Question : A and B can do a piece of work in 45 and 40 days, respectively. They began the work together, but A left after some days and B finished the remaining work in 23 days. A left after:
Option 1: 6 days
Option 2: 9 days
Option 3: 12 days
Option 4: 5 days
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Correct Answer: 9 days
Solution :
Given: A and B can do a piece of work in 45 and 40 days, respectively. They began the work together, but A left after some days and B finished the remaining work in 23 days.
Time taken by A to complete the work = 45 days
Work done by A in a 1 day = $\frac{1}{45}$ units
Time taken by B to complete the work = 40 days
Work done by B in a 1 day = $\frac{1}{40}$ units
Work done by B alone in 23 days = $(\frac{1}{40}×23)=\frac{23}{40}$ units
Work done by A and B together, in the beginning = $(1–\frac{23}{40})=\frac{17}{40}$ units
Work done by A and B together, in 1 day = $(\frac{1}{45}+\frac{1}{40})=\frac{17}{360}$ units
Time taken by A and B to complete $\frac{17}{40}$ units of work together = $\frac{\text{Total work done}}{\text{Work done by them in a day}}$
= $(\frac{360}{17}×\frac{17}{40})=9$ days
So, A left after 9 days.
Hence, the correct answer is 9 days.
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