The ages of Mohan and Sohan are in the ratio $5 : 7$ . If Mohan was $9$ years older and Sohan $9$ years younger, then their ages would be in the ratio $2 : 1$ . Find their present ages.

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Solution

Let $x$ be the present age of mohan and sohan then present age of mohan is $5 x$ and that of sohan is $7 x .$
According to 1st condition -
Mohan's age will be $5 x + 9$
Sohan's age will be $7 x - 9$
$\Rightarrow 5 x + 9 : 7 x - 9 = 2 : 1$
$\Rightarrow \frac{5 x + 9}{7 x - 9} = \frac{2}{1}$
$\Rightarrow (5 x + 9) = 2 (7 x - 9)$
$\Rightarrow 5 x + 9 = 14 x - 18$
$\Rightarrow 5 x - 14 x = - 18 - 9$
$\Rightarrow - 9 x = - 27$
$\Rightarrow x = 3$
Present age of mohan is $5 x = 5 \times 3 = 15$
Present age of sohan is $7 x = 7 \times 3 = 21$
hence, solved.

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The ages of Mohan and Sohan are in the ratio 5:7. If Mohan was 9 years older and Sohan 9 years younger, then their ages would be in the ratio 2:1. Find their present ages.

The ages of Mohan and Sohan are in the ratio $5 : 7$ . If Mohan was $9$ years older and Sohan $9$ years younger, then their ages would be in the ratio $2 : 1$ . Find their present ages.