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A can complete a piece of work in 10 days and B can complete the same work in 15 days, when each works individually. Both A and B work together for 3 days. After that, B leaves the work, and A alone completes the remaining work. How many days will A take to finish the remaining work alone?
8 days
5 days
6 days
10 days
5 days
Use LCM of 10 and 15 (which is 30) as total work. Then efficiency of A is 3 units/day and B is 2 units/day. In 3 days, they finish 3├Ч(3+2)=15 units. Remaining work is 30тИТ15=15 units, which A does in 15/3=5 days.
A completes work in 10 days, B completes work in 15 days, both work for 3 days, then B leaves.
Work=Time├ЧEfficiency
Use LCM of 10 and 15 (which is 30) as total work. Then efficiency of A is 3 units/day and B is 2 units/day. In 3 days, they finish 3├Ч(3+2)=15 units. Remaining work is 30тИТ15=15 units, which A does in 15/3=5 days.
A common mistake is calculating the work done by B alone instead of the remaining work, or miscalculating the combined efficiency as 10+15 instead of 1/10+1/15.
Calculate Total Work and Efficiencies
Assuming total work is the LCM of 10 and 15, which is 30 units. A's efficiency is 30/10=3 units/day and B's is 30/15=2 units/day.
EfficiencyA+BтАЛ=3+2=5┬аunits/day
Calculate Work Done in 3 Days
Since A and B work together for 3 days, the work completed is 3├Ч5=15 units.
WorkdoneтАЛ=3├Ч5=15┬аunits
Calculate Remaining Work
Subtract the completed work from the total work to find what remains for A.
WorkremтАЛ=30тИТ15=15┬аunits
Calculate Time Taken by A
A completes the remaining 15 units of work at his efficiency of 3 units/day.
TimeAтАЛ=315тАЛ=5┬аdays
B is correct because A requires exactly 5 days to complete the remaining 15 units of work.
This LCM approach is highly efficient for pipes and cisterns problems as well, where 'efficiency' is replaced by the 'rate of flow' of the pipe.
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