The ratio of ages of a mother and daughter is 14 ∶ 1 at present. After four years, the ratio of their ages will be 16 ∶ 3. What was the age of mother when the daughter was born?

Explanation:

The ratio of ages of a mother and daughter is 14 ∶ 1 at present.

Let the present age of mother is 14x and that of daughter is x

After 4 years, mother's age = 14x + 4 and daughter's age = x + 4

Therefore by given condition

 \(\frac{14x+4}{x+4}=\frac{16}3\)

42x + 12 = 16x + 64

42x - 16x = 64 - 12

26x = 52

x = 2

Hence mother's present age is 14 × 2 = 28 and daughter's present age is 2

So  the age of mother when the daughter was born = 28 - 2 = 26 (since age of daughter was 0 when she was born)

Option (1) is correct