Problems on Ages Quiz Set 016

Question 1

The sum of ages of two friends is 13, whereas the product of their ages is 42. What is the sum of squares of their ages?

A

85 years.

B

86 years.

C

84 years.

D

87 years.

Soln.
Ans: a

Let the ages be x and y. We are given x + y = 13, and xy = 42. Substituting in the identity \$x^2 + y^2 = (x + y)^2 - 2 × xy\$, we get \$x^2 + y^2 = 13^2 - 2 × 42\$ = 85.

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 ratio of present ages of two monuments A and B is \$2{1/9}\$. If the difference of their ages is 90, then what is the age of B?

A

81 years.

B

72 years.

C

63 years.

D

90 years.

Soln.
Ans: a

The ratio of ages of A and B is given as \${19/9}\$, which is same as: \$2{1/9}\$. So we can write the present ages of A and B, respectively, as 19r and 9r years. The difference is \$19r - 9r = 90\$ which gives r = 9. The age of B, therefore, is 9r = 9 × 9 = 81 years.

Question 4

The age of father tortoise is 14 times the age of his son. After 50 years his age will be 4 times the age of his son. What would be the ratio of their ages 180 years from today?

A

2.

B

5.

C

3.

D

4.

Soln.
Ans: a

If the age of the son today is s, the age of the father is 14s. After 50 years, we have 14s + 50 = 4(s + 50). Solving for s, we get s = 15 years. The ratio of their ages after 180 years = \${14s + 180}/{s + 180}\$. Substituting s and simplifying we get the ratio as 2.

Question 5

After 5 years from today the ages of three friends will be in an AP(arithmetic progression), and their sum would be 114. What is the age of the middle friend today?

A

33 years.

B

34 years.

C

32 years.

D

35 years.

Soln.
Ans: a

Let the ages after 5 years be a - d, a and a + d. The sum is given to us. So (a - d) + a + (a + d) = 3a = 114. We get a = 114/3 = 38. So, the age of the middle friend today is a - 5 = 33 years. This Blog Post/Article "Problems on Ages Quiz Set 016" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.