Problems on Ages Quiz Set 002

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Question 1

The ages of two friends are in the ratio 3:5. What is the age of the younger friend if the sum of their ages is 24 years?

 A

9 years.

 B

10 years.

 C

8 years.

 D

11 years.

Soln.
Ans: a

Let the ages be 3r and 5r. The younger is 3r. We have been given their sum. So (3 + 5)r = 24. Solving, we get r = 3. The younger is 3 × 3 = 9 years.


Question 2

The ages of three friends are in the ratio 19:2:3. What is the age of the youngest friend if the sum of their ages 5 years back was 129 years?

 A

12 years.

 B

13 years.

 C

11 years.

 D

14 years.

Soln.
Ans: a

Let the ages of three friends be 19r, 2r and 3r. The youngest of these is 2r. We have been given their sum 5 years back. So (19 + 2 + 3)r - (3 × 5) = 129. Solving, we get r = 6. The youngest is 2 × 6 = 12 years.


Question 3

The sum of the ages of 12 calves of a whale born at a gap of 8 years is 672. What is the age of the youngest calf?

 A

12 years.

 B

13 years.

 C

11 years.

 D

14 years.

Soln.
Ans: a

The ages of the calves are in an AP with d = 8, n = 12, and sum S = 672. We have to find the first term a. We know S = ${n/2} × (2a + (n-1)d)$ Putting the values 672 = ${12/2} × (2a + (12-1)×8)$. Solving, get a = 12 years.


Question 4

The sum of the ages of 14 calves of a whale born at a gap of 8 years is 924. What is the age of the youngest calf?

 A

14 years.

 B

15 years.

 C

13 years.

 D

16 years.

Soln.
Ans: a

The ages of the calves are in an AP with d = 8, n = 14, and sum S = 924. We have to find the first term a. We know S = ${n/2} × (2a + (n-1)d)$ Putting the values 924 = ${14/2} × (2a + (14-1)×8)$. Solving, get a = 14 years.


Question 5

The sum of ages of two friends is 15, whereas the product of their ages is 54. What is the sum of squares of their ages?

 A

117 years.

 B

118 years.

 C

116 years.

 D

119 years.

Soln.
Ans: a

Let the ages be x and y. We are given x + y = 15, and xy = 54. Substituting in the identity $x^2 + y^2 = (x + y)^2 - 2 × xy$, we get $x^2 + y^2 = 15^2 - 2 × 54$ = 117.


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This Blog Post/Article "Problems on Ages Quiz Set 002" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer


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