Question

The present ages of Kapil and Karuna are in the ratio 2 : 3. Six years later, the ratio will be 5 : 7. Find their present ages.

Answer 1

Let the present age of Kapil = x years and that of Karuna = y years
After 6 years,
Kapil's age = (x + 6) years
Kaurna's age = (y + 6) years
According to given information, we have
`x/y = (2)/(3)`
⇒ 3x = 2y
⇒ 3x - 2y = 0       ....(i)
And,
`(x + 6)/(y + 6) = (5)/(7)`
⇒ 7x + 42 = 5y + 30
⇒ 7x - 5y = -12   ....(ii)
Multiplying eqn. (i) by 5 and eqn. (ii) by 2, we get
15x - 10y = 0    ....(iii)
14x - 10y = -24 ....(iv)
Subtracting eqn. (iv) from eqn. (iii), we get
x = 24
⇒ 3(24) - 2y = 0
⇒ 72 - 2y = 0
⇒ 2y = 72
⇒ y = 36
Thus, the present age og Kapil is 24 years and that of Karuna is 36 years.