Question

The ratio of the present ages of A and B is 4:5. After 5 years, the ratio becomes 5:6. What is A's present age?

• A. 20 years
• B. 25 years
• C. 30 years
• D. 35 years

Hint:

Translate ratio problems into algebraic equations and solve systematically.

Answer 1

The Correct Option is A

Step 1: Let the present ages be \[ A = 4x, \quad B = 5x \] Step 2: After 5 years, the ratio is \[ \frac{4x + 5}{5x + 5} = \frac{5}{6} \] Step 3: Cross-multiply and solve for \(x\) \[ 6(4x + 5) = 5(5x + 5) \] \[ 24x + 30 = 25x + 25 \] \[ 25x - 24x = 30 - 25 \] \[ x = 5 \] Step 4: Calculate A's present age \[ A = 4x = 4 \times 5 = 20 \text{ years} \]