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A can do a work in 12 days and B can do the same in 18 days. They work together for 4 days. What fraction of the work is left?
31тАЛ
32тАЛ
94тАЛ
95тАЛ
94тАЛ
Use the LCM method to assume total work as 36 units. A's efficiency is 3 units/day and B's is 2 units/day, making their combined efficiency 5 units/day.
A can complete the work in 12 days, B can complete the work in 18 days, and they work together for 4 days.
Work┬аLeft=1тИТTotal┬аWorkWork┬аDoneтАЛ
Use the LCM method to assume total work as 36 units. A's efficiency is 3 units/day and B's is 2 units/day, making their combined efficiency 5 units/day.
Students often calculate the work done (5/9) and mistakenly select it as the final answer instead of subtracting it from 1 to find the work left.
Find Total Work via LCM
Assume total work is the LCM of 12 and 18, which is 36 units.
Total┬аWork=LCM(12,18)=36┬аunits
Calculate Individual Efficiencies
A's daily work rate is 1236тАЛ=3 units/day and B's daily work rate is 1836тАЛ=2 units/day.
EAтАЛ=3,EBтАЛ=2
Calculate Work Done in 4 Days
Combined efficiency is 3+2=5 units/day. In 4 days, they complete 4├Ч5=20 units of work.
Work┬аDone=4├Ч(3+2)=20┬аunits
Calculate Fraction of Work Left
The remaining work is 36тИТ20=16 units. The fraction left is 3616тАЛ=94тАЛ.
Work┬аLeft=3636тИТ20тАЛ=3616тАЛ=94тАЛ
C is correct because the fraction of work left after 4 days of joint work is 94тАЛ.
This LCM efficiency approach is also directly applicable to pipe and cistern problems involving filling and emptying rates.
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