The ages of Hari and Harry are in the ratio 5:7. Four years from now, the ratio of their ages will be 3:4. Find their present ages.

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Solution

Let the ages of Hari and Harry be 5x years and 7x years.

According to question,
$\frac{5 x + 4}{7 x + 4} = \frac{3}{4}$
$\Rightarrow 4 (5 x + 4) = 3 (7 x + 4) \Rightarrow 20 x + 16 = 21 x + 12$
$\Rightarrow 20 x - 21 x = 12 - 16 \Rightarrow - x = - 4$
$\Rightarrow x = 4$
Hence, the age of Hari = 5x = 5 $\times$ 4 = 20 years
And the age of Harry = 7x = 7 $\times$ 4 = 28 years

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