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All questions of Averages for SSC MTS / SSC GD Exam

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There are 7 members in a family whose average age is 25 years. Ram who is 12 years old is the second youngest in the family. Find the average age of the family in years just before Ram was born?
  • a)
    15.167
  • b)
    18.2
  • c)
    13
  • d)
    Cannot be determined
Correct answer is option 'D'. Can you explain this answer?

Rajeev Kumar answered
In order to find the average age of the family before Ram was born, we need to know the age of the youngest member of the family. 
Since, we do not know the age of the youngest member, we can not calculate the total age of the family before Ram was born.
Hence, we can not calculate the answer with the given conditions.
Thus, D is the right choice.

Can you explain the answer of this question below:
The average of 20 numbers is zero. Of them, How many of them may be greater than zero , at the most?
  • A:1
  • B:20
  • C:0
  • D:19

The answer is D.

Ishita Das answered
Average of 20 numbers = 0.
 Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).

Can you explain the answer of this question below:
 A car owner buys diesel at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of diesel if he spends Rs. 4000 each year?
  • A:Rs. 8
  • B:Rs. 7.98
  • C:Rs. 6.2
  • D:Rs. 8.1

The answer is B.

Ishani Rane answered
Average cost per litre of petrol = Total amount / Total quantity of petrol

Re. 4000 is spent each year, so total amount spent = 3 * Rs. 4000 = Rs. 12,000

Total quantity of petrol consumed in 3 years = (4000/7.50) + (4000/8) + (4000/8.50) litres

= 533.3 + 500 + 470.6 = 1505

Average cost = Total amount / Total quantity

= 12000/1504 = 7.98

To find quickly, you can take cube root of (7.50 * 8 * 8.50), and it will be slightly less than 8.

The correct option is B.

A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
  • a)
    39
  • b)
    35
  • c)
    42
  • d)
    40.5
Correct answer is option 'A'. Can you explain this answer?

Manoj Ghosh answered
Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
then average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
We know that Total runs scored in 16 innings + 87 = Total runs scored in 17 innings
=> 16(x-3) + 87 = 17x
=> 16x - 48 + 87 = 17x
=> x = 39

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, what is the average marks of all the students?
  • a)
    53.23
  • b)
    54.68
  • c)
    51.33
  • d)
    50
Correct answer is 'B'. Can you explain this answer?

Manoj Ghosh answered
Total marks of first batch(55) is= 55*50=2750
Total marks of second batch (60) is= 60*55=3300
Total marks of third batch(45)= 45*60=2700

Total marks of second batch= 2750+3300+2700 = 8750
Total number of Students= 55+60+45 =160
Avg= 8750/160= 54.68

The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:
  • a)
    3500
  • b)
    4000
  • c)
    4050
  • d)
    5000
Correct answer is 'B'. Can you explain this answer?

Arya Roy answered
Let monthly income of A = a
monthly income of B = b 
monthly income of C = c
a + b = 2 * 5050 .... (Equation 1)
b + c = 2 * 6250 .... (Equation 2)
a + c = 2 * 5200 .... (Equation 3)
(Equation 1) + (Equation 3) - (Equation 2)
= a + b + a + c - (b + c) = (2 * 5050) + (2 * 5200) - (2 * 6250)
= 2a = 2(5050 + 5200 - 6250)
= a = 4000
i.e., Monthly income of A = 4000

The average number of runs scored by Virat Kohli in four matches is 48. In the fifth match, Kohli scores some runs such that his average now becomes 60. In the 6th innings he scores 12 runs more than his fifth innings and now the average of his last five innings becomes 78. How many runs did he score in his first innings? (He does not remain not out in any of the innings)
  • a)
    30
  • b)
    50
  • c)
    70
  • d)
    90
Correct answer is option 'A'. Can you explain this answer?

Quantronics answered
Runs scored by Kohli in first 4 innings = 48*4 = 192
Average of 5 innings is 60, so total runs scored after 5 innings = 60*5 = 300
Hence runs scored by Kohli in fifth inning = 300 – 192 = 108
It is given that in 6th innings he scores 12 runs more than this, so he must score 120 in the sixth inning. Hence total runs scored in 6 innings = 300+120 = 420
Now average of last five innings is 78, so runs scored in last innings = 390
Hence runs scored in first inning = 420 – 390 = 30.

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. Find out the average age of the team.
  • a)
    23 years
  • b)
    20 years
  • c)
    24 years
  • d)
    21 years
Correct answer is option 'A'. Can you explain this answer?

Pallabi Deshpande answered
Number of members in the team = 11
Let the average age of of the team = x
=> Sum of the ages of all the 11 members of the team / 11 = x
=> Sum of the ages of all the 11 members of the team = 11 x
Age of the captain = 26
Age of the wicket keeper = 26 + 3 = 29
Sum of the ages of 9 members of the team excluding captain and wicket keeper 
= 11x − 26 − 29 =11x − 55
Average age of 9 members of the team excluding captain and wicket keeper
= 11x−55 / 9
Given that
11x−55 / 9 =(x−1)
⇒11x−55=9(x−1)
⇒11x−55=9x−9
⇒2x=46
⇒x = 46/2 = 23 years

A student's marks were wrongly entered as 83 instead of 63. Due to that, the average marks for the class got increased by 1/2. What is the number of students in the class?
  • a)
    45
  • b)
    40
  • c)
    35
  • d)
    30
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
To solve this problem, we can use the concept of average age and find the number of men in the group.

Let's assume there are 'x' men in the group.

First, we can find the sum of the ages of all the men in the group before the replacement. Since the average age is the sum of all ages divided by the number of men, we have:

Sum of ages before replacement = Average age before replacement * Number of men

Next, we need to find the sum of ages after the replacement. We know that when the person aged 26 years is replaced by a new person aged 56 years, the average age of the group increases by 6 years. Therefore, the new average age is the average age before replacement plus 6:

New average age = Average age before replacement + 6

We can now find the sum of ages after the replacement using the new average age:

Sum of ages after replacement = New average age * Number of men

Since the sum of ages after the replacement is greater than the sum of ages before the replacement by the age of the replaced person, we have:

Sum of ages after replacement = Sum of ages before replacement + Age of replaced person

Now we can equate the two equations and solve for 'x', the number of men in the group:

New average age * Number of men = Average age before replacement * Number of men + Age of replaced person

Substituting the values given in the problem, we have:

(Average age before replacement + 6) * x = Average age before replacement * x + 26

Simplifying the equation, we get:

6x = 26

Dividing both sides by 6, we find:

x = 26/6

x ≈ 4.33

Since the number of men in the group cannot be a fraction, we can round up to the nearest whole number. Therefore, there are 5 men in the group.

Hence, the correct answer is option B.

The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. What is the present age of the husband?
  • a)
    40
  • b)
    32
  • c)
    28
  • d)
    30
Correct answer is option 'A'. Can you explain this answer?

Arya Roy answered
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years  = 50 years.
Husband's present age = (90 - 50) years = 40 years.

The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, what is the weight of B?
  • a)
    31 kg
  • b)
    28 kg
  • c)
    32 kg
  • d)
    30 kg
Correct answer is option 'A'. Can you explain this answer?

Kavya Saxena answered
Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31.
 B's weight = 31 kg.

One collective farm got an average harvest of 21 tons of wheat and another collective farm that had 12 acres of land less given to wheat, got 25 tons from a hectare. As a result, the second farm harvested 300 tons of wheat more than the first. How many tons of wheat did each farm harvest?
  • a)
    3150, 3450
  • b)
    3250, 3550
  • c)
    2150, 2450 
  • d)
    3350, 3150
Correct answer is option 'A'. Can you explain this answer?

Dhruv Mehra answered
Let's solve the problem again step by step, ensuring accuracy:
  1. Let the area of the first farm be AAA acres.
  2. Therefore, the area of the second farm is A−12A - 12A−12 acres.
Given that:
  • The first farm gets an average harvest of 21 tons of wheat per acre.
  • The second farm gets an average harvest of 25 tons of wheat per acre.
  • The second farm harvested 300 tons more wheat than the first.
Set up the equations:
  1. The total harvest of the first farm: 21A21A21A tons
  2. The total harvest of the second farm: 25(A−12)25(A - 12)25(A−12) tons
  3. The difference in harvest: 25(A−12)−21A=30025(A - 12) - 21A = 30025(A−12)−21A=300
Solve the equation: 25A−300−21A=30025A - 300 - 21A = 30025A−300−21A=300 4A−300=3004A - 300 = 3004A−300=300 4A=6004A = 6004A=600 A=150A = 150A=150
The area of the first farm is 150 acres, and the area of the second farm is 150−12=138150 - 12 = 138150−12=138 acres.
Calculate the total harvest for each farm:
  1. The first farm: 21×150=315021 \times 150 = 315021×150=3150 tons
  2. The second farm: 25×138=345025 \times 138 = 345025×138=3450 tons
The correct answer is:
  1. 3150, 3450

The average weight of a class of 10 students is increased by 2 kg when one student of 30kg left and another student joined. After a few months, this new student left and another student joined whose weight was 10 less than the student who left now. What is the difference between the final and initial averages?
  • a)
    11
  • b)
    1
  • c)
    111
  • d)
    121
Correct answer is option 'B'. Can you explain this answer?

Rajeev Kumar answered
Change in total weight of 10 students = difference in weight of the student who joined and the student
=> weigth of first student who left = 30 + (10×2) = 50
weight of the student who joined last = 50 – 10 = 40...
Thus change in average weight = (40 – 30)/10 = 1...
 

Read the following passage and answer the following question that follows.
Aman, Binod, Charan, Dharam and Ehsaan are the members of the same family. Each and everyone loves one another very much. Their birthdays are in different months and on different dates. Aman remembers that his birthday is between 25th and 30th, of Binod it is between 20th and 25th, of Charan it is between 10th and 20th, of Dharam it is between 5th and 10th and of Ehsaan it is between 1st and 5th of the month. The sum of the date of birth is defined as the addition of the date and the month, for example 12th January will be written as 12/1 and will add to a sum of the date of 13. (Between 25th and 30th includes 25 and 30).
If the dates of birth, of four of them are prime numbers, then find the maximum average of the sum of their dates of birth? 
  • a)
    29
  • b)
    23
  • c)
    28
  • d)
    27.2
Correct answer is option 'D'. Can you explain this answer?

Alok Verma answered
It is given that the date of births of four of them are prime numbers
For the average to be maximum, the dates we need to choose must be closest to the maximum dates
Therefore, the four prime dates are 29th, 23th, 19 and 5th
Sum of the date of birth = 29+23+19+10+5+12+11+10+9+8 =136
Average = 136/5  = 27.2
The maximum average when the birth dates of four of them are prime numbers is 27.2

The average of 20 numbers is zero. Of them, How many of them may be greater than zero , at the most?
  • a)
    1
  • b)
    20
  • c)
    0
  • d)
    19
Correct answer is 'D'. Can you explain this answer?

Priyanka Datta answered
Average of 20 numbers = 0.
 Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).

Ram was born 30 years after his father was born and Ram's sister was born 25 years after Ram’s mother was born. The average age of the Ram family is 26.25 years right now. Ram's sister will get married 4 years from now and will leave the family. Then the sum of age of the family will be 107 years. What is the age of Ram's father?
  • a)
    30 year
  • b)
    35 year
  • c)
    40 year
  • d)
    45 years
Correct answer is option 'D'. Can you explain this answer?

Shilpa Nambiar answered
Let the present age of father be x and mother be y
∴ Ram age = (x – 30)
And Ram’s sister = (y – 25)
We know that
Average = Sum of all/total number of terms
⇒ 26.25 = Sum of all/4
Sum of their ages will be = 105
∴ x + y + (x - 30) + (y – 25) = 105
⇒ x + y = 80     ----(i)
After four years their total ages will be (excluding daughter age)
∴ (x + 4) + (y + 4) + (x – 30) + 4 = 107
⇒ 2x + y = 125     ----(ii)
By solving equation (i) and (ii) we get
⇒ x = 45 and y = 35
∴ The age of Ram’s father will be 45 years 

In 2001 there were 6 members in Barney’s family and their average age was 28 years. He got married between 2001 and 2004 and in 2004 there was an addition of a child in his family. In 2006, the average age of his family was 32 years. What is the present age (in 2006) of Barney’s wife (in years) is:
  • a)
    61
  • b)
    57
  • c)
    59
  • d)
    56
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
& Friends. The main characters were:

1. Barney - a purple anthropomorphic Tyrannosaurus rex who is the main protagonist and host of the show.

2. Baby Bop - a green Triceratops who is one of Barney's best friends. She is known for her love of music and dancing.

3. BJ - a yellow Protoceratops who is another of Barney's best friends. He is known for his love of sports and games.

4. Riff - a brown Hadrosaur who is a new character introduced in 2006. He is known for his love of music and playing the guitar.

5. Tosha - a human girl who is one of Barney's human friends. She is known for her love of singing and dancing.

6. Min - another human girl who is also one of Barney's human friends. She is known for her love of art and drawing.

The average age of a class of 30 students and a teacher reduces by 0.5 years if we exclude the teacher. If the initial average is 14 years, find the age of the class teacher. 
  • a)
    27 years
  • b)
    28 years
  • c)
    29 years
  • d)
    30 years
Correct answer is option 'C'. Can you explain this answer?

Bank Exams India answered
Let the age of the teacher be T.
The initial total age of the class (including the teacher) is (30+1)*14 = 434 years.
If we exclude the teacher, the total age of the 30 students is 30*(14-0.5) = 405 years.
So the teacher's age, T, must be:
434 - 405 = 29 years
Therefore, the age of the class teacher is 29 years.

Read the passage below and solve the questions based on it.
The average score of a batsman for a certain number of innings was 21 75 per inning. He played 3 innings more and scored 28. 34 and 37 runs respectively, thus increasing his average by 1.25.
Q. How many innings in all did he play?
  • a)
    35
  • b)
    60
  • c)
    30
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Rajeev Kumar answered
Let number of innings be x
average of the first (x-3) innings = 21.75
Total of the first (x-3) innings = 21.75(x-3)
Average of the x innings = (21.75+1.125) = 22.875
Total of the x innings = 22.875x
21.75(x-3) + 28+34+37= 22.875x
21.75(x-3) + 99 = 22.875x
21.75x - 65.25 + 99 = 22.875x
1.125x = 33.75
x = 30

The average mark of a class of n students is 64. When eight new students with an average mark of 73 join the class, the new average of the entire class is a whole number. Find the number of students now in the class, given that n lies between 25 and 60.
  • a)
    44
  • b)
    32
  • c)
    36
  • d)
    72
Correct answer is option 'C'. Can you explain this answer?

Arya Roy answered
Let ‘x’ be the increase in the average 


For ‘x’ to be a whole number 72 (= 9 * 8) should be divisible by (n + 8) 

From the choices it can be said that 36 and 72 are two such factors. But 72 does not lie within the range. 

∴ number of students in class are 36.

The average age of a family of 5 members is 20 years. If the age of the youngest member is 10 years, what was the average age of the family at the birth of the youngest member?
  • a)
    12.50
  • b)
    15.25
  • c)
    21.25 
  • d)
    18.75 
Correct answer is option 'D'. Can you explain this answer?

Rajeev Kumar answered
At present the total age of the family = 5 × 20 =100
The total age of the family at the time of the birth of the youngest member,
= 100 - 10 - (10 × 4)
= 50
Therefore, average age of the family at the time of birth of the youngest member,
= 50/4 =12.5

Practice Quiz or MCQ (Multiple Choice Questions) with solution are available for Practice, which would help you prepare for "Average" under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.
 
Q. In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
  • a)
    6.25
  • b)
    5.5
  • c)
    7.4
  • d)
    5
Correct answer is option 'A'. Can you explain this answer?

Arya Roy answered
Runs scored in the first 10 overs = 10 * 3.2 = 32
Total runs = 282
Remaining runs to be scored = 282 - 32 = 250
Remaining overs = 40
Run rate needed =250/40 = 6.25

 Read the following:
There are 3 classes having 20, 25 and 30 students respectively having average marks in an examination as 20, 25 and 30 respectively. If the three classes are represented by A, B and C and you have the following information about the three classes,
answer the questions that follow:
A Æ Highest score 22, Lowest score 18
B Æ Highest score 31, Lowest score 23
C Æ Highest score 33, Lowest score 26
In a transfer of 5 students from B to C
Which of these can be said about the average score of B?
  • a)
    Increases if C decreases
  • b)
    Decreases if C increases
  • c)
    Increases if A decreases
  • d)
    Decreases if B increases
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
- Class A has a total of 400 marks
- Class B has a total of 625 marks
- Class C has a total of 900 marks

B - If all three classes are combined, what is the total number of students and the overall average marks?

The total number of students is 75 (20+25+30). To find the overall average marks, we need to first find the total marks of all three classes combined, which is 400 + 625 + 900 = 1925. Then, we divide this total by the total number of students, which is 75. So, the overall average marks is 1925/75 = 25.67 (rounded to two decimal places).

C - If a student has scored 30 marks in each class, what is the student's overall average marks?

To find the overall average marks of a student who has scored 30 marks in each class, we need to find the total marks earned by the student and divide it by the total number of classes. The student has scored a total of 30 x 3 = 90 marks overall. The total number of classes is 3. So, the overall average marks of the student is 90/3 = 30.

The average of 20 numbers is zero. Of them, How many of them may be greater than zero , at the most?
  • a)
    1
  • b)
    20
  • c)
    0
  • d)
    19
Correct answer is option 'D'. Can you explain this answer?

Sagar Sharma answered
Problem:
The average of 20 numbers is zero. How many of them may be greater than zero, at the most?

Solution:
To find the maximum number of numbers that can be greater than zero, we need to understand the concept of average and the properties of numbers.

Understanding the Average:
The average of a set of numbers is found by summing all the numbers in the set and then dividing the sum by the total number of numbers.

Properties of Numbers:
1. The sum of positive numbers is always greater than zero.
2. The sum of negative numbers is always less than zero.
3. The sum of positive and negative numbers can be zero if the sum of positive numbers equals the sum of negative numbers.

Explanation:
Given that the average of 20 numbers is zero, we can conclude that the sum of these 20 numbers is also zero.

Let's assume that there are 'x' numbers greater than zero and 'y' numbers less than or equal to zero.

Since the sum of these 20 numbers is zero, we can write the equation:
(x * positive number) + (y * non-positive number) = 0

To maximize the number of numbers greater than zero, we need to minimize the number of non-positive numbers. The smallest non-positive number is zero. Therefore, we can rewrite the equation as:
(x * positive number) + (y * 0) = 0

Simplifying the equation, we get:
x * positive number = 0

In order for this equation to be true, the value of 'x' must be zero. This means that there can be zero numbers greater than zero in the set of 20 numbers.

Therefore, the maximum number of numbers that can be greater than zero is 0.

Hence, the correct answer is option 'C' - 0.

There are 3 classes having 20, 25 and 30 students respectively having average marks in an examination as 20, 25 and 30 respectively. If the three classes are represented by A, B and C and you have the following information about the three classes, answer the questions that follow:
A - Highest score 22, Lowest score 18
B - Highest score 31, Lowest score 23
C - Highest score 33, Lowest score 26
If five students are transferred from A to B. What will happen to the average score of B?
  • a)
    Definitely increase
  • b)
    Cannot Say 
  • c)
    Remain constant
  • d)
    Definitely decrease
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
- The highest marks in class A is 40 and the lowest marks is 10.
- The range of marks in class B is 20.
- The mode of marks in class C is 30.

B

- The total marks obtained by all students in class B is 1250.
- The median marks in class B is 25.

C

- The highest marks in class C is 50.
- The lowest marks in class C is 10.
- The mean marks in class C is 30.

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