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

Let Raju's cousin's present age be x years.

Therefore Raju 's present age = x – 19

After 5 years,

Raju's cousin's age = x + 5

Raju's age = (x – 19) + 5

The ratio between Raju and his cousin = 2 : 3

According to the question,

upon cross – multiplying,

⇒ 3 { (x – 19) + 5} = 2 (x – 5)

⇒ 3(x – 14) = 2(x + 5)

⇒ 3x – 42 = 2x + 10

⇒ 3x – 2x = 10 + 42

⇒ x = 52

Therefore,

Raja's cousins age = 52yrs

Raja's age = x – 19 = 33yrs