Question

The ratio of the ages of A and B is 3:4. Five years hence, the ratio will be 4:5. What is the present age of A?

• A. 15 years
• B. 20 years
• C. 25 years
• D. 30 years

Hint:

Set up ratios as equations and solve for the variable to find ages.

Answer 1

The Correct Option is A

- Step 1: Let A's age = $3x$, B's age = $4x$.
- Step 2: Five years hence: A's age = $3x + 5$, B's age = $4x + 5$. Ratio = $\frac{3x + 5}{4x + 5} = \frac{4}{5}$.
- Step 3: Solve: $5(3x + 5) = 4(4x + 5) \implies 15x + 25 = 16x + 20 \implies x = 5$.
- Step 4: A's age = $3x = 3 \times 5 = 15$ years.
- Step 5: Verify: B's age = $4 \times 5 = 20$. After 5 years: A = 20, B = 25, ratio = $\frac{20}{25} = \frac{4}{5}$, correct.
- Step 6: Option (1) is 15 years, correct.