A and B can do a piece of work in 36 days, B and C can do a it in 60 days, A and C can do it in 45 days. C alone can do it in:

August 30, 2016 August 30, 2016

A and B can do a piece of work in 36 days, B and C can do a it in 60 days, A and C can do it in 45 days. C alone can do it in :
[A]90 days
[B]120 days
[C]150 days
[D]180 days

180 days
(A + B)’s 1 day’s work $latex = \frac{1}{36}&s=1$
(B + C)’s 1 day’s work $latex = \frac{1}{60}&s=1$
(C + A)’s 1 day’s work $latex = \frac{1}{45}&s=1$
On adding,
2(A + B + C)’s 1 day’s work $latex = \frac{1}{36}+\frac{1}{60}+\frac{1}{45} = \frac{5+3+4}{180} = \frac{1}{15}&s=1$
∴ (A + B + C)’s 1 day’s work $latex = \frac{1}{30}&s=1$
∴ c’s 1 day’s work $latex = \frac{1}{30}-\frac{1}{36} = \frac{6-5}{180} = \frac{1}{180}&s=1$
∴ C alone will complete the work in 180 days.
Hence option [D] is correct answer.

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