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A and B together can complete a work in 12 days, B and C together take 3 days more than that of A and B to complete the same work while C and A together take 5 days more than that of B and C to complete the same work, how long C alone can complete the work?

A and B together can complete a work in 12 days, B and C together take 3 days more than that of A and B to complete the same work while C and A together take 5 days more than that of B and C to complete the same work, how long C alone can complete the work? Correct Answer 60 days

Given,

A and B together can complete a work in = 12 days

B and C together can complete the same work in = 12 + 3 = 15 days

C and A together can complete the same work in = 15 + 5 = 20 days

Formula:

Total work = Efficiency × time

Calculation:

Let, total work be 60 unit (LCM of 12, 15 and 20)

Efficiency of A and B = 5 units/day

Efficiency of B and C = 4 units/day

Efficiency of C and A = 3 units/day

Efficiency of A, B and C = (5 + 4 + 3)/2 = 12/2 = 6 unit/day

Hence, efficiency of C = 6 - 5 = 1 unit/day

∴ C alone can complete the same work in = 60/1 = 60 days

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