Question

One year ago, the ratio of Amit’s and Arun’s ages was $$6 : 7$$ respectively. Four years hence, their ages will be in the ratio $$7 : 8$$. How old is Amit?

Answer 1

Let the ages of Amit and Arun one year ago be $$6x$$ and $$7x$$ years.

Their present ages are $$(6x + 1)$$ and $$(7x + 1)$$ years.

Four years hence, their ages will be:

Amit: $$(6x + 1 + 4) = (6x + 5)$$

Arun: $$(7x + 1 + 4) = (7x + 5)$$

Given ratio 4 years hence: $$\frac{6x + 5}{7x + 5} = \frac{7}{8}$$ 

Cross-multiply: $$8(6x + 5) = 7(7x + 5)$$

$$48x + 40 = 49x + 35$$

$$49x - 48x = 40 - 35$$

$$\implies x = 5$$ 

Amit's present age = $$6x + 1 = 6(5) + 1 = 31\text{ years}$$.