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A and B can finish a work together in 30 days. B and C can finish the same work together in 24 days. A and C can finish the work together in 40 days. If all three work together, how long will it take them to complete the work?

A and B can finish a work together in 30 days. B and C can finish the same work together in 24 days. A and C can finish the work together in 40 days. If all three work together, how long will it take them to complete the work? Correct Answer 20 days

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Efficiency of (A + B) (B + C) and (C + A) together = A + B + B + C + C + A = 4 + 5 + 3 = 12

2(A + B + C) = 12

A + B + C = 6

Time taken by (A + B + C) to complete the work = 120/6 = 20 days

Alternate Solution∶

Efficiency of A and B when they work together = 1/30

Efficiency of B and C when they work together = 1/24

Efficiency of A and C when they work together = 1/40

⇒ Efficiency of (A + B), (B + C) and (C + A) when they work together = 1/30 + 1/24 + 1/40

= (4 + 5 + 3)/120 = 12/120 = 1/10

∴ Efficiency of A, B and C when they work together = 1/2 × 1/10 = 1/20

Time taken by A, B and C to complete the work when they work together

= 1/(1/20) = 20 days.

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