Problems on Ages Quiz Set 014

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Question 1

The sum of ages of two friends is 20, whereas the product of their ages is 91. What is the sum of squares of their ages?

 A

218 years.

 B

219 years.

 C

217 years.

 D

220 years.

Soln.
Ans: a

Let the ages be x and y. We are given x + y = 20, and xy = 91. Substituting in the identity $x^2 + y^2 = (x + y)^2 - 2 × xy$, we get $x^2 + y^2 = 20^2 - 2 × 91$ = 218.


Question 2

The sum of reciprocals of my ages 6 years back and 6 years later is ${16/247}$. What is my present age?

 A

32 years.

 B

33 years.

 C

31 years.

 D

34 years.

Soln.
Ans: a

Let the present age be x. Then $1/{x + 6} + 1/{x - 6}$ = ${16/247}$. At this stage a better option is that you try putting the given answers into this expression one by one. The other option is to simplify this expression into a quadratic equation ${2x}/{x^2 - 36}$ = ${16/247}$. This can now be solved to give x = 32 years.


Question 3

The ages of two friends are 4 and 25 years respectively. They are looking for a special third friend whose age is in-between their ages. What should be the age of the third friend if the ages of all three have to be in a GP(geometric progression)?

 A

10 years.

 B

11 years.

 C

9 years.

 D

12 years.

Soln.
Ans: a

If the age of the third friend is x. Then for a GP, x = $√(4 × 25)$ = 10 years.


Question 4

The ratio of present ages of two monuments A and B is $1{9/11}$. If the difference of their ages is 117, then what is the age of B?

 A

143 years.

 B

132 years.

 C

121 years.

 D

154 years.

Soln.
Ans: a

The ratio of ages of A and B is given as ${20/11}$, which is same as: $1{9/11}$. So we can write the present ages of A and B, respectively, as 20r and 11r years. The difference is $20r - 11r = 117$ which gives r = 13. The age of B, therefore, is 11r = 11 × 13 = 143 years.


Question 5

When the daughter was born, the age of her mother was same as the daughter's age today. What was the age of the daughter 5 years back, if the age of the mother today is 44 years?

 A

17 years.

 B

18 years.

 C

16 years.

 D

19 years.

Soln.
Ans: a

Clearly, the age of the mother is twice her daughter's present age. So the daughter's age today is 44/2 = 22 years. And, 5 years back the age of the daughter was 22 - 5 = 17 years.


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This Blog Post/Article "Problems on Ages Quiz Set 014" 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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