The ratio of the present ages of Anjali and Ashu is $2 : 3$ , five years hence, the ratio of there ages will be $3 : 4$ . Find their present ages.

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Solution

Ratio of the present ages of Anjali and Ashu is $= 2 : 3$
Let age of Anjali $= 2 x$
and age of Ashu $= 3 x$
$5$ years hence,
Age of Anjali $= 2 x + 5$
and age of Ashu $= 3 x + 5$
According to question,
Ratio of Anjali and Ashu after five years $= 3 : 4$
$\Rightarrow \frac{2 x + 5}{3 x + 5} = \frac{3}{4}$
$\Rightarrow 4 (2 x + 5) = 3 (3 x + 5)$
$\Rightarrow 8 x + 20 = 9 x + 15$
$\Rightarrow 9 x - 8 x = 20 - 15$
$\Rightarrow x = 5$
Present ages of Anjali $= 2 x = 2 \times 5 = 10 y e a r s$
and age of Ashu $= 3 x = 3 \times 5 = 15 y e a r s$

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