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A and B together can complete a work in 12 days, B and C together can complete a work in 40 days and A and C together can complete a work in 30 days. If they all work together then how many days would it take to complete the work?

A and B together can complete a work in 12 days, B and C together can complete a work in 40 days and A and C together can complete a work in 30 days. If they all work together then how many days would it take to complete the work? Correct Answer 240/17

Given:

A + B can complete a work in 12 days

B + C can complete a work 40 days

A + C can complete a work in 30 days

Formula used:

Efficiency = Total work/Total time

Calculation:

Let the total work be 1 unit.

(A + B)`s one days` work = 1/12

(B + C)`s one days` work = 1/40

(A + C)`s one days` work = 1/30

⇒ 2(A + B+ C)`s one day`s work = (1/12 + 1/40 + 1/30)

⇒ (A + B+ C)`s one day`s work = (10 + 3 + 4)/240

⇒ 17/240

Time to complete whole work together = 1/(17/240) = 240/17 days

∴ A, B, C together can complete the work in 240/17 days.

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