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A and B can complete a work in 12 days and 8 days, respectively. They started doing the work together but after 2 days, B had to leave, and A completed the remaining work alone. The whole work was completed in ________ days. 4044
10
9
7
8
9
Calculate total units as LCM(12, 8) = 24. A's efficiency = 2, B's = 3. Together they do 5 units/day. In 2 days, 10 units done. Remaining 14 units done by A at rate 2, taking 7 days. Total days = 2 + 7 = 9.
A completes work in 12 days, B completes work in 8 days. They worked together for 2 days, then B left.
Work=Time├ЧEfficiency
Calculate total units as LCM(12, 8) = 24. A's efficiency = 2, B's = 3. Together they do 5 units/day. In 2 days, 10 units done. Remaining 14 units done by A at rate 2, taking 7 days. Total days = 2 + 7 = 9.
Students often calculate the 'remaining days' (7) and mark it as the answer, forgetting to add the initial 2 days of joint work.
Calculate Total Work and Efficiencies
Assuming total work is the LCM of 12 and 8, which is 24 units. A's efficiency = 24/12=2 units/day, B's efficiency = 24/8=3 units/day.
EfficiencyA+BтАЛ=2+3=5┬аunits/day
Calculate Work done in 2 days
Both worked together for 2 days. The total units completed in this duration is 2├Ч(2+3)=10 units.
WorkdoneтАЛ=5├Ч2=10
Calculate remaining work and days for A
Remaining work is 24тИТ10=14 units. Since B leaves, A completes this at an efficiency of 2 units/day.
TimeAтАЛ=214тАЛ=7┬аdays
Calculate total time taken
Total time = days worked together + days worked by A alone = 2+7=9 days.
Total┬аTime=2+7=9
B is correct because the sum of the initial 2 days of collaborative work and the 7 days taken by A alone results in 9 total days.
This logic is identical to mixture problems where one component is removed or added; always track the 'unit' value remaining to simplify calculations.
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