# 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 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.

## PM

May 7, 2018 at 8:19 pmGood you know it