Question
Download Solution PDFA can complete a work in 15 days, and B can complete the same work in 25 days. In how many days will A and B together complete this work?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Time taken by A to complete the work = 15 days
Time taken by B to complete the work = 25 days
Formula Used:
Total Work = LCM of (Time taken by A, Time taken by B)
Efficiency = Total Work / Time taken
Combined Efficiency = Efficiency of A + Efficiency of B
Time taken by A and B together = Total Work / Combined Efficiency
Calculation:
LCM(15, 25)
Multiples of 15: 15, 30, 45, 60, 75, ...
Multiples of 25: 25, 50, 75, ...
LCM(15, 25) = 75 units (Total Work)
Efficiency of A = Total Work / Time taken by A = 75 / 15 = 5 units/day
Efficiency of B = Total Work / Time taken by B = 75 / 25 = 3 units/day
Combined Efficiency of A and B = Efficiency of A + Efficiency of B = 5 + 3 = 8 units/day
Time taken by A and B together = Total Work / Combined Efficiency = 75 / 8 days
⇒ Time taken by A and B together = \(9\frac{3}{8}\) days
∴ A and B together will complete the work in \(9\frac{3}{8}\) days.
Last updated on Dec 9, 2024
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