Question
A, B, and C are hired to complete a task. A and B
together can finish the work in 12 days, B and C together in 15 days, and A and C together in 20 days. How many days will it take for all three to complete the work together?Solution
Let the total work be 1 unit. Let A’s efficiency be a, B’s efficiency be b, and C’s efficiency be c. From the problem: 1/(A + B) = 1/12 1/(B + C) = 1/15 1/(A + C) = 1/20. To find 1/(A + B + C), = ½ {1/(A + B) + 1/(B + C) + 1/(A + C)} = ½ {1/12 + 1/15 + 1/20} = ½ { (5 + 4 + 3)/60 }= 12/120 = 1/10. This gives us the efficiency of (A + B + C) together, which is 1/10. Thus, all three together will take 10 days to complete the work. Final Answer: (b) 10 days
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