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A and B can do a piece of work in 12 and 18 days. They work together for 4 days. What fraction of work is left?
94тАЛ
95тАЛ
31тАЛ
92тАЛ
94тАЛ
Assume total work as the LCM of individual times to convert fractions into whole numbers, making calculations faster.
A can finish the work in 12 days, B can finish the work in 18 days, and they work together for 4 days.
Fraction┬аLeft=Total┬аWorkTotal┬аWorkтИТWork┬аDoneтАЛ
Assume total work as the LCM of individual times to convert fractions into whole numbers, making calculations faster.
Calculating the work done (5/9) instead of the work left (4/9) and accidentally selecting the wrong option.
Find Total Work via LCM
Take the LCM of the individual completion days (12 and 18) to represent the total units of work.
LCM(12,18)=36┬аunits
Calculate Individual Efficiencies
A's 1-day work is 36/12=3 units/day, and B's 1-day work is 36/18=2 units/day.
A=3┬аunits/day,B=2┬аunits/day
Calculate Work Done in 4 Days
Combined 1-day work of A and B is 3+2=5 units. In 4 days, they complete 5├Ч4=20 units of work.
20┬аunits
Find Fraction of Work Left
Remaining work is 36тИТ20=16 units. The fraction left is 16/36, which simplifies to 4/9.
3616тАЛ=94тАЛ
A is correct because the fraction of work left after 4 days of joint work is 94тАЛ.
The LCM efficiency approach used here is identical to solving Pipe and Cistern problems in quantitative aptitude.
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