Question

Present ages of Anu and Raj are in the ratio 4: 5. Eight years from now the ratio of their ages will be 5: 6. Find their present ages.

Answer 1

Let the present ages of Anu and Raj be 4x years and 5x years respectively.

After eight years, Anu's age = (4x + 8) years;

After eight years, Raj's age = (5x + 8) years.

Therefore, the ratio of their ages after eight years = `(4x + 8)/(5x + 8)`

This is given to be 5: 6

Therefore,

`(4x + 8)/(5x + 8) = 5/6`

Cross-multiplication gives

6(4x + 8) = 5(5x + 8)

or 24x + 48 = 25x + 40

or 24x + 48 - 40 = 25x

or 24x + 8 = 25x

or 8 = 25x - 24x

or 8 = x

Therefore,
Anu's present age = 4x = 4 × 8 = 32 years.
Raj's present age = 5x = 5 × 8 = 40 years.