A and B together can complete a piece of work in 12 days. They worked together for 4 days and then A left. B finished the remaining work alone in 14 more days. In how many days can A alone complete the work? MCQ with Answer and Explanation
A and B together can complete a piece of work in 12 days. They worked together for 4 days and then A left. B finished the remaining work alone in 14 more days. In how many days can A alone complete the work?
A. 42 days
B. 28 days
C. 35 days
D. 21 days
Answer: Option B
Solution (By JKSSB Mock Tests)
Let combined efficiency of A and B be 1 unit/day, so total work = 12 units. In 4 days, they complete 4 units. Remaining work = 12 - 4 = 8 units. B completes 8 units in 14 days, so B's efficiency = 8 / 14 = 4/7 units/day. Efficiency of A = 1 - 4/7 = 3/7 units/day. Time taken by A alone = 12 / (3/7) = (12 * 7) / 3 = 28 days.
A and B can do a piece of work in 20 days and 12 days respectively. A started the work alone and then after 4 days B joined him till the completion of the work. How long did the work last?
Explanation:
Total work = LCM(20, 12) = 60 units. Efficiency of A = 3, B = 5. In 4 days, A alone completes = 4 * 3 = 12 units. Remaining work = 60 - 12 = 48 units. Combined efficiency of A and B = 3 + 5 = 8. Time taken together for remaining work = 48 / 8 = 6 days. Total duration of work = 4 + 6 = 10 days.
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