Problems On Ages - Aptitude MCQ Questions and Solutions with Explanations

1

Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?

A) 2 times B) $$2\frac{1}{2}\,{\text{times}}$$ C) $$2\frac{3}{4}\,{\text{times}}$$ D) 3 times

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Let}}\,{\text{Ronit's}}\,{\text{present}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}. \cr & {\text{Then,}}\,{\text{father's}}\,{\text{present}}\,{\text{age}}\, \cr & = \left( {x + 3x} \right)\,{\text{years}} \cr & = 4x\,{\text{years}} \cr & \therefore \left( {4x + 8} \right) = \frac{5}{2}\left( {x + 8} \right) \cr & \Rightarrow 8x + 16 = 5x + 40 \cr & \Rightarrow 3x = 24 \cr & \Rightarrow x = 8 \cr & {\text{Hence,}}\,{\text{required}}\,{\text{times}} \cr & = \frac{{ {4x + 16} }}{{ {x + 16} }} \cr & = \frac{{48}}{{24}} \cr & = 2 \cr} $$

2

The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

A) 4 years B) 8 years C) 10 years D) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⇒ 5x = 20
⇒ x = 4.
∴ Age of the youngest child = x = 4 years.

3

A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:

A) 14 years B) 19 years C) 33 years D) 38 years

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the son's present age be x years. Then, (38 - x) = x
⇒ 2x = 38.
⇒ x = 19.
∴ Son's age 5 years back (19 - 5) = 14 years.

4

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?

A) 7 B) 8 C) 9 D) 10 E) 11

Discuss

Answer & Solution

Answer: Option D

Solution:

Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.

∴ (2x + 2) + 2x + x = 27
⇒ 5x = 25
⇒ x = 5.
Hence, B's age = 2x = 10 years.

5

Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

A) 24 B) 27 C) 40 D) Cannot be determined E) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{present}}\,{\text{ages}}\,{\text{of}}\,{\text{Sameer}}\,{\text{and}}\,{\text{Anand}}\,{\text{be}}\, \cr & 5x\,{\text{years}}\,{\text{and}}\,4x\,{\text{years}}\,{\text{respectively}} \cr & {\text{Then,}}\,\frac{{5x + 3}}{{4x + 3}} = \frac{{11}}{9} \cr & \Rightarrow 9\left( {5x + 3} \right) = 11\left( {4x + 3} \right) \cr & \Rightarrow 45x + 27 = 44x + 33 \cr & \Rightarrow 45x - 44x = 33 - 27 \cr & \Rightarrow x = 6 \cr & \therefore {\text{Anand's}}\,{\text{present}}\,{\text{age}} \cr & = 4x \cr & = 24\,{\text{years}}\, \cr} $$

6

A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

A) 14 years B) 18 years C) 20 years D) 22 years E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the son's present age be x years. Then, man's present age = (x + 24) years.
∴ (x + 24) + 2 = 2(x + 2)
⇒ x + 26 = 2x + 4
⇒ x = 22

7

Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

A) 16 years B) 18 years C) 20 years D) Cannot be determined E) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{ages}}\,{\text{of}}\,{\text{Kunal}}\,{\text{and}}\,{\text{Sagar}}\,{\text{6}}\,{\text{years}}\,{\text{ago}}\, \cr & {\text{be}}\,6x\,{\text{and}}\,5x\,{\text{years}}\,{\text{respectively}} \cr & {\text{Then,}}\,\frac{{\left( {6x + 6} \right) + 4}}{{\left( {5x + 6} \right) + 4}} = \frac{{11}}{{10}} \cr & \Rightarrow 10\left( {6x + 10} \right) = 11\left( {5x + 10} \right) \cr & \Rightarrow 5x = 10 \cr & \Rightarrow x = 2 \cr & \therefore {\text{Sagar's}}\,{\text{present}}\,{\text{age}} \cr & = \left( {5x + 6} \right)\,{\text{years}} \cr & = 16\,{\text{years}}\, \cr} $$

8

The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

A) 12 years B) 14 years C) 18 years D) 20 years E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the present ages of son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
⇒ 54 - x = 5x - 30
⇒ 6x = 84
⇒ x = 14
∴ Son's age after 6 years = (x + 6) = 20 years.

9

At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?

A) 12 years B) 15 years C) 19 and half D) 21 years E) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
4x + 6 = 26
⇒ 4x = 20
⇒ x = 5
∴ Deepak's age = 3x = 15 years.

10

Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

A) 16 years B) 18 years C) 28 years D) 24.5 years E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & {\text{Let}}\,{\text{Rahul's}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}. \cr & {\text{Then,}}\,{\text{Sachin's}}\,{\text{age}} = \left( {x - 7} \right)\,{\text{years}}. \cr & \therefore \frac{{x - 7}}{x} = \frac{7}{9} \cr & \Rightarrow 9x - 63 = 7x \cr & \Rightarrow 2x = 63 \cr & \Rightarrow x = 31.5 \cr & {\text{Hence,}}\,{\text{Sachin's}}\,{\text{age}} \cr & = \left( {x - 7} \right)\,{\text{years}} \cr & = 24.5\,{\text{years}} \cr} $$