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**