Question
Download Solution PDFB and C can finish a task in 8 days when working together. Together, A and B and A and C may finish the identical task in 12 and 16 days, respectively. How many days will combined to finish the identical task?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
B and C together can finish a task in 8 days.
A and B together can finish the same task in 12 days.
A and C together can finish the same task in 16 days.
Formula Used:
Total Work = LCM of the number of days taken by each pair.
Efficiency = Total Work / Number of days.
Combined Efficiency = Efficiency of A + Efficiency of B + Efficiency of C.
Number of days taken by A, B, and C together = Total Work / Combined Efficiency.
Calculations:
Number of days taken by (B + C) = 8 days.
Number of days taken by (A + B) = 12 days.
Number of days taken by (A + C) = 16 days.
Total Work = LCM(8, 12, 16) = 48 units.
Efficiency of (B + C) = Total Work / Days by (B + C) = 48 / 8 = 6 units/day.
Efficiency of (A + B) = Total Work / Days by (A + B) = 48 / 12 = 4 units/day.
Efficiency of (A + C) = Total Work / Days by (A + C) = 48 / 16 = 3 units/day.
Adding the efficiencies of the pairs:
Efficiency(B + C) + Efficiency(A + B) + Efficiency(A + C) = 6 + 4 + 3
⇒ 2 × (Efficiency of A + Efficiency of B + Efficiency of C) = 13
Combined Efficiency of (A + B + C) = 13 / 2 = 6.5 units/day.
Number of days taken by A, B, and C together = Total Work / Combined Efficiency
Number of days taken by A, B, and C together = 48 / 6.5
Number of days taken by A, B, and C together = 480 / 65
Number of days taken by A, B, and C together = 96 / 13 days.
∴ A, B, and C together will take 96/13 days to finish the identical task.
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