Question

The ages of Sonu and Monu 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 Sonu and Monu = 7 : 5

Let age of Sonu = 7x years

and age of Monu = 5x years

10 years hence,

the age of Sonu = 7x + 10 years

and age of Monu = 5x + 10 years

According to the condition :

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

By cross multiplication,

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

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

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

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

$\therefore$ Sonu's present age $=7x=7\times 5=35$ years and Monu's present age $=5x=5\times 5=25$ years

Check : 10 years hence, their ages will be

Sonu's = 35 + 10 = 45 years

Monu's = 25 + 10 = 35 years

$\therefore$ Ratio 45 : 35 = 9 : 7 (Dividing by 5)

Which is given. Therefore our answer is correct.