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A can complete a piece of task in 10 hours; B and C together can complete it in 12 hours, while A and C together can complete it in 6 hours. How long will B alone take to complete it?

A can complete a piece of task in 10 hours; B and C together can complete it in 12 hours, while A and C together can complete it in 6 hours. How long will B alone take to complete it? Correct Answer 60 hours

Given:

A can complete a piece of task in = 10 hrs

B and C together can complete in = 12 hrs

A and C together can complete it in = 6 hrs

Formula:

Total work = Efficiency × Time Taken

Calculation:

Total work = 60 unit (LCM of 10, 12, 6)

⇒ Efficiency of A = 60/10 = 6 units/day

⇒ Efficiency of C = (60/6) – 6 = 4 units/day

⇒ Efficiency of B = (60/12) – 4 = 1 unit/day

∴ B alone can complete the whole work in = 60/1 = 60 hrs

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