
average score of girls?
Higher Secondary 27/06/2023 (Shift - 3)
(a) 50 (b) 54 (c) 48 (d) 52
Q.8. A is the average of 10 given
numbers. B is the average after 2 of the
numbers were replaced by 3 other
different numbers. The average of the
removed numbers is 48 and the average
of the newly included numbers is 56. If A
+ B = 438, then the value of A - B is:
Matriculation Level 27/06/2023 (Shift - 2)
(a) 21 (b) 14 (c) 12 (d) 26
Q.9. Average of 8 numbers is 44. The
average of ?rst three numbers is 50 and
the average of next two numbers is 52. If
the sixth number is 6 and 8 less than
seventh and eighth number respectively,
then what is the value of eighth number?
SSC MTS 16/05/2023 (Morning)
(a) 36 (b) 32 (c) 40 (d) 56
Q.10. Eleven friends spent Rs. 18 each
on a tour and the twelfth friend spent Rs.
11 less than the average expenditure of
all twelve of them. What is the total
money spent by twelve friends
SSC MTS 02/05/2023 (Afternoon)
(a) Rs.204 (b) Rs.215
(c) Rs.212 (d) Rs.208
Q.11. Sonali applied for a job of Science
teacher in a school. In the test for job,
she scored 8 in physics, 8 in chemistry, 6
in biology, and 6.5 in the interview. For
calculating the ?nal score, weightage of
2, 3, 3, and 4 were assigned to Physics,
Chemistry, Biology and interview,
respectively. What is the weighted
average score of Sonali ?
SSC CGL 06/12/2022 (1st Shift)
(a) 7 (b) 8.4 (c) 7.2 (d) 21
Q.12. The batting average for 27 innings
of a cricket player is 47 runs. His highest
score in an innings exceeds his lowest
score by 157 runs. If these two innings
are excluded, the average score of the
remaining 25 innings is 42 runs. Find his
highest score in an innings.
SSC CGL 01/12/2022 (1st Shift)
(a) 176 (b) 188 (c) 186 (d) 174
Q.13. In an o?ce, 80% workers are men
while 20% are women. The average age
of the men is 30 and the average age of
the women is 40. What is the average
age of all the workers in that o?ce?
Graduate Level 04/08/2022 (Shift - 2)
(a) 50 (b) 32 (c) 30 (d) 35
Q.14. The average age of a husband and
his wife 3 years ago was 39 years. The
average age of the husband, wife and
their child 2 years hence will be 34 years.
Find the present age of the child.
SSC MTS 11/07/2022 (Afternoon)
(a) 12 years (b) 16 years
(c) 15 years (d) 18 years
Q.15. In a family of six males and a few
females, the average monthly
consumption of grain head is 14.4 kg. If
the average monthly consumption per
head is 20 kg in the case of males and 6
kg in the case of females. Find the
number of females in the family?
SSC MTS 11/07/2022 (Morning)
(a) 8 (b) 4 (c) 6 (d) 7
Q.16. A is the average marks of a group
of 10 students in a class and A+8 is the
average of a group of 15 students which
includes the group of 10 students as
given. The total marks obtained by the
group of 10 students is X and the total
marks obtained by the group of 15
students is Y. If X : Y = 3 : 5, then the
value of A + X + Y is _________.
SSC CHSL 30/05/2022 (Afternoon)
(a) 1964 (b) 1845 (c) 2012 (d) 1992
Q.17. A retailer opens her outlet on all
seven days of the week. It is observed
that her average sales for Saturdays and
Sundays combined is 300, and 200 ? ?
for the remaining ?ve days combined.
For a month starting on saturday, it was
found that the total sales were 7,000. ?
Which among the following months it
could be
SSC MTS 05/10/2021 (Morning)
(a) March (b) April (c) Jan (d) Feb
Q.18. Consider ten consecutive odd
numbers starting from 5. Multiply each
of them, except the ?rst and the second,
with three. What will be the average of
the ten numbers so formed?
SSC MTS 5/10/2021 (Morning)
(a) 39.6 (b) 39 (c) 42 (d) 38.4
Q.19. What is the average of numbers
from 1 to 50 which are multiples of 2 or
5? (correct to one decimal place)
SSC CGL 24/8/2021 (Evening)
(a) 25.4 (b) 25.9 (c) 26.4 (d) 25.8
Q.20. The average weight of students of
section A and B having 40 students each
is 45.5 kg and 44.2 kg respectively. Two
students of section A having average
weight 48.75 kg were shifted to B and 2
students of section B were shifted to
section A, making the average weight of
both the sections equal. What is the
average weight (in kg) of the students
who were shifted from section B to
section A?
SSC CGL 23/8/2021 (Afternoon)
(a) 34.5 (b) 35 (c) 35.75 (d) 34.25
Q.21. In an examination, the average
score of a student was 67.6. If he would
have got 27 more marks in Mathematics,
10 more marks in Computer Science, 18
more marks in History and retained the
same marks in other subjects, then his
average score would have been 72.6.
How many papers were there in the
examination?
SSC CGL 23/8/2021 (Morning)
(a) 11 (b) 10 (c) 12 (d) 9
Q.22. The average monthly salary of 60
employees of a factory is Rs.29900. If
two o?cers are getting Rs.90,000 each
and the average salary of 8 supervisors
is Rs.65,000, then what is the average
salary (in Rs.) of the remaining
employees?
SSC CGL 20/8/2021 (Afternoon)
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(a) 21080 (b) 22680 (c) 29080 (d) 21880
Q.23. What is the ratio of the average of
?rst eight prime numbers to the average
of ?rst ten even natural numbers?
SSC CGL 16/8/2021 (Afternoon)
(a) 1 : 7 (b) 7 : 80 (c) 8 : 70 (d) 7 : 8
Q.24. x, y and z are three positive
numbers such that y is times of x and
4
5
z is times of y. If the average of
5
8
reciprocals of the numbers x, y and z is
, then the average of 3 times of x
17
240
and 5 times of y will be:
SSC CHSL 10/8/2021 (Afternoon)
(a) 70 (b) 60 (c) 40 (d) 45
Q.25. The numbers 2, 3, 4 and 5 occur (2
+ 5k), (5k - 7), (2k - 3) and (k + 2) times,
respectively. The average of the number
is 2.85. Later on, the number 2 was
replaced by 6 in all the places. What is
the average of the new numbers?
SSC CHSL 5/8/2021 (Evening)
(a) 2.4 (b) 5.25 (c) 3.85 (d) 4.75
Q.26. If the average of the 3-digit
numbers 335, 2x5, x35, 63x and 406 is
411, then what will be the average of (x -
1), (x - 3), (x + 3) and (x + 5) ?
SSC CHSL 16/4/2021 (Afternoon)
(a) 6 (b) 3 (c) 5 (d) 4
Q.27. The average of the numbers a, b, c
and d is 2d + 4, Also, the averages of the
numbers a and b, b and c, c and d are 8, 5
and 4, respectively. If e = a + d + 1, then
what is the average of the numbers d and
e ?
SSC CHSL 13/4/2021 (Evening)
(a) 8 (b) 8.5 (c) 3 (d) 7
Q.28. The average of four consecutive
odd natural numbers is eight less than
the average of three consecutive even
natural numbers. If the sum of these
even numbers is equal to the sum of
above four odd numbers, then the
average of four original odd numbers is:
SSC CHSL 20/10/2020 (Afternoon)
(a) 36 (b) 24 (c) 18 (d) 32
Q.29. The average of nine 2 digit
numbers is decreased by 6 when the
digits of one of the 2 digit numbers is
interchanged. Find the difference
between the digits of that number.
SSC CHSL 20/10/2020 (Morning)
(a) 6 (b) 4 (c) 2 (d) 8
Q.30. The numbers 24, 45, a, 35, 59, 83,
46, b, 29, 74 are serially numbered as
they appear in the sequence. When each
number is added to its serial number,
then the average of the new numbers
formed is 55. The average of the missing
numbers (a and b) is:
SSC CHSL 13/10/2020 (Afternoon)
(a) 38 (b) 58 (c) 62 (d) 50
Q.31. The average of 35 consecutive
natural numbers is N. Dropping the ?rst
10 numbers and including the next 10
numbers, the average is changed to M. If
the value of M - N = 600, then the
2 2
average of 3M and 5N is:
SSC CHSL 13/10/2020 (Morning)
(a) 90 (b) 120 (c) 100 (d) 115
Q.32. A batsman in his 11th innings
makes a score of 77 runs, thereby
increasing his average scores by 3. What
is his average score after the 11th
innings?
SSC CHSL 17/03/2020 (Morning )
(a) 46 (b) 49 (c) 47 (d) 48
Q.33. The average age of husband, wife
and child 7 years ago was 42 years and
that of wife and child 9 years ago was 36
years. The present age of the husband is:
SSC CPO 12/12/2019(Evening)
(a) 50 (b) 55 (c) 48 (d) 57
Q.34. A batsman scores 92 runs in the
15th innings and thus increases his
average by 4. What is his average after
the 15th innings?
SSC CPO 12/12/2019(Evening)
(a) 40 (b) 32 (c) 35 (d) 36
Q.35. The average age of 120 students in
a group is 13.56 years, 35% of the
number of students are girls and the rest
are boys. If the ratio of the average age
of boys and girls is 6:5, then what is the
average age (in years) of the girls?
SSC CGL Tier II (13/09/2019)
(a) 12 (b) 11.6 (c) 10 (d) 14.4
Q.36. The average of 18 numbers is 37.5.
If six numbers of average x are added to
them, then the average of all the
numbers increases by one. The value of x
is : :
SSC CGL Tier II (13/09/2019)
(a) 40 (b) 41.5 (c) 42 (d) 38.5
Q.37. The average weight of a certain
number of students in a group is 72 kg. If
10 students having an average weight of
78 kg leave and 4 students having an
average weight of 80 kg join the group,
the average weight of the students in the
group decreases by 0.7 kg. The number
of students initially in the group is :
SSC CGL Tier II (12/09/2019)
(a) 56 (b) 46 (c) 44 (d) 54
Q.38. The average of 33 numbers is 74.
The average of the ?rst 17 numbers is
72.8 and that of the last 17 numbers is
77.2. If the 17th number is excluded, then
what will be the average of the remaining
numbers (correct to one decimal place)?
SSC CGL Tier II (12/09/2019)
(a) 72.9 (b) 73.4 (c) 71.6 (d) 70.8
Q.39. The number of students in a class
is 75, out of which 33 % are boys and
1
3
the rest are girls. The average score in
mathematics of the boys is 66 % more
2
3
than that of the girls. If the average score
of all the students is 66, then the average
score of the girls is:
SSC CGL Tier II (11/09/2019)
(a) 52 (b) 55 (c) 54 (d) 58
Q.40. The owner of a bike buys petrol at
the rate of Rs. 64, Rs. 80 and Rs. 320 per
litre for three consecutive years. If he
spends Rs. 32000 on petrol every year,
then what is the average price (Rs.) of
petrol per litre ?
SSC MTS 16/08/2019 (Evening)
(a) 120 (b) 84 (c) 108 (d) 96
Q.41. An art exhibition was held in the
month of november. The numbers of
visitors on weekdays and on weekends
were 450 and 750 respectively. If the ?rst
day of the month was Monday, then what
was the average number of visitors in the
month ?
SSC MTS 16/08/2019 (Evening)
(a) 520 (b) 530 (c) 510 (d) 540
Q.42. A person was asked to guess his
own weight. He estimated his weight to
be over 70 kg but less than 80 kg. His
friend estimated his weight to be more
than 74 kg but less than 84 kg. His
mother said that his weight is less than
78 kg. Assuming that the weights are a
whole number and that the three had
correctly guessed, then what is the
average of the possible weights(in Kg)?
SSC MTS 14/08/2019 (Morning)
(a) 76.5 (b) 76 (c) 77 (d) 75
Q.43. A party was held for 50 people on
their own expenses. Out of them, 48
people paid Rs. 950 each and the other
two persons paid Rs. 1200 more than the
average expenses of the group. The total
amount spent was :
SSC MTS 14/08/2019 (Morning)
(a) Rs 75,000 (b) Rs 40,000
(c) Rs 25,000 (d) Rs 50,000
Q.44. Out of four numbers the average of
the ?rst three is 16 and that of the last
three is 15. If the last number is 21 then
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the ?rst number is:
SSC MTS 13/08/2019 (Evening)
(a) 28 (b) 22 (c) 21 (d) 24
Q.45. The average of all the prime and
composite numbers upto 100 is:
SSC MTS 9/08/2019 (Morning)
(a) 51 (b) 50 (c) 50.5 (d) 49.5
Q.46. What is the average of the ?rst 15
whole numbers?
SSC MTS 08/08/2019 (Morning)
(a) 8 (b) 7 (c) 9 (d) 10
Q.47. What is the average of the ?rst 8
multiples of 6 among the natural
numbers?
SSC MTS 07/08/2019 (Evening)
(a) 24 (b) 26 (c) 27 (d) 28
Q.48. The average of a and b is 36. The
average of b and c is 42. What is the
difference between c and a ?
SSC MTS 6/08/2019 (Afternoon)
(a) 18 (b) 12 (c) 16 (d) 14
Q.49. The average of 1088 real numbers
is zero. At most how many of them can
be negative?
SSC CHSL 11/07/2019 (Morning)
(a) 100 (b) 88 (c) 544 (d) 1087
Q.50. The difference between the average
of ?rst ten prime numbers and the ?rst ten
prime numbers of two digits is:
SSC CHSL 10/07/2019 (Evening)
(a) 14.5 (b) 16.5 (c) 12.5 (d) 13.5
Q.51. The average of the ?rst 101 ______
numbers is equal to 102.
SSC CHSL 10/07/2019 (Afternoon)
(a) natural (b) odd
(c) even (d) perfect square
Q.52. The average of the ?rst 1234
_______ numbers is equal to 1234.
SSC CHSL 10/07/2019 (Morning)
(a) odd (b) even (c) prime (d) natural
Q.53. The average of a number and its
reciprocal is 4. The average of its cube
and cube of its reciprocal is equal to:
SSC CHSL 9/07/2019 (Evening)
(a) 256 (b) 142 (c) 288 (d) 244
Q.54. The average age of four brothers is
15 years. If their father is included, the
average is increased by 5 years. The age
of the father (in years) is:
SSC CHSL 5/07/2019 (Afternoon)
(a) 35 (b) 40 (c) 38 (d) 36
Q.55. 10 years ago, the average age of a
family of ?ve members was 38 years.
Now, two new members join, whose age
difference is 8 years. If the present
average age of the family is the same as
it was 10 years ago, what is the age (in
years) of the new younger member?
SSC CHSL 4/07/2019 (Afternoon)
(a) 15 (b) 9 (c) 10 (d) 17
Q.56. The average of n number is 36. If
each of 75% of the numbers is increased
by 6 and each of the remaining numbers
is decreased by 9, then the new average
of the numbers is:
SSC CHSL 4/07/2019 (Morning)
(a) 37.125 (b) 33.75 (c) 38.25 (d) 36.25
Q.57. The average weight of the students
in a group was 75.4 kg. Later on, four
students having weights, 72.9 kg, 73.8
kg, 79.5 kg and 87.4 kg joined the group.
As a result, the average weight of all the
students in the group increased by 0.24
kg. What was the number of students in
the group, initially ?
SSC CHSL 3/07/2019 (Morning)
(a) 46 (b) 36 (c) 50 (d) 48
Q.58. In a class of 80 students, 60%
participate in games and the rest do not.
The average weight of the former group
is 5% more than that of the latter. If the
average weight of all the students is 51
kg, then what is the average weight (in
1
2
kg) of the former group?
SSC CHSL 2/07/2019 (Afternoon)
(a) 57.6 (b) 54.5 (c) 60 (d) 52.5
Q.59. The average of 27 numbers is zero.
Out of them, how many may be greater
than zero, at the most?
SSC CGL 13/06/2019 (Evening)
(a) 0 (b) 15 (c) 26 (d) 20
Q.60. In a class of 40 students, 45% are
girls and the remaining are boys. If the
average marks of the girls is 54 and that
of the boys is 46, what is the average of
the whole class?
SSC CGL 11/06/2019 (Afternoon)
(a) 49.8 (b) 49.7 (c) 49.6 (d) 49.5
Q.61. The average marks of 40 students
was found to be 68. If the marks of two
students were incorrectly entered as 48
and 64 instead of 84 and 46 respectively,
then what is the correct average?
SSC CGL 10/06/2019 (Afternoon)
(a) 68.25 (b) 68.15 (c) 68.45 (d) 68.35
Q.62. Four different positive numbers are
written in ascending order. One-third of
the average of all the four numbers is 19
less than the greatest of these numbers.
If the average of the ?rst three numbers
is 12, the greatest number among the
given numbers is:
SSC CGL 7/06/2019 (Evening)
(a) 25 (b) 22 (c) 24 (d) 21
Q.63. The total number of students in
section A and B of a class is 110. The
number of students in section A is 10
more than that of section B. The average
score of the students in B, in a test, is
20% more than that of students in A. If
the average score of all the students in
the class is 72, then what is the average
score of the students in A?
SSC CGL 7/06/2019 (Afternoon)
(a) 66 (b) 68 (c) 63 (d) 70
Q.64. Three numbers are such that if the
average of any two of them is added to
the third number, the sums obtained are
168, 174 and 180 respectively. What is
the average of the original three
numbers?
SSC CGL 4/06/2019 (Evening)
(a) 86 (b) 87 (c) 89 (d) 84
Q.65. The average weight of a certain
number of students in a class is 68.5 kg.
If 4 new students having weights 72.2 kg,
70.8kg, 70.3kg and 66.7 kg join the class,
then the average weight of all the
students increases by 300 g. The number
of students in the class, initially is:
SSC CGL 4/06/2019 (Afternoon)
(a) 21 (b) 16 (c) 11 (d) 26
Q.66. The average of twelve numbers is
42. The average of the last ?ve numbers
is 40 and that of the ?rst four numbers is
44. The 6th number is 6 less than the
?fth and 5 less than the 7th number. The
average of the 5th and the 7th numbers
is:
SSC CGL 4/06/2019 (Morning)
(a) 44 (b) 44.5 (c) 43 (d) 43.5
Practice Questions
SSC CHSL 2023 Tier - 2
Q.67. At a Yoga center, 60% of the
members are men and 40% of the
members are women. If the average age
of the men is 55 years and the average
age of the women is 45 years, then what
is the average age (in years) of all the
members ?
SSC CHSL Tier II 02/11/2023
(a) 51 (b) 48 (c) 50 (d) 49
Q.68. The average weight of 40 students
of a school is 52 kg. If the weight of the
teacher is included, the average weight
rises by 500 grams. Find the weight (in
kg) of the teacher.
SSC CHSL Tier II 02/11/2023
(a) 72.5 (b) 74.5 (c) 73.5 (d) 71.5
Q.69. The average salary of all 40
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Pinnacle Day: 84th - 86th Average
Average
Key Points:
1) An average or arithmetic mean of
given data is the sum of the given
observations divided by the number of
observations.
For example : If we have to ?nd out the
average of 10, 15, 25 and 30, then
required average will be equal to:
= 20
10 + 15 + 25 + 30
4
=
80
4
Therefore, we can say, Average (A) =
?????? ???? ??h?? ?????????? ???????????????????????? ( ?? )
???????????? ???? ???????????????????????? ( ?? )
2) If all the numbers increase by ‘a’ then
the average of the numbers will also
increase by ‘a’.
3) If all the numbers decrease by ‘a’ then
the average of the numbers will also
decrease by ‘a’.
4) If all the numbers are multiplied by ‘a’
then their average must also be
multiplied by ‘a’.
5) If all the numbers are divided by ‘a’
then their average must also be divided
by ‘a’.
6) Average of ?rst n natural numbers
=
?? + 1
2
( )
7) Average of ?rst n even numbers
= ( ?? + 1 )
8) Average of ?rst n odd numbers = ??
9) Average of consecutive numbers
=
?????????? ???????????? + ???????? ????????????
2
10) Average of 1 to n odd numbers
=
???????? ?????? ???????????? + 1
2
11) Average of 1 to n even numbers
=
???????? ???????? ???????????? + 2
2
12) Average of squares of ?rst n natural
numbers =
( ?? + 1 )( 2 ?? + 1 )
6
13) Average of cubes of ?rst n natural
numbers =
?? ( ?? + 1 )
2
4
14) Average of n multiples of any number
=
???????????? × ( ?? + 1 )
2
15) Combined mean or combined
average :
If the mean of and observations are ??
1
??
2
and respectively then, ??
1
??
2
Combined mean =
??
1
??
1
+ ??
2
??
2
??
1
+ ??
2
Ex : If the average marks of 30 boys is 50
and 40 girls is 60, then ?nd the combined
average marks of the whole class.
Soln : Combined average marks of whole
class = =
30 × 50 + 40 × 60
30 + 40
= = 55.71 marks
1500 + 2400
70
3900
70
16) Basically the term Run Rate means
how many runs have been scored in one
over of a cricket match. Higher run rate is
good for batsmen.
Run rate =
?????????? ???????? ????????????
???????????? ???? ?????????? ????????????
Ex : If the batsman has scored 225 runs
in 9 overs, ?nd his run rate.
Soln : Run rate = = 25 runs/over
225
9
17) Bowling Average
=
?????????? ???????? ??????????????
?????????? ???????????? ???? ?????????????? ??????????
Lower Bowling average is good for
bowlers.
Ex : If the bowler has taken 3 wickets
allowing 120 runs, ?nd his bowling
average.
Bowling Average = = 40
120
3
runs/wicket
18) If the average is x and a number
having value greater than x is added then
the new average will be greater than x.
Similarly, if a number having value less
than x is added then the new average will
be less than x.
Ex 1. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
adding 6.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 6 is greater than the old
average, the new average is going to be
greater than the old average.
So, new average = = = 3.5
15 + 6
5 + 1
21
6
which is greater than 3.
Ex 2. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
adding 2.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 2 is less than the old average,
the new average is going to be less than
the old average.
So, new average = = = 2.83
15 + 2
5 + 1
17
6
which is less than 3.
19) If the average is x and a number
having value less than x is removed then
the new average will be greater than x.
Similarly, if a number having value
greater than x is removed then the new
average will be less than x.
Ex 1. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
removing 2.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 2 is less than the old average,
the new average is going to be greater
than the old average.
So, new average = = = 3.25
15 - 2
5 - 1
13
4
which is greater than 3.
Ex 2. The average of the ?rst ?ve natural
numbers is 3. Find a new average after
removing 4.
Soln : The ?rst ?ve natural numbers are :
1, 2, 3, 4, 5.
Sum of ?rst ?ve natural numbers
= 3 5 = 15 ×
As number 4 is greater than the old
average, the new average is going to be
less than the old average.
So, new average = = = 2.75
15 - 4
5 - 1
11
4
which is less than 3.
Variety Questions
Q.1. Rajender is working as a delivery
boy in a multinational company. The
company is paying him ?90 per delivery.
In a fortnight comprising 15 consecutive
working days, his average earnings per
day was ?540. If his average earnings of
the ?rst 7 days was ?519 per day and
that of the last 7 days was ?546 per day,
then at was his earning on the 8th day of
the fortnight?
SSC CHSL 07/08/2023 (3rd Shift)
(a) ?571 (b) ?681 (c) ?661 (d) ?645
Q.2. The average weight of a group of 12
children is 66 kg. If 2 children, X and Y,
replace A and B, the new average weight
becomes 65 kg. The weight of A= weight
of B and the weight of X = weight of Y.
Another child, C, is included in the group,
and the new average weight remains 65
kg. Weight of C= weight of X. Find the
weight of A.
SSC CHSL 04/08/2023 (3rd Shift)
(a) 69 kg (b) 72 kg (c) 71 kg (d) 67 kg
Q.3. Sudesh is the owner of a
multipurpose shop. For a speci?c month,
his pro?ts are detailed below.
Category Pro?t earned in ?
Groceries 50,000
Cosmetics 20,000
Ladies' dresses 10,000
In order to estimate the expected pro?t
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for the next month, he assigns the
weights of 6, 5 and 8 to the different
categories in the same order. What will
be the weighted average of his pro?ts?
SSC CHSL 03/08/2023 (2nd Shift)
(a) 25,265.18 (nearly) ?
(b) 24,863.16 (nearly) ?
(c) 25,163.16 (nearly) ?
(d) 25,263.16 (nearly) ?
Q.4. During a school excursion each
student of junior school was charged
?325 and each student of senior school
was charged ?400. If there were 80
students from junior school and the
combined average amount charged per
student was ?352, then how many
students from senior school went for the
excursion?
SSC CGL 24/07/2023 (1st shift)
(a) 55 (b) 45 (c) 50 (d) 40
Q.5. In ?150, B buys 10 pens for ?8 each,
10 erasers for ?5 each and some
sharpeners for ?4 each. What is the
average price per item in ??
SSC CGL 19/07/2023 (3rd shift)
(a) 8 (b) 7 (c) 10 (d) 6
Q.6. 20 students of a college went to a
hotel. 19 of them spent ?175 each on
their meal and the 20
th
student spent ?19
more than the average of all the 20.
Find the total money spent by them.
SSC CGL 17/07/2023 (4th shift)
(a) ?3,490 (b) ?3,540
(c) ?3,520 (d) ?3,500
Q.7. The average score in a test for 50
students is 44. Out of the total students,
40% of the students are girls and the rest
are boys. The average score of boys is
20% less than that of girls. What is the
average score of girls?
Higher Secondary 27/06/2023 (Shift - 3)
(a) 50 (b) 54 (c) 48 (d) 52
Q.8. A is the average of 10 given
numbers. B is the average after 2 of the
numbers were replaced by 3 other
different numbers. The average of the
removed numbers is 48 and the average
of the newly included numbers is 56. If A
+ B = 438, then the value of A - B is:
Matriculation Level 27/06/2023 (Shift - 2)
(a) 21 (b) 14 (c) 12 (d) 26
Q.9. Average of 8 numbers is 44. The
average of ?rst three numbers is 50 and
the average of next two numbers is 52. If
the sixth number is 6 and 8 less than
seventh and eighth number respectively,
then what is the value of eighth number?
SSC MTS 16/05/2023 (Morning)
(a) 36 (b) 32 (c) 40 (d) 56
Q.10. Eleven friends spent Rs. 18 each
on a tour and the twelfth friend spent Rs.
11 less than the average expenditure of
all twelve of them. What is the total
money spent by twelve friends
SSC MTS 02/05/2023 (Afternoon)
(a) Rs.204 (b) Rs.215
(c) Rs.212 (d) Rs.208
Q.11. Sonali applied for a job of Science
teacher in a school. In the test for job,
she scored 8 in physics, 8 in chemistry, 6
in biology, and 6.5 in the interview. For
calculating the ?nal score, weightage of
2, 3, 3, and 4 were assigned to Physics,
Chemistry, Biology and interview,
respectively. What is the weighted
average score of Sonali ?
SSC CGL 06/12/2022 (1st Shift)
(a) 7 (b) 8.4 (c) 7.2 (d) 21
Q.12. The batting average for 27 innings
of a cricket player is 47 runs. His highest
score in an innings exceeds his lowest
score by 157 runs. If these two innings
are excluded, the average score of the
remaining 25 innings is 42 runs. Find his
highest score in an innings.
SSC CGL 01/12/2022 (1st Shift)
(a) 176 (b) 188 (c) 186 (d) 174
Q.13. In an o?ce, 80% workers are men
while 20% are women. The average age
of the men is 30 and the average age of
the women is 40. What is the average
age of all the workers in that o?ce?
Graduate Level 04/08/2022 (Shift - 2)
(a) 50 (b) 32 (c) 30 (d) 35
Q.14. The average age of a husband and
his wife 3 years ago was 39 years. The
average age of the husband, wife and
their child 2 years hence will be 34 years.
Find the present age of the child.
SSC MTS 11/07/2022 (Afternoon)
(a) 12 years (b) 16 years
(c) 15 years (d) 18 years
Q.15. In a family of six males and a few
females, the average monthly
consumption of grain head is 14.4 kg. If
the average monthly consumption per
head is 20 kg in the case of males and 6
kg in the case of females. Find the
number of females in the family?
SSC MTS 11/07/2022 (Morning)
(a) 8 (b) 4 (c) 6 (d) 7
Q.16. A is the average marks of a group
of 10 students in a class and A+8 is the
average of a group of 15 students which
includes the group of 10 students as
given. The total marks obtained by the
group of 10 students is X and the total
marks obtained by the group of 15
students is Y. If X : Y = 3 : 5, then the
value of A + X + Y is _________.
SSC CHSL 30/05/2022 (Afternoon)
(a) 1964 (b) 1845 (c) 2012 (d) 1992
Q.17. A retailer opens her outlet on all
seven days of the week. It is observed
that her average sales for Saturdays and
Sundays combined is 300, and 200 ? ?
for the remaining ?ve days combined.
For a month starting on saturday, it was
found that the total sales were 7,000. ?
Which among the following months it
could be
SSC MTS 05/10/2021 (Morning)
(a) March (b) April (c) Jan (d) Feb
Q.18. Consider ten consecutive odd
numbers starting from 5. Multiply each
of them, except the ?rst and the second,
with three. What will be the average of
the ten numbers so formed?
SSC MTS 5/10/2021 (Morning)
(a) 39.6 (b) 39 (c) 42 (d) 38.4
Q.19. What is the average of numbers
from 1 to 50 which are multiples of 2 or
5? (correct to one decimal place)
SSC CGL 24/8/2021 (Evening)
(a) 25.4 (b) 25.9 (c) 26.4 (d) 25.8
Q.20. The average weight of students of
section A and B having 40 students each
is 45.5 kg and 44.2 kg respectively. Two
students of section A having average
weight 48.75 kg were shifted to B and 2
students of section B were shifted to
section A, making the average weight of
both the sections equal. What is the
average weight (in kg) of the students
who were shifted from section B to
section A?
SSC CGL 23/8/2021 (Afternoon)
(a) 34.5 (b) 35 (c) 35.75 (d) 34.25
Q.21. In an examination, the average
score of a student was 67.6. If he would
have got 27 more marks in Mathematics,
10 more marks in Computer Science, 18
more marks in History and retained the
same marks in other subjects, then his
average score would have been 72.6.
How many papers were there in the
examination?
SSC CGL 23/8/2021 (Morning)
(a) 11 (b) 10 (c) 12 (d) 9
Q.22. The average monthly salary of 60
employees of a factory is Rs.29900. If
two o?cers are getting Rs.90,000 each
and the average salary of 8 supervisors
is Rs.65,000, then what is the average
salary (in Rs.) of the remaining
employees?
SSC CGL 20/8/2021 (Afternoon)
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(a) 21080 (b) 22680 (c) 29080 (d) 21880
Q.23. What is the ratio of the average of
?rst eight prime numbers to the average
of ?rst ten even natural numbers?
SSC CGL 16/8/2021 (Afternoon)
(a) 1 : 7 (b) 7 : 80 (c) 8 : 70 (d) 7 : 8
Q.24. x, y and z are three positive
numbers such that y is times of x and
4
5
z is times of y. If the average of
5
8
reciprocals of the numbers x, y and z is
, then the average of 3 times of x
17
240
and 5 times of y will be:
SSC CHSL 10/8/2021 (Afternoon)
(a) 70 (b) 60 (c) 40 (d) 45
Q.25. The numbers 2, 3, 4 and 5 occur (2
+ 5k), (5k - 7), (2k - 3) and (k + 2) times,
respectively. The average of the number
is 2.85. Later on, the number 2 was
replaced by 6 in all the places. What is
the average of the new numbers?
SSC CHSL 5/8/2021 (Evening)
(a) 2.4 (b) 5.25 (c) 3.85 (d) 4.75
Q.26. If the average of the 3-digit
numbers 335, 2x5, x35, 63x and 406 is
411, then what will be the average of (x -
1), (x - 3), (x + 3) and (x + 5) ?
SSC CHSL 16/4/2021 (Afternoon)
(a) 6 (b) 3 (c) 5 (d) 4
Q.27. The average of the numbers a, b, c
and d is 2d + 4, Also, the averages of the
numbers a and b, b and c, c and d are 8, 5
and 4, respectively. If e = a + d + 1, then
what is the average of the numbers d and
e ?
SSC CHSL 13/4/2021 (Evening)
(a) 8 (b) 8.5 (c) 3 (d) 7
Q.28. The average of four consecutive
odd natural numbers is eight less than
the average of three consecutive even
natural numbers. If the sum of these
even numbers is equal to the sum of
above four odd numbers, then the
average of four original odd numbers is:
SSC CHSL 20/10/2020 (Afternoon)
(a) 36 (b) 24 (c) 18 (d) 32
Q.29. The average of nine 2 digit
numbers is decreased by 6 when the
digits of one of the 2 digit numbers is
interchanged. Find the difference
between the digits of that number.
SSC CHSL 20/10/2020 (Morning)
(a) 6 (b) 4 (c) 2 (d) 8
Q.30. The numbers 24, 45, a, 35, 59, 83,
46, b, 29, 74 are serially numbered as
they appear in the sequence. When each
number is added to its serial number,
then the average of the new numbers
formed is 55. The average of the missing
numbers (a and b) is:
SSC CHSL 13/10/2020 (Afternoon)
(a) 38 (b) 58 (c) 62 (d) 50
Q.31. The average of 35 consecutive
natural numbers is N. Dropping the ?rst
10 numbers and including the next 10
numbers, the average is changed to M. If
the value of M - N = 600, then the
2 2
average of 3M and 5N is:
SSC CHSL 13/10/2020 (Morning)
(a) 90 (b) 120 (c) 100 (d) 115
Q.32. A batsman in his 11th innings
makes a score of 77 runs, thereby
increasing his average scores by 3. What
is his average score after the 11th
innings?
SSC CHSL 17/03/2020 (Morning )
(a) 46 (b) 49 (c) 47 (d) 48
Q.33. The average age of husband, wife
and child 7 years ago was 42 years and
that of wife and child 9 years ago was 36
years. The present age of the husband is:
SSC CPO 12/12/2019(Evening)
(a) 50 (b) 55 (c) 48 (d) 57
Q.34. A batsman scores 92 runs in the
15th innings and thus increases his
average by 4. What is his average after
the 15th innings?
SSC CPO 12/12/2019(Evening)
(a) 40 (b) 32 (c) 35 (d) 36
Q.35. The average age of 120 students in
a group is 13.56 years, 35% of the
number of students are girls and the rest
are boys. If the ratio of the average age
of boys and girls is 6:5, then what is the
average age (in years) of the girls?
SSC CGL Tier II (13/09/2019)
(a) 12 (b) 11.6 (c) 10 (d) 14.4
Q.36. The average of 18 numbers is 37.5.
If six numbers of average x are added to
them, then the average of all the
numbers increases by one. The value of x
is : :
SSC CGL Tier II (13/09/2019)
(a) 40 (b) 41.5 (c) 42 (d) 38.5
Q.37. The average weight of a certain
number of students in a group is 72 kg. If
10 students having an average weight of
78 kg leave and 4 students having an
average weight of 80 kg join the group,
the average weight of the students in the
group decreases by 0.7 kg. The number
of students initially in the group is :
SSC CGL Tier II (12/09/2019)
(a) 56 (b) 46 (c) 44 (d) 54
Q.38. The average of 33 numbers is 74.
The average of the ?rst 17 numbers is
72.8 and that of the last 17 numbers is
77.2. If the 17th number is excluded, then
what will be the average of the remaining
numbers (correct to one decimal place)?
SSC CGL Tier II (12/09/2019)
(a) 72.9 (b) 73.4 (c) 71.6 (d) 70.8
Q.39. The number of students in a class
is 75, out of which 33 % are boys and
1
3
the rest are girls. The average score in
mathematics of the boys is 66 % more
2
3
than that of the girls. If the average score
of all the students is 66, then the average
score of the girls is:
SSC CGL Tier II (11/09/2019)
(a) 52 (b) 55 (c) 54 (d) 58
Q.40. The owner of a bike buys petrol at
the rate of Rs. 64, Rs. 80 and Rs. 320 per
litre for three consecutive years. If he
spends Rs. 32000 on petrol every year,
then what is the average price (Rs.) of
petrol per litre ?
SSC MTS 16/08/2019 (Evening)
(a) 120 (b) 84 (c) 108 (d) 96
Q.41. An art exhibition was held in the
month of november. The numbers of
visitors on weekdays and on weekends
were 450 and 750 respectively. If the ?rst
day of the month was Monday, then what
was the average number of visitors in the
month ?
SSC MTS 16/08/2019 (Evening)
(a) 520 (b) 530 (c) 510 (d) 540
Q.42. A person was asked to guess his
own weight. He estimated his weight to
be over 70 kg but less than 80 kg. His
friend estimated his weight to be more
than 74 kg but less than 84 kg. His
mother said that his weight is less than
78 kg. Assuming that the weights are a
whole number and that the three had
correctly guessed, then what is the
average of the possible weights(in Kg)?
SSC MTS 14/08/2019 (Morning)
(a) 76.5 (b) 76 (c) 77 (d) 75
Q.43. A party was held for 50 people on
their own expenses. Out of them, 48
people paid Rs. 950 each and the other
two persons paid Rs. 1200 more than the
average expenses of the group. The total
amount spent was :
SSC MTS 14/08/2019 (Morning)
(a) Rs 75,000 (b) Rs 40,000
(c) Rs 25,000 (d) Rs 50,000
Q.44. Out of four numbers the average of
the ?rst three is 16 and that of the last
three is 15. If the last number is 21 then
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the ?rst number is:
SSC MTS 13/08/2019 (Evening)
(a) 28 (b) 22 (c) 21 (d) 24
Q.45. The average of all the prime and
composite numbers upto 100 is:
SSC MTS 9/08/2019 (Morning)
(a) 51 (b) 50 (c) 50.5 (d) 49.5
Q.46. What is the average of the ?rst 15
whole numbers?
SSC MTS 08/08/2019 (Morning)
(a) 8 (b) 7 (c) 9 (d) 10
Q.47. What is the average of the ?rst 8
multiples of 6 among the natural
numbers?
SSC MTS 07/08/2019 (Evening)
(a) 24 (b) 26 (c) 27 (d) 28
Q.48. The average of a and b is 36. The
average of b and c is 42. What is the
difference between c and a ?
SSC MTS 6/08/2019 (Afternoon)
(a) 18 (b) 12 (c) 16 (d) 14
Q.49. The average of 1088 real numbers
is zero. At most how many of them can
be negative?
SSC CHSL 11/07/2019 (Morning)
(a) 100 (b) 88 (c) 544 (d) 1087
Q.50. The difference between the average
of ?rst ten prime numbers and the ?rst ten
prime numbers of two digits is:
SSC CHSL 10/07/2019 (Evening)
(a) 14.5 (b) 16.5 (c) 12.5 (d) 13.5
Q.51. The average of the ?rst 101 ______
numbers is equal to 102.
SSC CHSL 10/07/2019 (Afternoon)
(a) natural (b) odd
(c) even (d) perfect square
Q.52. The average of the ?rst 1234
_______ numbers is equal to 1234.
SSC CHSL 10/07/2019 (Morning)
(a) odd (b) even (c) prime (d) natural
Q.53. The average of a number and its
reciprocal is 4. The average of its cube
and cube of its reciprocal is equal to:
SSC CHSL 9/07/2019 (Evening)
(a) 256 (b) 142 (c) 288 (d) 244
Q.54. The average age of four brothers is
15 years. If their father is included, the
average is increased by 5 years. The age
of the father (in years) is:
SSC CHSL 5/07/2019 (Afternoon)
(a) 35 (b) 40 (c) 38 (d) 36
Q.55. 10 years ago, the average age of a
family of ?ve members was 38 years.
Now, two new members join, whose age
difference is 8 years. If the present
average age of the family is the same as
it was 10 years ago, what is the age (in
years) of the new younger member?
SSC CHSL 4/07/2019 (Afternoon)
(a) 15 (b) 9 (c) 10 (d) 17
Q.56. The average of n number is 36. If
each of 75% of the numbers is increased
by 6 and each of the remaining numbers
is decreased by 9, then the new average
of the numbers is:
SSC CHSL 4/07/2019 (Morning)
(a) 37.125 (b) 33.75 (c) 38.25 (d) 36.25
Q.57. The average weight of the students
in a group was 75.4 kg. Later on, four
students having weights, 72.9 kg, 73.8
kg, 79.5 kg and 87.4 kg joined the group.
As a result, the average weight of all the
students in the group increased by 0.24
kg. What was the number of students in
the group, initially ?
SSC CHSL 3/07/2019 (Morning)
(a) 46 (b) 36 (c) 50 (d) 48
Q.58. In a class of 80 students, 60%
participate in games and the rest do not.
The average weight of the former group
is 5% more than that of the latter. If the
average weight of all the students is 51
kg, then what is the average weight (in
1
2
kg) of the former group?
SSC CHSL 2/07/2019 (Afternoon)
(a) 57.6 (b) 54.5 (c) 60 (d) 52.5
Q.59. The average of 27 numbers is zero.
Out of them, how many may be greater
than zero, at the most?
SSC CGL 13/06/2019 (Evening)
(a) 0 (b) 15 (c) 26 (d) 20
Q.60. In a class of 40 students, 45% are
girls and the remaining are boys. If the
average marks of the girls is 54 and that
of the boys is 46, what is the average of
the whole class?
SSC CGL 11/06/2019 (Afternoon)
(a) 49.8 (b) 49.7 (c) 49.6 (d) 49.5
Q.61. The average marks of 40 students
was found to be 68. If the marks of two
students were incorrectly entered as 48
and 64 instead of 84 and 46 respectively,
then what is the correct average?
SSC CGL 10/06/2019 (Afternoon)
(a) 68.25 (b) 68.15 (c) 68.45 (d) 68.35
Q.62. Four different positive numbers are
written in ascending order. One-third of
the average of all the four numbers is 19
less than the greatest of these numbers.
If the average of the ?rst three numbers
is 12, the greatest number among the
given numbers is:
SSC CGL 7/06/2019 (Evening)
(a) 25 (b) 22 (c) 24 (d) 21
Q.63. The total number of students in
section A and B of a class is 110. The
number of students in section A is 10
more than that of section B. The average
score of the students in B, in a test, is
20% more than that of students in A. If
the average score of all the students in
the class is 72, then what is the average
score of the students in A?
SSC CGL 7/06/2019 (Afternoon)
(a) 66 (b) 68 (c) 63 (d) 70
Q.64. Three numbers are such that if the
average of any two of them is added to
the third number, the sums obtained are
168, 174 and 180 respectively. What is
the average of the original three
numbers?
SSC CGL 4/06/2019 (Evening)
(a) 86 (b) 87 (c) 89 (d) 84
Q.65. The average weight of a certain
number of students in a class is 68.5 kg.
If 4 new students having weights 72.2 kg,
70.8kg, 70.3kg and 66.7 kg join the class,
then the average weight of all the
students increases by 300 g. The number
of students in the class, initially is:
SSC CGL 4/06/2019 (Afternoon)
(a) 21 (b) 16 (c) 11 (d) 26
Q.66. The average of twelve numbers is
42. The average of the last ?ve numbers
is 40 and that of the ?rst four numbers is
44. The 6th number is 6 less than the
?fth and 5 less than the 7th number. The
average of the 5th and the 7th numbers
is:
SSC CGL 4/06/2019 (Morning)
(a) 44 (b) 44.5 (c) 43 (d) 43.5
Practice Questions
SSC CHSL 2023 Tier - 2
Q.67. At a Yoga center, 60% of the
members are men and 40% of the
members are women. If the average age
of the men is 55 years and the average
age of the women is 45 years, then what
is the average age (in years) of all the
members ?
SSC CHSL Tier II 02/11/2023
(a) 51 (b) 48 (c) 50 (d) 49
Q.68. The average weight of 40 students
of a school is 52 kg. If the weight of the
teacher is included, the average weight
rises by 500 grams. Find the weight (in
kg) of the teacher.
SSC CHSL Tier II 02/11/2023
(a) 72.5 (b) 74.5 (c) 73.5 (d) 71.5
Q.69. The average salary of all 40
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employees, including 35 non-teaching
staff members, of a school is ?4,000. If
the average salary of the non-teaching
staff members is ?4,200, ?nd the average
salary of the remaining staff of the
school.
SSC CHSL Tier II 10/01/2024
(a) ?3,600 (b) ?2,600
(c) ?2,800 (d) ?2,300
Q.70. The average of the ?rst eight
multiples of 6 is:
SSC CHSL Tier II 10/01/2024
(a) 24 (b) 27 (c) 30 (d) 25
Q.71. Find the average of the prime
numbers lying between 69 and 92.
SSC CHSL Tier II 10/01/2024
(a) 79 (b) 82 (c) 80 (d) 81
SSC CGL 2023 Tier - 2
Q.72. The average weight of the ?rst
thirteen persons among fourteen
persons is 78 kg. The weight of the 14th
person is 39 kg more than the average
weight of all the fourteen persons. Find
the weight of the 14th person.
SSC CGL Tier II ( 26/10/2023 )
(a) 118 kg (b) 98 kg
(c) 110 kg (d) 120 kg
SSC CPO 2023 Tier - 1
Q.73. The average weight of 15 people
increases by 3.2 kg when a new person
comes in place of one of them weighing
52 kg. The weight of the new person is:
SSC CPO 03/10/2023 (3rd Shift)
(a) 96 kg (b) 100 kg
(c) 52 kg (d) 48 kg
Q.74. The average weight of A, B and C is
77 kg. If the average weight of A and B is
68 kg and that of B and C is 83 kg, then
the weight (in kg) of B is:
SSC CPO 04/10/2023 (3rd Shift)
(a) 71 (b) 74 (c) 67 (d) 73
Q.75. The average of 45 numbers was
found to be 39. Later on, it was detected
that a number 65 was misread as 56.
Find the correct average of the given
numbers.
SSC CPO 05/10/2023 (2nd Shift)
(a) 36.2 (b) 37.2 (c) 38.2 (d) 39.2
Q.76. What is the average of the ?rst six
prime numbers?
SSC CPO 05/10/2023 (3rd Shift)
(a) 6 (b) 6 (c) 6 (d) 6
2
3
5
6
1
6
1
3
Q.77. Rakesh runs a coaching institute
having 50 faculty members. The average
monthly salary of 35 faculty members is
?37,500. What will be the average
monthly salary (in ?) of the other 15
faculty members, if the average monthly
salary of all the 50 faculty members is
found to be ?30,000?
SSC CPO 05/10/2023 (3rd Shift)
(a) 12,000 (b) 13,000
(c) 12,500 (d) 13,500
SSC MTS 2023 Tier - 1
Q.78. In a class of 37 students, there are
22 girls. The average weight of these
girls is 46 kg and the average weight of
the whole class is 50 kg. What is the
average weight (in kg) of the boys in that
class ? (Rounded off to 2 decimal
places)
SSC MTS 01/09/2023 (1st Shift)
(a) 60.74 (b) 55.87
(c) 61.35 (d) 58.25
Q.79. Student gets 62, 58, 72, 58 and 83
marks in Sanskrit, English, Mathematics,
Social and Computer Science,
respectively. His average marks in
Mathematics, Social and Computer
Science are ______ more than the average
marks in Sanskrit, English and
Mathematics.
SSC MTS 01/09/2023 (2nd Shift)
(a) 9 (b) 8 (c) 6 (d) 7
Q.80. The average marks of 13 students
in a subject is 66. If the average of the
?rst seven students is 67 and that of the
last seven students is 69, then the marks
of the seventh student is:
SSC MTS 01/09/2023 (2nd Shift)
(a) 99 (b) 91 (c) 97 (d) 94
Q.81. The average of the ?rst 10 prime
number is:
SSC MTS 04/09/2023 (1st Shift)
(a) 12.9 (b) 9.7 (c) 11.9 (d) 13.4
Q.82. The average of the ?rst 69 natural
numbers is:
SSC MTS 04/09/2023 (1st Shift)
(a) 34 (b) 35 (c) 33 (d) 36
Q.83. What is the average of the ?rst 13
multiples of 3 ?
SSC MTS 05/09/2023 (1st Shift)
(a) 21 (b) 39 (c) 42 (d) 35
Q.84. The average age of a family of
three members (mother, father and Son)
is 44 years. After the son's marriage, the
average age of the family becomes 39
years. What is the age of the
daughter-in-law ?
SSC MTS 05/09/2023 (2nd Shift)
(a) 24 years (b) 25 years
(c) 23 years (d) 22 years
Q.85. The average weight of 20 students
of a class was 30.5 kg. After 6 new
students joined the class, its average
weight increased by 2 kg. Find the
average weight of the 6 new students
who joined the class (rounded off to one
decimal place).
SSC MTS 06/09/2023 (1st Shift)
(a) 30.5 kg (b) 32.5 kg
(c) 39.2 kg (d) 38.5 kg
Q.86. A batsman makes 96 runs in the
13
th
innings and thus his average
increases by 3. Find his average after 13
innings.
SSC MTS 06/09/2023 (1st Shift)
(a) 65 (b) 50 (c) 70 (d) 60
Q.87. The average of four consecutive
odd numbers is 58. What is the lowest
number ?
SSC MTS 06/09/2023 (2nd Shift)
(a) 51 (b) 57 (c) 55 (d) 53
Q.88. In April, Mr. Khan observed that his
balance in his bank account is ?5,600 for
the ?rst 24 days, ?12,000 for the next two
days and ?37,500 in the last 4 days of the
month. What is his daily average balance
for April ?
SSC MTS 06/09/2023 (3rd Shift)
(a) ?10,280 (b) ?15,280
(c) ?10,480 (d) ?14,280
Q.89. There are 48 students in a class.
Their average weight is 48 kg. When one
student leaves the class, the average
weight reduces by 200 grams. What is
the weight of the student who left the
class?
SSC MTS 08/09/2023 (1st Shift)
(a) 57.4 kg (b) 54.7 kg
(c) 45.7 kg (d) 47.5 kg
Q.90. The average weight of A, B and C is
43 kg. If the average weight of A and B is
40 kg and that of B and C is 41 kg, then
the weight (in kg) of B is ?
SSC MTS 08/09/2023 (1st Shift)
(a) 41 (b) 43 (c) 33 (d) 37
Q.91. The speed of a bus from station A
to B is 55 km/h, and while coming back
from station B to A, the speed of the bus
is 95 km/h. The average speed (in km/h)
of the bus during the whole journey is :
SSC MTS 08/09/2023 (2nd Shift)
(a) (b) (c) (d) 72
1
3
67
1
3
62
2
3
69
2
3
Q.92. A student's marks were incorrectly
entered as 44 instead of 86. Due to this,
the average of the class got decreased
by . What is the number of students in
3
2
the class ?
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