Raju is 19 years younger than his cousin. After 5 years, their ages will be in the ratio 2 : 3. Find their present ages.

Given:

Raju is 19 years younger than his cousin.

After 5 years, their ages will be in the ratio 2 : 3.

To do: Here we have to find the present ages of Raju and his cousin.

Solution:

Let the present age of Raju = $x$

So,

Present age of Raju's cousin = $x\ +\ 19$

Ages after 5 years:

Age of Raju = $x\ +\ 5$

Age of Raju's cousin = $x\ +\ 19\ +\  5\ =\ x\ +\ 24$

The ratio of their ages = 2 : 3

Thus, we have

$\frac{x\ +\ 5}{x\ +\ 24}\ =\ \frac{2}{3}$

After cross multiplication, we get:

$3(x\ +\ 5)\ =\ 2(24\ +\ x)$

$3x\ +\ 15\ =\ 48\ +\ 2x$

$3x\ -\ 2x\ =\ 48\ -\ 15$

$x\ =\ 33$

So,

Present age of Raju = $x$ = 33 years

Present age of Raju's cousin = $x\ +\ 19$ = 33 $+$ 19 = 52 years

Therefore, the age of Raju is 33 years and the age of his cousin is 52 years.

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Updated on: 10-Oct-2022

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