Question
Download Solution PDFA and B together can finish a job in 20 days. B and C together can finish the same job in 30 days. If A and C together can finish it in 24 days, in how many days can A alone finish the job?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A and B = 20 days
B and C = 30 days
A and C = 24 days
Formula used:
Total work = LCM of days
Efficiency = Total work / Days
Calculation:
LCM of 20, 30, and 24 = 120 units
Efficiency of A and B = 120 / 20 = 6 units/day
Efficiency of B and C = 120 / 30 = 4 units/day
Efficiency of A and C = 120 / 24 = 5 units/day
Adding all efficiencies:
(A + B) + (B + C) + (A + C) = 6 + 4 + 5
2(A + B + C) = 15
A + B + C = 15 / 2 = 7.5 units/day
Efficiency of A = (A + B + C) - (B + C)
Efficiency of A = 7.5 - 4 = 3.5 units/day
Days taken by A alone = Total work / Efficiency of A
Days taken by A alone = 120 / 3.5
Days taken by A alone = 1200 / 35
Days taken by A alone = 240 / 7
Days taken by A alone = 34 2/7 days
∴ A alone can finish the job in 34 2/7 days.
Last updated on Jun 24, 2025
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