Question 108

The ages of Sonal and Nitya are in the ratio of 9 : 5 respectively. After 8 years the ratio of their ages will be 13 : 9. What is the difference in years between their ages ?

Solution

Let Sonal's age = $$9x$$ years

=> Nitya's age = $$5x$$ years

Acc. to ques, => $$\frac{9x + 8}{5x + 8} = \frac{13}{9}$$

=> $$81x + 72 = 65x + 104$$

=> $$16x = 104 - 72 = 32$$

=> $$x = \frac{32}{16} = 2$$

$$\therefore$$ Difference in ages = $$9x - 5x = 4x$$

= $$4 \times 2 = 8$$ years

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