Four years ago, the ratio of the ages of Aarav and Rohan was 7:3. Six years hence, Aarav’s age will be 50% more than Rohan’s age at that time. If Mehul’s present age is 60% more than Rohan’s present age, find Mehul’s present age.

ATQ, Four years ago, the ratio of ages of Aarav and Rohan was 7:3. Let Aarav’s age four years ago = 7x years. Let Rohan’s age four years ago = 3x years. Present age of Aarav = 7x + 4. Present age of Rohan = 3x + 4. Six years hence: Aarav’s age = 7x + 4 + 6 = 7x + 10. Rohan’s age = 3x + 4 + 6 = 3x + 10. Aarav’s age will be 50% more than Rohan’s age. So, Aarav’s age = 150% of Rohan’s age = 3/2 of Rohan’s age. 7x + 10 = 3/2 × (3x + 10) Cross multiply: 2(7x + 10) = 3(3x + 10) 14x + 20 = 9x + 30 14x − 9x = 30 − 20 5x = 10 x = 10/5 x = 2 Rohan’s present age = 3x + 4 = 3 × 2 + 4 = 10 years. Mehul’s present age is 60% more than Rohan’s present age. 60% more means 160% of Rohan’s age. Mehul’s present age = 160/100 × 10 = 16 years.