Question
Download Solution PDFA and B can complete a piece of work in 10 days. B and C can do it in 15 days. A and C can do it in 12 days. A, B and C together can complete it in how many days ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A and B can complete the work in 10 days.
B and C can complete the work in 15 days.
A and C can complete the work in 12 days.
Formula used:
Work done per day = 1 / Number of days to complete the work
Calculation:
Work done per day by A and B:
(A + B) = 1/10 units per day
Work done per day by B and C:
(B + C) = 1/15 units per day
Work done per day by A and C:
(A + C) = 1/12 units per day
Adding all the equations:
(A + B) + (B + C) + (A + C) = 1/10 + 1/15 + 1/12
Finding the LCM of 10, 15, and 12:
LCM of 10, 15, and 12 = 60
1/10 = 6/60, 1/15 = 4/60, 1/12 = 5/60
2(A + B + C) = (6 + 4 + 5)/60 = 15/60 = 1/4
Work done by A, B, and C together:
A + B + C = 1/8 units per day
Total time taken by A, B, and C together:
Time = 1 / (A + B + C) = 8 days
∴ A, B, and C together can complete the work in 8 days.
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