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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?

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? Correct Answer 960 / 13 days

Given:

A and C together can complete the work in days = 120

C and E together can complete the work in days = 80

A and E together can complete the work in days = 160

Concept:

In this type of question always consider the total work as LCM of individual number of days.

Formula used:

Efficiency = Total work / Number of days

Calculation:

Let the total number of work be LCM of 120, 80, 160 i.e. 480 unit

Efficiency of A and C together = 480 / 120 = 4 unit / day

Efficiency of C and E together = 480 / 80 = 6 unit / day

Efficiency of A and E together = 480 / 160 = 3 unit / day

So efficiency of A, C, and E together = (4 + 6 + 3) / 2 = 13 / 2

∴ A, C, and E together can complete the work in days = 480 / (13 / 2) = 960 / 13 days

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