Question
Download Solution PDFA, B, C alone can do a piece of work in 9, 12 and 18 days, respectively. They all started the work together, but A left after 3 days. In how many days was the remaining work completed?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A can do the work in 9 days.
B can do the work in 12 days.
C can do the work in 18 days.
A, B, and C worked together for 3 days.
Formula used:
Total work = LCM of individual work days.
Efficiency = Total work / Individual work days.
Calculation:
Let the total work be 36 units.(LCM of 9, 12, and 18 = 36)
Efficiency of A = 36 / 9 = 4 units/day
Efficiency of B = 36 / 12 = 3 units/day
Efficiency of C = 36 / 18 = 2 units/day
Combined efficiency of A, B, and C = 4 + 3 + 2 = 9 units/day
Work done by A, B, and C in 3 days = 9 × 3 = 27 units
Remaining work = 36 - 27 = 9 units
Combined efficiency of B and C = 3 + 2 = 5 units/day
Time taken by B and C to complete the remaining work = 9 / 5
∴ The remaining work was completed in 9 / 5 days.
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