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A and B can complete a task in 10 and 15 days respectively. They work together for 3 days, and then A leaves. How many more days will B take to complete the remaining work?
7.5 ┬аdays
6 ┬аdays
8 ┬аdays
9 ┬аdays
7.5 ┬аdays
Assume total work as the LCM (30 units) to avoid fractions entirely during intermediate steps.
A completes work in 10 days, B in 15 days, working together for 3 days.
T=rBтАЛWтИТ(rAтАЛ+rBтАЛ)├ЧdтАЛ
Assume total work as the LCM (30 units) to avoid fractions entirely during intermediate steps.
Dividing the remaining work by the combined efficiency instead of B's individual efficiency after A leaves.
Find Efficiencies
Assume total work is 30 units (LCM of 10 and 15). A's efficiency is 30/10=3 units/day and B's efficiency is 30/15=2 units/day.
W=30,rAтАЛ=3,rBтАЛ=2
Calculate Work Done in 3 Days
Combined efficiency is 3+2=5 units/day. Work completed together in 3 days is 5├Ч3=15 units.
WdoneтАЛ=5├Ч3=15
Calculate Remaining Days for B
Remaining work is 30тИТ15=15 units. B completes this alone at 2 units/day in 15/2=7.5 days.
T=215тАЛ=7.5
A is correct because B requires 7.5 days to finish the remaining work alone.
This same LCM technique applies directly to pipes and cisterns problems where pipes are opened or closed at specific intervals.
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