A alone can complete a task in 56 days while B alone can complete the same task in 42 days. A and B. A and B took upon the work to complete it together. However, A left 12 days before the scheduled completion of work. Find how many days did B work alone?
Explanation:
Let the work to be done = LCM (56, 42) = 168 units.
∴ Efficiency of A = 168/56 = 3 units/day, and Efficiency of B = 168/42 = 4 units/day
If A and B worked together, the work should have finished in 168/(3 + 4) = 24 days.
However, A and B together work for 12 days after which A leaves and B completes the remaining work.
Let B complete the remaining work in x days.
Work done by A and B in first 12 days = 12 × (3 + 4) = 84 units. ∴ Work remaining for B = 168 - 84 = 84
⇒ Time taken by B to complete 84 units of work = 84/4 = 21 days.
∴ B worked alone for 21 days.
Hence, option (c).
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