A alone can finish a work in 10 days and B alone can do it in 15 days. If they…
2025
A alone can finish a work in 10 days and B alone can do it in 15 days. If they work together and finish , the out of the total wages of Rs. 75. A will get -
- A.
Rs. 30
- B.
Rs 37.50
- C.
Rs 45
- D.
Rs 50
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Correct answer: C
Solution: Find A's share of Rs.75 when A alone finishes in 10 days and B alone in 15 days.
Step 1: Compute individual work rates. A's rate = 1/10 work per day. B's rate = 1/15 work per day.
Step 2: Find the ratio of work done in the same time: 1/10 : 1/15 = 3 : 2.
Step 3: Split the wages in the ratio 3:2. A's share = 3/(3+2) × 75 = 3/5 × 75 = Rs.45.
Common mistake: Using the time-taken ratio (10:15) directly is wrong because wages depend on amount of work done (rates), not time taken. The correct approach uses the inverse relationship between time and work rate.