A and B can complete a work in 12 days, B and C in 15 days, and A and C in 20 days. How many days will A, B and C together take to finish the work?
Solution:
Let total work = 60 units (LCM of 12, 15, 20).
Work rates: A + B = 60/12 = 5 units/day B + C = 60/15 = 4 units/day
A + C = 60/20 = 3 units/day
Add all three equations:
(A + B) + (B + C) + (A + C) = 5 + 4 + 3 = 12 units/day
This equals: 2(A + B + C)
So, 2(A + B + C) = 12 A + B + C = 6 units/day
Total time = Total work ÷ total rate = 60 ÷ 6 = 10 days
Correct Answer: (c)
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