The present ages of A and B are 42 and 36 years, respectively. After K years,…
2025
The present ages of A and B are 42 and 36 years, respectively. After K years, the ratio of ages of B to A will be 15:17. What is value of K?
- A.
9 years
- B.
12 years
- C.
5 years
- D.
3 years
Attempted by 30 students.
Show answer & explanation
Correct answer: A
Solution:
Let K be the number of years after which the ratio of B to A is 15:17.
Ages after K years: A = 42 + K, B = 36 + K.
Set up the ratio: (36 + K) / (42 + K) = 15 / 17.
Cross-multiply and solve: 17(36 + K) = 15(42 + K) → 612 + 17K = 630 + 15K → 2K = 18 → K = 9.
Verification: After 9 years B = 36 + 9 = 45 and A = 42 + 9 = 51, and 45:51 simplifies to 15:17, so K = 9 is correct.
Answer: 9 years