A and B together can complete a piece of work in 45 days, while A alone can complete it in 60 days. So, B alone can complete the work in how many days?
Explanation:
(A+B)’s 1 day’s work = 1/45 and A’s day’s work = 1/60
∴ B’s 1 day’s work = 1/45 - 1/60 = (4-3)/180 = 1/180
Hence, B alone will finish the work in 180 days
Alternately,
Let the total work to be done = LCM(45, 60) = 180 units
A can complete this work in 60 days, hence A’s efficiency = 180/60 = 3 units/day
A and B together can complete this work in 45 days, hence their combined efficiency = 180/45 = 4 units/day
∴ B’s efficiency = 5 – 4 = 1 unit/day
Time taken by B alone to complete the whole work = 180/1 = 180 days.
Hence, option (d).
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