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A, B and C can complete a task together in 8 days. A and B would need 16 days if only the two of them worked, while A and C would take 12 days if only the two of them worked. If A worked alone, how many days would A take to compete the task?

A, B and C can complete a task together in 8 days. A and B would need 16 days if only the two of them worked, while A and C would take 12 days if only the two of them worked. If A worked alone, how many days would A take to compete the task? Correct Answer 48

(A + B + C) can complete a work in = 8 days

⇒ (A + B + C)’s 1 day’s work = 1/8

(A + B) can complete a work in = 16 days

⇒ (A + B)’s 1 day’s work = 1/16

⇒ C’s 1 day’s work = 1/8 – 1/16 = 1/16

(A + C) can complete a work in = 12 days

⇒ (A + C)’s 1 day’s work = 1/12

⇒ A’s 1 day’s work = 1/12 – 1/16 = 1/48

∴ A takes 48 days to complete the work alone.

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