Question

Age of A : Age of B is 3 : 2. Ten years hence, the sum of their ages will be 80. What are their present ages?

• A. 36, 24
• B. 42, 28
• C. 27, 18
• D. 45, 30

Answer 1

Answer:

A. 36, 24

1. Define the variables:

• Let A's present age be 3x.

• Let B's present age be 2x.

2. Set up the equation for their ages ten years hence:

• A's age after 10 years: 3x + 10

• B's age after 10 years: 2x + 10

• The sum of their ages after 10 years is 80: (3x + 10) + (2x + 10) = 80

3. Solve the equation:

• 5x + 20 = 80

• 5x = 80 - 20

• 5x = 60

• x = 60 / 5

• x = 12

4. Calculate their present ages:

• A's present age: 3x = 3 * 12 = 36 years

• B's present age: 2x = 2 * 12 = 24 years

Therefore, A's present age is 36 years, and B's present age is 24 years.