Question

The ratio of the ages of husband, wife and their son is 10 : 9 : 3. In order to calculate the age of the son, which of the following piece of information would be additionally required which would also be sufficient
1. 6 years ago, son's age was 20% of his mother's age at that time.
2. After 10 years, the sum of the ages of all three will be 30 more than the sum of their present ages.
3. Age difference between father and son is more than age difference between mother and son.
4. The sum of the ages of all three is a perfect multiple of 11.

Answer 1

Correct Answer - Option 1 : 6 years ago, son's age was 20% of his mother's age at that time.

Given:

The ratio of ages of husband, wife, and son = 10 : 9 : 3

Calculation:

Let the age of Husband, wife and son be 10x, 9x and 3x

Option 1:

6 years ago age of wife was 9x - 6 and son was 3x - 6

According to option 1

3x - 6 = 20% of (9x - 6)

⇒ 3x - 6 = (9x - 6)/5

⇒ 15x - 30 = 9x - 6

⇒ 6x = 24

⇒ x = 4

Son's age = 3 × 4 = 12

As Option (1) is correct so we do not need to check other options in the actual exam

Option 2:

After 10 years their ages will be 10x + 10, 9x + 10, and 3x + 10

Sum of their age after 10 years = 10x + 10 + 9x + 10 + 3x + 10 = 22x + 30

And from the option we we get the same data i.e. 10x + 9x + 3x + 30 = 22x + 30

These equations are same hence we cannot find the age of son

Option 3:

It is evident that the difference of age of father and son (i.e. 10x - 3x = 7x) is greater than the difference in the age of mother and son (i.e. 9x - 3x = 6x)

Hence option 3 does not provide any extra information to find the age of the son.

Option 4:

Sum of their ages = 10x + 9x + 3x = 22x which is a multiple of 11.

But here x can take multiple values for example 2, 3, 4, and so on

Hence option 4 also does not provide any extra information to find the age of the son.

∴ Option 1 is correct