A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In how many days all three together can do the work ?
A. 80 days
B. 100 days
C. 60 days
D. 150 days
Answer: Option C
Solution(By Examveda Team)
In these kind 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)
$$\eqalign{ & = \frac{{360}}{6} \cr & = 60{\text{ days}} \cr} $$
Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
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