Question
A can complete a piece of work in 12 days, B in 18 days,
and C in 36 days. They all work together for a few days, after which A leaves. B and C continue working and finish the remaining work in 3 days. How many days did they all work together initially?Solution
Let the total work be 1 unit. A’s efficiency = 1/12, B’s efficiency = 1/18, and C’s efficiency = 1/36. Let them work together for x days. Work done in x days = (1/12 + 1/18 + 1/36) × x = (12/72) × x = x/6. Remaining work = 1 - x/6 = 5x/6 B and C finish the remaining work in 3 days: Remaining work = (1/18 + 1/24) × 3 = (7 × 3)/72 = 21/72 Now, 1 - 5x/6 = 21/72. 5x/6 = 1 - 21/72 = 51/72 = 17/24 x = 17/20 = 0.85 days. Final Answer: (b) 0.85 days
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