Present ages of Shreya and Kavita are in the ratio $3 : 4$ . Five years after, the ratio of their ages will be $4 : 5$ . Find their present ages.

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Solution

Given:
Present ages of Shreya and Kavita are in the ratio $3 : 4$
Let the common multiple of the given ratio be $x$ .
Now, Present age of Shreya $= 3 x$
Present age of Kavita $= 4 x$
After five years:
Age of Shreya $= 3 x + 5$
Age of Kavita $= 4 x + 5$
Given condition:
Ratio of the ages after five years $= 4 : 5$
$\Rightarrow \frac{3 x + 5}{4 x + 5} = \frac{4}{5}$
$\Rightarrow (3 x + 5) 5 = 4 (4 x + 5)$
$\Rightarrow 15 x + 25 = 16 x + 20$
$\Rightarrow 25 - 20 = 16 x - 15 x$
$\Rightarrow 5 = x$
Therefore, Present age of Shreya $= 3 x = 3 \times 5 = 15$ years
Present age of Kavita $= 4 x = 4 \times 5 = 20$ years

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