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A, B and C can do a work in 36, 72 and 54 days respectively. They started the work together but A left 8 days before the completion of the work and C left 12 days before the completion of the work. In how many days was the work completed?

A, B and C can do a work in 36, 72 and 54 days respectively. They started the work together but A left 8 days before the completion of the work and C left 12 days before the completion of the work. In how many days was the work completed? Correct Answer 24

Given:

A, B and C can do a work in 36, 72 and 54 days respectively.

A left 8 days before the completion of the work.

C left 12 days before the completion of the work.

Formula used:

Work = Time × Efficiency

Calculation:

Efficiency of A = 1/36

Efficiency of B = 1/72

Efficiency of C = 1/54

Suppose work is completed in d days.

Work done by A = (d - 8)/36

Work done by B = d/72

Work done by C = (d - 12)/54

Total work done by A, B and C = (d - 8)/36 + d/72 + (d - 12)/54 

(6d - 48 + 3d + 4d - 48)/216 = 1

⇒ 13d = 216 + 96 = 312

⇒ d = 24 days

∴ Required number of days = 24 days

Alternate Solution:

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Work done by A in 8 days = 6 × 8 = 48

Work done by C in 12 days = 12 × 4 = 48

Work done = 216 + 48 + 48 = 312

∴ Required number of days = 312/13 = 24 days

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