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20 Questions MCQ Test Quantitative Techniques for CLAT | Test: Average- 2

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Test: Average- 2 - Question 1

If the sum of five consecutive odd numbers is 255 then find the sum of largest and smallest number.

Detailed Solution for Test: Average- 2 - Question 1

SUm of 5 odd numbers = 255
Average = 255/5 = 51
47…..49…..51……53……55
Average = 51
Sum of largest and small number = 47+55 = 102

Test: Average- 2 - Question 2

Nine students of a class contribute a certain sum. Seven of them give Rs. 5 each and the other two give Rs. 5 & 9 more then the average contribution of all the 9 students. The average contribution of the class of 9 students is.

Detailed Solution for Test: Average- 2 - Question 2

Average = sum/n
Average of 9 students = x
n = 9

Seven of them give Rs. 5 = 7 x 5 = 35
35+(5+x)+(9+x)
∴ other two give Rs. 5 and Rs. 9 more than the average contribution

9x = 49 + 2x
9x - 2x = 49
7x = 49
x = 7

Test: Average- 2 - Question 3

Sonam calculates average of 10 positive 2 digit integers. By mistake she interchanges the digits of one number while calculating the average. Because of which, the average becomes 2.7 less than the correct answer. What is the difference between the two digits of the number which was reversed while calculating the average?

Detailed Solution for Test: Average- 2 - Question 3

Let the original number be (10b+a)

  ​​ ​​​​ Because of interchange, the mistaken number is (10a+b)

  ​​ ​​​​ Given that, 10b+a = 10a+b +(2.7*10) => 9b-9a = 27 => b-a = 3

So, the correct answer is A. 

Test: Average- 2 - Question 4

There are total 600 students in a school. Average age of boys is 12 years and of girls is 11 years while average age of all students is 11 yrs. And 9 months. Find the number of girls in the school. 

Detailed Solution for Test: Average- 2 - Question 4

Test: Average- 2 - Question 5

Ratio between present ages of A, B and C is 5:4:6. Total of the ages of A and C after 5 years will be 54 years. What will be the ratio of ages of B and C after 4 years?

Detailed Solution for Test: Average- 2 - Question 5

Option (2) 5:7 is correct✅answer. 

Explanation:-

Let age of A = 5 x

                   B=  4x

                   C = 6x 

Then, according to the question;

( 5x+5) + (6x+5) = 54

11x + 10   = 54

=> 11x  = 54-10

=> 11x = 44

=> x =  4

B's age after 4 years;

 = 4x +4 

=> 4*4+4 

=>  20 years. 

C's age after 4 years ;

= 6x+4 

=>6*4+4

=  28 years 

Therefore,  ratio = 20/28

=>       ratio = 5:7

Test: Average- 2 - Question 6

A farmer wants to mix 100 kg of Rs. 40/kg rice and some quantity of Rs. 60/kg rice. What quantity of 60kg rice should be mixed to get Rs. 50 /kg rice mix?​​ 

Detailed Solution for Test: Average- 2 - Question 6

 Let the rice quantity of Rs. 60 /kg rice be x.

Price for Rs. 40 /kg = 200*40

Price for Rs. 60/kg = x*60

After mixing the two types of rice the price = 50*(200+x)

The price will remain same after and before mixing, hence the equation becomes:

200*40 + x*60 = 50(200+x)

x(60-50) = 200*(50-40)

10x = 200*10

X = 200 kg​​ 
 

So, the correct answer is A.

Test: Average- 2 - Question 7

Sum of the ages of a father and son is 45 years. Five years, ago product of their ages was 4 times the father’s age at that time. Present ages of father and his son, respectively are:

Detailed Solution for Test: Average- 2 - Question 7

Let the present age of the father be x 

∴ The present age of the son is (45−x) 

Five years ago Age of father =(x−5)
Age of son =((45−x)−5)=(40−x) 


⇒(x−5)(40−x)=4×(x−5)
⇒40x−200−x2+5x=4x−20
⇒x2−41x+180=0
⇒(x−36)(x−5)=0

⇒x=36 or x=5 (Not possible)
∴x=36 years   

∴ Present age of father =36 years  

∴ Present age of son =45−36=9 years

So, the correct answer is B.

Test: Average- 2 - Question 8

Kamla got married 6 years ago. Today her age is 1(1/4) times her age at the time of marriage. Her son age is 1/10 times her age. Her son age is:

Detailed Solution for Test: Average- 2 - Question 8

Let Kamla's age 6 years ago be x years.
So, Kamla's present age = (x + 6) years
∴ x + 6 = 5x / 4
⇒ 4x + 24 = 5x
⇒ x = 24
So, Kamla's Present age = (x + 6) years = 30 years
∴ Son's present age = 30/10 = 3 years

So, the correct answer is B

Test: Average- 2 - Question 9

 John inherits Rs. 200000, and invests a part of money in bonds with an interest rate of 11% per annum, and saves the remainder at 9% per annum. He receives Rs. 20400 as interest for 1 year. What amount he invested at 11% and 9 % respectively?

Detailed Solution for Test: Average- 2 - Question 9

Let x be the amount invested in bonds then 200000-x will be saved by John.

As per the questions, the interest earned is 20400 which includes both bonds and savings. Hence x*11/100 + 9*(200000-x) /100 = 20400

2x = 2040000-1800000 =​​ 240000

X= 120000 (Invested in bonds)

Savings = 200000-120000 = 80000 ​​​​ 

 

So, the correct option is A.

Test: Average- 2 - Question 10

Ratio of father’s age to his son’s age is 7:3. Product of their ages is 756. Ratio of their ages after 6 years will be

Detailed Solution for Test: Average- 2 - Question 10

Let the father's age be 7x
and son's age be 3x
So, 7x*3x=756
21x^2=756
X^2=756/21
X^2=36
X=6
Father's age=7x=6*7=42
Son's age=3x=3*6=18
Father's age 6 year hence =42+6=48
Son's age 6 year hence=18+6=24
So, ratio of their ages after 6 years will be 48/24=2=2:1

Test: Average- 2 - Question 11

The ratio of Vipan’s age & Sonia’s age is 3:5 and the sum of their age is 80 years. The ratio of their ages after 10 years will be.

Detailed Solution for Test: Average- 2 - Question 11

Let the age of the Vimal and Arun be 3x, 5x resp.
From the given condition, we get
3x+5x=80 ⇒8x=80 ⇒ x=80/8=10Then, Vimal′s age is 3x=3×10=30 and Arun′s age is 5x=5×10=50
After ten years, Vimal's age will be 30 + 10 = 40
Arun’s age will be 50 + 10 = 60
Then their ratio = 40 : 60 = 2 : 3

 

So, the correct answer is A. 

Test: Average- 2 - Question 12

Average of five numbers is 15 while average of three of those numbers​​ is 11. Find the average of remaining two numbers.

Detailed Solution for Test: Average- 2 - Question 12

Average of 5 numbers = 15

  ​​ ​​​​ Sum of these 5 numbers = 15*5 = 75

  ​​ ​​​​ Average of 3 of those numbers = 11

  ​​ ​​​​ Sum of these 3 numbers = 11*3 = 33

  ​​ ​​​​ Sum of remaining two numbers = 75-33 = 42

  ​​ ​​​​ Average of remaining two numbers = 42/2 = 21

 

So, the correct answer is B 

Test: Average- 2 - Question 13

The age of father is 5 times that of his son. 3 years ago, the age of father was 8 times that of his son. Find the present age of father.

Detailed Solution for Test: Average- 2 - Question 13

Given:

Present age

Age of father = 5 × Age of Son

3 years ago,

Age of father = 8 × Age of son

Calculation:

Let the age of father and son be F and S.

According to the question,

F = 5S      ----(1)

Again according to the question,

⇒ (F - 3) = 8(S - 3)      ----(2)

After equating the equation (1) and equation (2)

⇒ 5S - 3 = 8S - 24

⇒ -3S = -21

⇒ S = 7 years

From equation (1)

⇒ F = 5 × 7

⇒ F = 35 years

∴ The present age of the father is 35 years.

So, the correct option is A . 

Test: Average- 2 - Question 14

A cricketer has completed 10 innings and his average is 21.5 runs. How many runs must he make in his next innings so as raise his average to 24?

Detailed Solution for Test: Average- 2 - Question 14

Option (a) 49 is correct

Explanation:- 

  total run scored in 10 innings :-

=> 21.5 * 10 = 215

Total run he must score after 11 innings=  24*11 = 264

He must score in 11 th innings:-

( 264- 215) = 49

Test: Average- 2 - Question 15

The ratio of father’s age to the son’s age is 4:1 the product of their ages is 196. What will be the ratio of their ages after 5 years?

Detailed Solution for Test: Average- 2 - Question 15

Let the ages of father and son be 4x and x respectively.

 

Product of ages = 196

4x X x = 196

4x^2 = 196

So, x^2 = 49

Thus x = 7

 

So, father's age and son's age = 28 and 7 respectively.

 

So, ratio after 5 years becomes;

28 + 5 : 7 + 5

= 33 : 12

= 11 : 4

So, the correct answer is C. 

Test: Average- 2 - Question 16

The ratio of the ages of father and the son at present is 6:1. After 5 years the ratio will become 7:2. What is present age of the son?

Detailed Solution for Test: Average- 2 - Question 16

According to the question,

We have the following statements:

The ratio of the ages of father and son at present is 6: 1. After 5 years the ratio will become 7:2

Now, let's take the age of the father to be 6x years and that of his son to be x years.

So, according to the second statement:

Using the cross multiplication method,

2(6x+5) = 7(x+5)

12x+10 = 7x+35

12x-7x = 35-10

5x = 25

x = 25/5

x = 5 years

Hence, the present age of the son is 5 years.

 

So, the correct option is C.

⠀⠀⠀⠀⠀

Test: Average- 2 - Question 17

After 5 years, the age of father will be thrice the age of his son, whereas five years ago he was 7 times as old as his son was. What is the present age of father?

Detailed Solution for Test: Average- 2 - Question 17

After 5 years, father's age = 3 × Son's age
5 years ago, father's age = 7 × Son's age

Calculation:
Let 5 years ago, son's age be s.
5 years ago, Father's age = 7 × s = 7s
After 5 years, son's age = s + 5 + 5 = s + 10
After 5 years, father's age = 7s + 5 + 5 = 7s + 10      ----(1)
After 5 years, father's age = 3 × Son's age = 3 × (s + 10)      ----(2)
Equating equation (1) and (2),
⇒ 7s + 10 = 3s + 30 
⇒ 7s – 3s = 30 – 10
⇒ 4s = 20
⇒ s = 20/4
⇒ s = 5
Present age of father = 7s + 5
⇒ 7 × 5 + 5
⇒ 35 + 5 = 40
∴ The present age of the father is 40 years.

Test: Average- 2 - Question 18

The ratio of the age of Rahul five years before to the age of Shiv 5 years hence is 3 : 5 and the ratio of the present age of Rahul to the present age of Riya is 5 : 4. If the average present age of Shiv and Riya is 18 years, then the present age of Riya is? 

Detailed Solution for Test: Average- 2 - Question 18

Given:

Rahul's age 5 years ago : shiv's age 5 years hence = 3 : 5

Rahul : Riya = 5 : 4

(Shiv + Riya)'s average = 18 years

Calculation:

Let the present ages of Rahul and Riya be 5x and 4x.

Rahul's age 5 years ago = 5x - 5

so, Shiv's age after 5 years = 5/3(5x - 5)

∴ Shiv's present age = 5/3(5x - 5) - 5

A.T.Q

5/3(5x - 5) - 5 + 4x = 18 × 2 = 36

⇒ 25x/3 - 25/3 - 5 + 4x = 36

⇒ 37x/3 = 148/3

⇒ x = 148/37 = 4 years

Riya's present age = 4 × 4 = 16 years

∴ Riya's present age is 16 years.
 

So, the correct answer is E. 

Test: Average- 2 - Question 19

The average age of a board of 10 consultants of a firm is same as it was 2 yrs back on account of the replacement of one of the older consultants by a younger man.​​ Find the difference between the age of the old consultant and the young man.

Detailed Solution for Test: Average- 2 - Question 19

Let the average age of board of consultants before replacement by a old consultant be a years. The sum of the ages of the consultants on the board = 10*a

The average age of the board of consultants 2 years age = a-2

The sum of the ages of the consultants on the board 2 years ago = 10(a-2)​​ 

After the older consultant was replaced with a younger man, the average remains the same as it was 2 yrs ago i.e., 10a hence, the younger man was 20 years younger to the old consultant.​​

 

So, the correct option is B.  

Test: Average- 2 - Question 20

The average age of a group of 10 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?

Detailed Solution for Test: Average- 2 - Question 20
The average age of a group of 10 students = 20 years
Sum of the ages of these 10 students = 10 * 20 = 200 years.
when 2 new students joined the average age is increased by = 2 years
Hence the average age becomes 22 years and total students become 12.
Therefore, the sum of the ages of the 12 students = 12 * 22 = 264 years
So, the difference between the sum of the ages of 12 students and 10 students = 264 - 200 = 64 years.
Sum of the ages of the 2 new students = 64 years.
Average age of the 2 new students = 64/2 
= 32 years.
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