A alone can finish a work in 10 days and B alone can do it in 15 days. If they…
2026
A alone can finish a work in 10 days and B alone can do it in 15 days. If they work together to complete the work, out of the total wages of Rs. 75, A will get?
- A.
Rs. 30
- B.
Rs 37.50
- C.
Rs 45
- D.
Rs 50
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept: When two or more people work together and are paid wages for a job, the wages are divided in the ratio of the WORK DONE by each person — that is, in the ratio of their efficiencies (work rates) — not in the ratio of the time each person takes. Since efficiency is inversely proportional to the time taken to finish the work alone, a faster worker (less time) gets a larger share of the wages.
Application:
Time taken by A : Time taken by B = 10 : 15 = 2 : 3.
Efficiency is inversely proportional to time, so Efficiency of A : Efficiency of B = 1/2 : 1/3 = 3 : 2.
Wages are divided in the same ratio as efficiency, so A : B = 3 : 2, giving a total of 3 + 2 = 5 parts.
A's share = Rs. 75 × 3/5 = Rs. 45.
Cross-check: B's share = Rs. 75 × 2/5 = Rs. 30. A's share + B's share = Rs. 45 + Rs. 30 = Rs. 75, which matches the total wages, and the ratio 45 : 30 simplifies back to 3 : 2 — confirming the split.