Choose the correct answer from the alternatives given.
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?

80 days

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100 days

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60 days

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150 days

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Solution

The correct option is B 60 days
Let the total unit of work be 360 units (LCM of 7; 120 & 90)
(A + B) do = $\frac{360}{72}$ = 5 units/day
(B + C) do = $\frac{360}{120}$ =3 units / day
(C + A) do = $\frac{360}{90}$ 4 units/day
2(A + B + C)s per day work $= 5 + 3 + 4 = 12$ units.
(A + B + C)s per day work $= 6$ units
Time taken by (A + B + C) together to complete the work
$= \frac{360}{6}$ = 60 days.

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