a) 80 days
b) 100 days
c) 60 days
d) 150 days
Answer: c
Explanation: In these type of questions, always take total work as L.C.M. of number of days.
Here L.C.M. of Total Work = 360
One day work of A + B = $$\frac{{360}}{{72}}$$ = 5 unit/day
One day work of B + C = $$\frac{{360}}{{120}}$$ = 3 unit/day
One day work of C + A = $$\frac{{360}}{{90}}$$ = 4 unit/day
Total units/day = 5 + 3 + 4 = 12
(Here , 12 unit represents twice of the work done by A, B and C. So we will divide it by 2)
Work done by (A + B + C) per day = $$\frac{{12}}{2}$$ = 6 units/day
Total time taken by (A + B + C)
$$\eqalign{
& = \frac{{360}}{6} \cr
& = 60{\text{ days}} \cr} $$
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