Question
Download Solution PDFA and B can do a piece of work in 12 days. A and C can do it in 15 days. If all three together can complete the work in 10 days, in how many days will B and C complete the work?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Total work = LCM of 12, 15 & 10 = 60 units.
A and B can complete the work in 12 days = A + B = 60 ÷ 12 = 5 units/day
A and C can complete the work in 15 days = A + C = 60 ÷ 15 = 4 units/day
A, B, and C together can complete the work in 10 days = A + B + C = 60 ÷ 10 = 6 units/day
A + B + C = 6 units
A + B = 5 units
⇒ (A + B + C) − (A + B) = C
⇒ 6 − 5 = 1 unit
⇒ C = 1 unit/day
A + C = 4 units
⇒ (A + C) − C = A
⇒ 4 − 1 = 3 units
⇒ A = 3 units/day
From A + B = 5 units
⇒ 5 − A = B
⇒ 5 − 3 = 2 units
⇒ B = 2 units/day
Now, efficiency of B + C = 2 + 1 = 3 units/day
Total work = 60 units
Time taken by B and C = 60 ÷ 3 = 20 days
∴ B and C together can complete the work in 20 days.
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