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A can finish a work in 18 days and B can finish the same work in 24 days. If they work together for 6 days, what fraction of the work is left?
1/4
1/2
7/12
5/12
7/12
Find the LCM of 18 and 24 (which is 72). A's efficiency is 4 units/day, B's is 3 units/day. Total work per day = 7. In 6 days, they finish 42 units. Remaining = (72-42)/72 = 30/72 = 5/12.
Time taken by A is 18 days, time taken by B is 24 days, and they work together for 6 days.
Work┬аDone=(RateAтАЛ+RateBтАЛ)├ЧTime
Find the LCM of 18 and 24 (which is 72). A's efficiency is 4 units/day, B's is 3 units/day. Total work per day = 7. In 6 days, they finish 42 units. Remaining = (72-42)/72 = 30/72 = 5/12.
Many students calculate the work done (5/12) and accidentally mark it as the answer, forgetting the question asks for the 'work left' (1тИТ5/12=7/12).
Calculate total work and efficiencies
Let total work be the LCM of 18 and 24, which is 72 units. A's efficiency = 72/18=4 units/day. B's efficiency = 72/24=3 units/day.
Total┬аWork=72,EfficiencyA+BтАЛ=4+3=7
Calculate work done in 6 days
Since they work together for 6 days, the combined work completed is the sum of their efficiencies multiplied by the time.
Work┬аDone=7├Ч6=42
Calculate remaining work and fraction
Remaining work is 72тИТ42=30 units. The fraction of work left is the remaining work divided by total work.
Fraction=7230тАЛ=125тАЛ
C is correct because the fraction of work completed is 5/12, leaving 7/12 of the total work unfinished.
This LCM method is identical to solving Pipe and Cistern problems where filling rates are treated as positive work and emptying rates as negative work.
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