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A and B can complete a task in 10 days, B and C can complete it in 15 days while C and A can do the same task together in 12 days. How many days will they together take to complete the task?

A and B can complete a task in 10 days, B and C can complete it in 15 days while C and A can do the same task together in 12 days. How many days will they together take to complete the task? Correct Answer 8

(A + B) can complete the task in = 10 days

⇒ (A + B)’s 1 day’s work = 1/10

(B + C) can complete the task in = 15 days

⇒ (B + C)’s 1 day’s work = 1/15

(C + A) can complete the task in = 12 days

⇒ (C + A)’s 1 day’s work = 1/12

⇒ 2(A + B + C) = 1/10 + 1/15 + 1/12

⇒ A + B + C = 1/8

∴ A, B and C together can complete the task in = 8 days

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