# A and B can do a piece of work in 72 days. B and C can do it in 120 days, A and C can do it in 90 days. In how many days all the three together can do the work ?

A and B can do a piece of work in 72 days. B and C can do it in 120 days, A and C can do it in 90 days. In how many days all the three together can do the work ?
[A]150 days
[B]60 days
[C]80 days
[D]100 days

60 days
According to question,
(A + B)’s one day’s work $= \frac{1}{72}$
(B + C)’s one day’s work $= \frac{1}{120}$
and (C + A)’s one day’s work $= \frac{1}{90}$
On adding all three,
2 (A + B + C)’s one day’s work $= \frac{1}{72}+ \frac{1}{120}+ \frac{1}{90}$
$= \frac{5+3+4}{360} = \frac{1}{30}$
∴ (A + B + C)’s one day’s work $= \frac{1}{60}$
∴ A, B and C together can finish the whole work in 60 days.
Hence option [B] is the right answer.

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