A B and C working alone can complete a piece of work in 12 15 and 20 days respectively Each one does...........

Quant (SSC) Time and work

A, B and C working alone can complete a piece of work in 12, 15 and 20 days respectively.Each one does equal amount of work one by one. As soon as one’s part of work is done, the one can leave. In how many days will the work get finished?

11 2/3 days

13 2/3 days

15 2/3 days

9 2/3 days

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Explanation:

Part of work done by each person = 1/3
Let A, B and C can complete 1/3rd of the work in x, y and z days respectively,
Part of work done by A in one day = 1/12
Part of work done by B in one day = 1/15
Part of work done by C in one day = 1/20
According to the question,
x/12 = 1/3
⇒ x = 12/3 = 4 days
y/15 = 1/3
⇒ y = 15/3 = 5 days
z/20 = 1/3
⇒ z = 20/3 = 6 2/3 days
Total number of days = 4 + 5 + 6 2/3 = 15 2/3 days