A can complete a piece of work in 10 days, B in 15 days, and C in 20 days. A and C worked together for 2 days and then A was replaced by B. In how many days altogether was the work completed? MCQ with Answer and Explanation
A can complete a piece of work in 10 days, B in 15 days, and C in 20 days. A and C worked together for 2 days and then A was replaced by B. In how many days altogether was the work completed?
A. 7 days
B. 9 days
C. 8 days
D. 6 days
Answer: Option C
Solution (By JKSSB Mock Tests)
Total work = LCM(10, 15, 20) = 60 units. Efficiency of A = 6, B = 4, C = 3. A and C work for 2 days: work done = 2 * (6 + 3) = 18 units. Remaining work = 60 - 18 = 42 units. B and C complete remaining work together with efficiency = 4 + 3 = 7 units/day. Time taken for remaining work = 42 / 7 = 6 days. Total time = 2 + 6 = 8 days.
Explanation:
Total work = LCM(8, 12, 6) = 24 units. Efficiency of (A+B) = 3, (B+C) = 2, (A+B+C) = 4. Efficiency of C = (A+B+C) - (A+B) = 4 - 3 = 1. Efficiency of A = (A+B+C) - (B+C) = 4 - 2 = 2. Combined efficiency of A and C = 2 + 1 = 3. Time taken by A and C together = 24 / 3 = 8 days.
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