The sum of the ages of X, Y, and Z is 120 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Y?

Question: The sum of the ages of X, Y, and Z is 120 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Y?

Solution:
Let, X, Y, and Z's ages 10 years ago be 2a, 3a, and 4a years respectively

ATQ,
(2a + 10) + (3a + 10) + (4a + 10) = 120
⇒ 9a + 30 = 120
⇒ 9a = 90
∴ a = 10

So, the age of Y = 3 × 10 + 10 = 40 years.