Question : A and B together can complete a piece of work in 15 days and B alone can complete it in 21 days. In how many days can A complete it alone?
Option 1: $41 \frac{1}{2}$ days
Option 2: $52 \frac{1}{2}$ days
Option 3: $31 \frac{1}{2}$ days
Option 4: $57 \frac{1}{2}$ days
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Correct Answer: $52 \frac{1}{2}$ days
Solution :
Given: A and B together can complete a piece of work in 15 days and B alone can complete it in 21 days.
A and B together in 1 day can complete $\frac{1}{15}$ part of the work.
B alone in 1 day can complete $\frac{1}{21}$ part of the work.
So, A alone in 1 day can complete $(\frac{1}{15}–\frac{1}{21})=\frac{2}{105}$ part of the work.
Therefore, A alone can complete the work in $(1÷\frac{2}{105})=\frac{105}{2}=52\frac{1}{2}$ days.
Hence, the correct answer is $52\frac{1}{2}$ days.
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