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A can complete a 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?
31тАЛ
52тАЛ
158тАЛ
157тАЛ
158тАЛ
Calculate LCM of 15 and 20 as 60. Efficiency of A is 4 and B is 3. Total efficiency is 7. Total work done in 4 days is 7├Ч4=28. Work left is 60тИТ28=32. Fraction left is 32/60=8/15.
A can finish work in 15 days, B can finish work in 20 days. They work together for 4 days.
WorkleftтАЛ=1тИТ(EfficiencyA+BтАЛ├ЧTime)
Calculate LCM of 15 and 20 as 60. Efficiency of A is 4 and B is 3. Total efficiency is 7. Total work done in 4 days is 7├Ч4=28. Work left is 60тИТ28=32. Fraction left is 32/60=8/15.
Many students calculate the work done (7/15) instead of the work remaining (1тИТ7/15=8/15).
Calculate Total Work
Assume total work is the LCM of 15 and 20, which is 60 units.
LCM(15,20)=60
Determine Daily Efficiency
Calculate daily work rate for A (60/15=4) and B (60/20=3). Combined efficiency is 4+3=7.
EA+BтАЛ=4+3=7┬аunits/day
Calculate Remaining Work
Total work done in 4 days is 7├Ч4=28 units. Remaining work is 60тИТ28=32 units.
WorkremтАЛ=60тИТ28=32
Calculate Final Fraction
The fraction of work remaining is the remaining work divided by total work: 32/60, which simplifies to 8/15.
6032тАЛ=158тАЛ
C is correct because the remaining work after 4 days of combined labor is 8/15 of the total task.
This LCM method is identical to solving pipe and cistern problems, where LCM of rates helps determine how fast a tank fills.
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