Question : X can do a piece of work in 24 days. When he had worked for 4 days, Y joined him. If complete work was finished in 16 days, Y can alone finish that work in:
Option 1: 18 days
Option 2: 27 days
Option 3: 36 days
Option 4: 42 days
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Correct Answer: 36 days
Solution : Time taken by X to complete the work = 24 days
Work done by X in 1 day = $\frac{1}{24}$th of the total work.
Work done by X in 4 days = $4×\frac{1}{24}=\frac{1}{6}$
The remaining work = $1-\frac{1}{6}=\frac{5}{6}$
X and Y together completed the remaining work in (16 – 4) days = 12 days
Therefore, Work done by X and Y together in a day = $\frac{\frac{5}{6}}{12}=\frac{5}{72}$ of the work
Now, Work done by X in a day + Work done by Y in a day = $\frac{5}{72}$ of the work
So, Y alone can do $=\frac{5}{72} - \frac{1}{24}=\frac{2}{72}=\frac{1}{36}$ of the work in one day
$\therefore$ Y alone can do the work in = 36 days
Hence, the correct answer is 36 days.
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