Question
Download Solution PDFX and Y can complete a piece of work in 12 days and 16 days, respectively. They worked together for 6 days, after which Y left the work. How long did X take to finish the remaining work?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
X completes work in 12 days
Y completes work in 16 days
They worked together for 6 days
Calculations:
Total work = LCM of (12, 16) = 48 units
X's efficiency (work per day) = Total work / X's days = 48 / 12 = 4 units/day
Y's efficiency (work per day) = Total work / Y's days = 48 / 16 = 3 units/day
Combined efficiency of X and Y = X's efficiency + Y's efficiency = 4 + 3 = 7 units/day
Work done by X and Y in 6 days = Combined efficiency × Days worked = 7 units/day × 6 days = 42 units
Remaining work = Total work - Work done together = 48 - 42 = 6 units
Time taken by X to finish remaining work = Remaining work / X's efficiency = 6 units / 4 units/day = 1.5 days
Last updated on Apr 24, 2025
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