Question

The ages of A and B are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.

Answer 1

Ratio in the present ages of A and B = 7 : 5

Let age of A = 7x years

Let age of B = 5x years

10 years hence,

Then age of A = 7x + 10 years

and age of B = 5x + 10 years

According to the condition,

$\frac{7x+10}{5x+10}=\frac{9}{7}$

By crossing multiplication

7(7x + 10) = 9(5x + 10)

$\Rightarrow 49x+70=45x+90$

$\Rightarrow 49x-45x=90-70\Rightarrow 4x=20$

$\Rightarrow x=\frac{20}{4}=5$

$\therefore$ Present age of A = 7x = $7\times 5=35years$

and present age of B = 5x = $5\times 5$ = 25 years