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Question 64
A and C together can complete a work in 120 days, C and E together can complete the same work in 80 days and A and E together can complete the same work in 160 days. In how many days A, C and E together can complete the same work?
Solution
Let the total work be 480 units. (LCM of 120, 80 and 160)
Efficiency of A+C = 480/120 = 4 units/day
Efficiency of C+E = 480/80 = 6 units/day
Efficiency of A+E = 480/160 = 3 units/day
Efficiency of 2(A+C+E) = 13 units/day
Efficiency of A+C+E = $$\dfrac{13}{2}$$ units/day
Therefore, Total work will be completed in $$\dfrac{480}{\dfrac{13}{2}} = \dfrac{960}{2}$$ days
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