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A, 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?
411тАЛ
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59тАЛ
59тАЛ
Use LCM of (9, 12, 18) = 36 units as total work. Efficiency (A,B,C) = (4, 3, 2). Total efficiency = 9. In 3 days they finish 27 units. Remaining = 9 units. Since B+C efficiency = 5, they finish 9 units in 9/5 days.
A, B, and C can complete a work in 9, 12, and 18 days respectively. They all work together for 3 days before A leaves.
Remaining┬аWork=Total┬аWorkтИТWork┬аdone┬аby┬а(A+B+C)┬аin┬а3┬аdays
Use LCM of (9, 12, 18) = 36 units as total work. Efficiency (A,B,C) = (4, 3, 2). Total efficiency = 9. In 3 days they finish 27 units. Remaining = 9 units. Since B+C efficiency = 5, they finish 9 units in 9/5 days.
Students often calculate the total days from the start instead of identifying that the question specifically asks for the 'remaining' work completion time.
Calculate Efficiency
Assuming total work is the LCM of 9, 12, and 18, which is 36 units. The daily efficiency of A, B, and C are 36/9=4, 36/12=3, and 36/18=2 units/day.
EfficiencyA+B+CтАЛ=4+3+2=9┬аunits/day
Work done in 3 days
A, B, and C work together for 3 days, completing 3├Ч9=27 units of work.
Work┬аDone=3├Ч9=27┬аunits
Remaining work calculation
The remaining work is 36тИТ27=9 units. After A leaves, only B and C continue. Their combined efficiency is 3+2=5 units/day.
Remaining┬аWork=36тИТ27=9┬аunits
Time to complete remaining work
The time required for B and C to finish the remaining 9 units is 9/5 days.
Time=59тАЛ┬аdays
D is correct because the remaining 9 units of work are completed by B and C at a combined rate of 5 units/day, taking 9/5 days.
This concept of 'Efficiency = Work/Time' is foundational for Pipe and Cistern problems, where rates are often negative if a pipe drains water.
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