Question : A can complete a task in 25 days while B can complete the same task in 30 days. They work on alternate days, starting with A. Both A and B follow this pattern for 5 days and then, A leaves. In how many days will B finish the remaining work?
Option 1: $24 \frac{2}{5}$
Option 2: $5 \frac{2}{5}$
Option 3: $5 \frac{3}{5}$
Option 4: $24 \frac{3}{5}$
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Correct Answer: $24 \frac{2}{5}$
Solution :
A can complete the task in 25 days.
Work done by A in one day = $\frac{1}{25}$
B can complete the task in 30 days.
Work done by B in one day = $\frac{1}{30}$
They work on alternate days for 5 days.
In 5 days, A worked for 3 days and B worked for 2 days.
Work done in 5 days = $\frac{3}{25} + \frac{2}{30} = \frac{28}{150}$
After 5 days, A leaves, and B continues.
The remaining work = $ 1 - \frac{28}{150} = \frac{122}{150}$
If B can do $\frac{1}{30}$ work in one day, the number of days B needs to complete the work = $\frac{\frac{122}{150}}{\frac{1}{30}} =24\frac{2}{5}$ days
Hence, the correct answer is $24 \frac{2}{5}$.
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