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: Assign algebraic expressions to the current ages. \[A = 4x, \quad B = 5x\]Step 2: Formulate the equation for the ages in 5 years. \[\frac{4x + 5}{5x + 5} = \frac{5}{6}\]Step 3: Solve the equation for \(x\). \[6(4x + 5) = 5(5x + 5)\]\[24x + 30 = 25x + 25\]\[25x - 24x = 30 - 25\]\[x = 5\]Step 4: Determine A's current age. \[A = 4x = 4 \times 5 = 20 \text{ years}\]