Question

The ratio of ages of A and B is 3:4. After 6 years, their ages will be in the ratio 4:5. What is A's current age? 
 

• A. 18
• B. 24
• C. 30
• D. 36

Hint:

When given ratios now and in the future, represent present ages with variables, add the time to both, and solve.

Answer 1

The Correct Option is A

- Step 1: Represent present ages - Let A's current age = $3x$ and B's current age = $4x$. 
- Step 2: After 6 years - A's age = $3x + 6$, B's age = $4x + 6$. 
- Step 3: Given ratio after 6 years - \[ \frac{3x + 6}{4x + 6} = \frac{4}{5} \] 
- Step 4: Cross-multiply - \[ 5(3x + 6) = 4(4x + 6) \] \[ 15x + 30 = 16x + 24 \] \[ x = 6 \] 
- Step 5: Find A's current age - $3x = 18$. 
- Step 6: Conclusion - A's current age is 18 years, matching option (1).