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Question

A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. In how many days will they finish it together and separately?

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Solution

Work done by A and B in 1 day =112
Work done by B and C in 1 day =115
Work done by C and A in 1 day =120
Work done by (A+B)+(B+C)+(C+A) in 1 day =112+115+120
Work done by (2A+2B+2C) in 1 day =5+4+360
Work done by 2(A+B+C) in 1 day =1260
Work done by A, B and C together in 1 day =12×1260=110
A, B and C will finish the work in 10 days.
Work done by A in 1 day
(i.e.) [(A+B+C)swork(B+C)swork]=110115=3230=130
A will finish the work in 30 days.
Work done by B in 1 day
(i.e.) [(A+B+C)swork(C+A)swork]=110120=2120=120
B will finish the work in 20 days.
Work done by C in 1 day
(i.e.) [(A+B+C)swork(A+B)swork]=110112=6560=160
C will finish the work in 60 days.

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