The ages of X and Y are in the ratio of 3 : 1. Fifteen years hence, the ratio will be 2 : 1. Their present ages (in year) are

Age Ratio Problem

The ages of X and Y are in the ratio of 3 : 1. Fifteen years hence, the ratio will be 2 : 1. Their present ages (in years) are:

Solution:

Let the present ages of X and Y be 3x and x respectively, according to the given ratio 3:1.

After 15 years, their ages will be:

• X: 3x + 15
• Y: x + 15

According to the problem, the ratio of their ages after 15 years is 2:1. So,

(3x + 15) / (x + 15) = 2 / 1

Cross-multiplying,

3x + 15 = 2(x + 15)

Expanding,

3x + 15 = 2x + 30

Rearranging,

3x - 2x = 30 - 15

Which gives,

x = 15

Therefore, their present ages are:

• X's present age = 3x = 3 × 15 = 45 years
• Y's present age = x = 15 years

Answer:

The present ages of X and Y are 45 years and 15 years respectively.