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A and B together complete a work in 20 days, B and C together complete same work in 30 days, C and A together complete the same work in 24 days. In how many days A, B and C together can complete the same work?

A and B together complete a work in 20 days, B and C together complete same work in 30 days, C and A together complete the same work in 24 days. In how many days A, B and C together can complete the same work? Correct Answer 16

⇒ A and B’s 1 day’s work = 1/20

⇒ B and C’s 1 day’s work = 1/30

⇒ C and A’s 1 day’s work = 1/24

Adding all three:

⇒ 2 × (A + B + C)’s 1 day’s work = 1/20 + 1/30 + 1/24 = 1/8

⇒ A + B + C 1 day’s work = 1/16

∴ A, B and C will finish the work in 16 days.

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