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A can complete a piece of work in 15 days, and B can complete the same work in 20 days. If they work together for 4 days, what fraction of the work is left?
8/15
7/15
2/5
11/15
8/15
Calculate LCM of 15 and 20 (which is 60). Efficiencies are 60/15=4 and 60/20=3. Total efficiency is 7. In 4 days, 7├Ч4=28 units are done. Remaining is 60тИТ28=32. Fraction left is 32/60=8/15.
Time taken by A is 15 days, time taken by B is 20 days, and they work together for 4 days.
Work┬аDone=Efficiency├ЧTime
Calculate LCM of 15 and 20 (which is 60). Efficiencies are 60/15=4 and 60/20=3. Total efficiency is 7. In 4 days, 7├Ч4=28 units are done. Remaining is 60тИТ28=32. Fraction left is 32/60=8/15.
Many students calculate the fraction of work completed (28/60=7/15) instead of the fraction of work left (1тИТ7/15=8/15).
Calculate Total Work and Efficiencies
Assuming total work is the LCM of 15 and 20, which is 60 units. A's efficiency = 60/15=4 units/day and B's efficiency = 60/20=3 units/day.
60┬аunits,EffAтАЛ=4,EffBтАЛ=3
Calculate Work Completed
Combined efficiency of A and B is 4+3=7 units/day. In 4 days, total work done is 7├Ч4=28 units.
WdoneтАЛ=7├Ч4=28┬аunits
Calculate Remaining Work and Fraction
Remaining work is 60тИТ28=32 units. The fraction of work left is 32/60. Simplifying by dividing numerator and denominator by 4, we get 8/15.
6032тАЛ=158тАЛ
A is correct because the fraction of work remaining after 4 days of combined labor is 8/15.
This LCM approach is identical to the method used for pipes and cisterns problems, where filling capacity replaces units of work.
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