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A and B can do a piece of work in 12 days and 16 days, respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
12 days
15 days
10 days
9 days
9 days
Calculate LCM of 12 and 16 (48). Efficiency of (A+B) is 4+3=7. Work done in 3 days is 7*3=21. Remaining work is 48-21=27. B takes 27/3=9 days.
A completes work in 12 days, B completes work in 16 days. Both work for 3 days, then A leaves.
WorkremainingтАЛ=TotalтИТ(EfficiencyA+BтАЛ├ЧDaysworkedтАЛ)
Calculate LCM of 12 and 16 (48). Efficiency of (A+B) is 4+3=7. Work done in 3 days is 7*3=21. Remaining work is 48-21=27. B takes 27/3=9 days.
Students often calculate the total time taken instead of the 'remaining' time requested in the question.
Calculate Total Work and Efficiencies
Let total work be the LCM of 12 and 16, which is 48 units. Efficiency of A is 48/12=4 units/day and B is 48/16=3 units/day.
EfficiencyAтАЛ=4,EfficiencyBтАЛ=3,Total┬аWork=48
Calculate Work done by A and B in 3 days
Together they complete 4+3=7 units per day. In 3 days, they complete 7├Ч3=21 units.
WorkdoneтАЛ=(4+3)├Ч3=21
Calculate Remaining Work and time for B
Remaining work is 48тИТ21=27 units. B takes 27/3=9 days to complete this.
DaysBтАЛ=327тАЛ=9
D is correct because B takes 9 days to complete the remaining 27 units of work.
This concept of 'Efficiency' is identical to the 'Rate' concept used in Pipes and Cisterns problems.
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