## Problem on Ages Questions and Answers Part-1

1. The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
a) 7 : 3
b) 5 : 2
c) 13 : 4
d) 9 : 2

Explanation: Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⇒ 3x + 20 = 2x + 40
⇒ x = 20
∴ Required ratio
= (3x + 10) : (x + 10)
= 70 : 30
= 7 : 3

2. The ages of Shakti and Kanti are in the ratio of 8 : 7 respectively. After 10 years, the ratio of their ages will be 13 : 12. What is the difference between their ages ?
a) 4 Years
b) 6 Years
c) 2 Years
d) 8 Years

Explanation: Let Shakti's age be 8$$x$$ years,
Then Kanti's age = 7$$x$$ years
\eqalign{ & \therefore \frac{{8x + 10}}{{7x + 10}} = \frac{{13}}{{12}} \cr & \Rightarrow 12\left( {8x + 10} \right) = 13\left( {7x + 10} \right) \cr & \Rightarrow 96x + 120 = 91x + 130 \cr & \Rightarrow 5x = 10 \cr & \Rightarrow x = 2 \cr}
Difference between their ages
\eqalign{ & = \left( {8x - 7x} \right) \cr & = {\text{ }}x\,{\text{years}} \cr & {\text{ = 2}}\,{\text{years}} \cr}

3. At present Suresh's age is twice the age of his daughter. After 6 year from now, the ratio of the ages of Suresh and his daughter will be 23 : 13. What is the present age of Suresh ?
a) 36 years
b) 40 years
c) 46 years
d) Cannot be determined

Explanation: Let daughter's age be x years.
Suresh's age = 2x years
\eqalign{ & \therefore \frac{{2x + 6}}{{x + 6}} = \frac{{23}}{{13}} \cr & 13\left( {2x + 6} \right) = 23\left( {x + 6} \right) \cr & 26x + 78 = 23x + 138 \cr & 3x = 60 \cr & x = 20 \cr}
Present age of Suresh = 2x years
\eqalign{ & {\text{ = }}\left( {2 \times 20} \right){\text{ years }} \cr & {\text{ = 40 years}} \cr}

4. A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
a) 32 years
b) 36 years
c) 40 years
d) 48 years

Explanation:
\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{mother's}}\,{\text{present}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}{\text{.}} \cr & {\text{Then,}}\,{\text{the}}\,{\text{person's}}\,{\text{present}}\,{\text{age}} \cr & = {\frac{2}{5}x} \,\,{\text{years}} \cr & {\frac{2}{5}x + 8} = \frac{1}{2}\left( {x + 8} \right) \cr & 2\left( {2x + 40} \right) = 5\left( {x + 8} \right) \cr & x = 40 \cr}

5. 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

Explanation: 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.

6. The present age of Mr. Sanyal is three times the age of his son. Six years hence , the ratio of their ages will be 5 : 2. What is the present age of Mr. Sanyal ?
a) 60 years
b) 54 years
c) 48 years
d) 50 years

Explanation: Let the son's age be $$x$$ years ,
Then Mr. Sanyal's age = 3$$x$$ years
\eqalign{ & \therefore \frac{{3x + 6}}{{x + 6}} = \frac{5}{2} \cr & \Rightarrow 2\left( {3x + 6} \right) = 5\left( {x + 6} \right) \cr & \Rightarrow 6x + 12 = 5x + 30 \cr & \Rightarrow x = 18 \cr}
∴ Present age of Mr. Sanyal = 3x years
= (3 × 18) years
= 54 years

7. Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
a) 6 years
b) 2 years
c) 8 years
d) 4 years

Explanation: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
∴ Required difference = (42 - 36) years = 6 years.

8. The ages of Nitish and Vinnee are in the ratio 6 : 5 respectively. After 9 years the ratio of their ages will be 9 : 8. What is the difference in their ages now ?
a) 9 Years
b) 7 Years
c) 3 Years
d) 5 Years

Explanation: Let Nishi's age be 6x years,
Then Vinnee's age = 5x years
\eqalign{ & \therefore \frac{{6x + 9}}{{5x + 9}} = \frac{9}{8} \cr & \Rightarrow 8\left( {6x + 9} \right) = 9\left( {5x + 9} \right) \cr & \Rightarrow 48x - 45x = 81 - 72 \cr & \Rightarrow 3x = 9 \cr & \Rightarrow x = 3 \cr & {\text{Difference in their ages}} \cr & {\text{ = }}\left( {6x - 5x} \right) \cr & = x {\text{ years}} \cr & = {\text{3 years}} \cr}

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

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

10. The age of a mother today is thrice that of her daughter. After 12 years , the age of the mother will be twice that of her daughter. The present age of the daughter is = ?
a) 12 Years
b) 14 Years
c) 18 Years
d) 16 Years