A, B and C can do a piece of work in 20, 30 and 60 days respectively. If A works everyday and is assisted by B and C together on every third day, then in how many days will the work be completed? MCQ with Answer and Explanation
A, B and C can do a piece of work in 20, 30 and 60 days respectively. If A works everyday and is assisted by B and C together on every third day, then in how many days will the work be completed?
A. 15 days
B. 12 days
C. 20 days
D. 18 days
Answer: Option A
Solution (By JKSSB Mock Tests)
Total work = LCM(20, 30, 60) = 60 units. Efficiency of A = 3, B = 2, C = 1. Day 1: A works = 3 units. Day 2: A works = 3 units. Day 3: A+B+C work = 3 + 2 + 1 = 6 units. Work done in 3 days = 3 + 3 + 6 = 12 units. Number of 3-day cycles to complete 60 units = 60 / 12 = 5 cycles. Total days = 5 * 3 = 15 days.
A and B can complete a piece of work in 18 days and 24 days respectively. They worked together for 6 days and then A left. In how many days will B complete the remaining work?
Explanation:
Total work = LCM(18, 24) = 72 units. Efficiency of A = 4, B = 3. Combined efficiency = 7. In 6 days, work done = 6 * 7 = 42 units. Remaining work = 72 - 42 = 30 units. Time taken by B to finish remaining work = 30 / 3 = 10 days.
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