Question
Download Solution PDFX and Y can do a piece of work together in 12 days, Y and Z together in 15 days, X and Z together in 20 days. Then the number of days taken by X alone to complete the work is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Time taken by X and Y together = 12 days
Time taken by Y and Z together = 15 days
Time taken by X and Z together = 20 days
Calculations:
⇒ Total work = LCM of (12, 15, 20) = 60 units
⇒ (X + Y)'s efficiency = 60 / 12 = 5 units/day
⇒ (Y + Z)'s efficiency = 60 / 15 = 4 units/day
⇒ (X + Z)'s efficiency = 60 / 20 = 3 units/day
Find the combined efficiency of X, Y, and Z.
⇒ 2 × (X + Y + Z)'s efficiency = (X+Y) + (Y+Z) + (X+Z) = 5 + 4 + 3 = 12 units/day
⇒ (X + Y + Z)'s efficiency = 12 / 2 = 6 units/day
Find X's efficiency.
⇒ X's efficiency = (X + Y + Z)'s efficiency - (Y + Z)'s efficiency
⇒ X's efficiency = 6 - 4 = 2 units/day
⇒ Time taken by X = Total work / X's efficiency
⇒ Time taken by X = 60 / 2 = 30 days
∴ X alone can complete the work in 30 days.
Last updated on Jul 15, 2025
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