- A man is now 3 times as old as his son.

- In ten (10) years time, the sum of their ages will be 76.

- The age of the man at the time of his child’s birth can be figure out in this way.

Note: This question was asked in Competitive Examination (CSS) – 2021 General Science & Ability under Section – B [Q. 6. (a)].

## Explanation

Following ages are need to discuss here.

- Age of man.
- Age of child.

Following things are given.

- Current age of man and child.
- Age of man and child after 10 years.

__Case I__

Let suppose

- Current age of man = y
- Current age of his child = z

According to the first given condition.

A man is now 3 times as old as his son.

The current age of son is z so age of his father will be 3z as given in condition.

y = 3z ________ (i)

__Case II__

According to second given condition.

In ten (10) years time, the sum of their ages will be 76.

After 10 years, age of child becomes z + 10 and age of his father becomes y + 10.

y + 10 + z + 10 = 76 ________ (ii)

By putting the value of first equation (y = 3z) in second equation we can easily figure out the age of the man at the time of his child’s birth.

## To Find

The age of the man at the time of his child’s birth = ?

## Solution

__Method I__

Let suppose

- Current age of man = y
- Current age of his child = z

According to the first given condition.

y = 3z ________ (i)

According to second given condition.

y + 10 + z + 10 = 76 ________ (ii)

Putting value of equation (i) into equation (ii), we have

3z + 10 + z + 10 = 76

4z + 20 = 76

4z = 76 – 20

4z = 56

z = 56/4

z = 14 years

Current age of man = 3z

Current age of man = 3 x 14

Current age of man = 42 years

The age of the man at the time of his child’s birth = (42 – 14) years

**The age of the man at the time of his child’s birth = 28 years answer**

### __Method II__

Let suppose

- Current age of child = z
- Current age of his father = 3z

After 10 years

- Age of child = z + 10
- Age of his father = 3z + 10

Sum of their ages become 76.

z + 10 + 3z + 10 = 76

4z + 20 = 76

4z = 76 – 20

4z = 56

z = 56/4

z = 14 years

Current age of his father = 3z

Current age of his father = 3 x 14

Current age of his father = 42 years

The age of the man at the time of his child’s birth = (42 – 14) years

**The age of the man at the time of his child’s birth = 28 years answer**

## Conclusion

A man is now 3 times as old as his son. In ten (10) years time, the sum of their ages will be 76. The age of the man at the time of his child’s birth was 28 years.