Question : X alone can complete a piece of work in 16 days, while Y alone can complete the same work in 24 days. They work on alternate days starting with Y. In how many days will 50% of the total work be completed?
Option 1: $\frac{24}{3}$ days
Option 2: $\frac{29}{3}$ days
Option 3: $\frac{32}{3}$ days
Option 4: 9 days
Correct Answer: $\frac{29}{3}$ days
Solution :
Time taken by X to complete the work = 16 days
Part of work done by X in a day = $\frac{1}{16}$
Time taken by X to complete the work = 24 days
Part of work done by X in a day = $\frac{1}{24}$
Part of work done by X and Y in 2 days = $\frac{1}{24}+\frac{1}{16}=\frac{2+3}{48}=\frac{5}{48}$
Part of work done by X and Y in 8 days = $\frac{5×4}{48} = \frac{20}{48}$
Part of work done by Y in 9th day = $\frac{1}{24} = \frac{2}{24}$
Remaining work = $\frac{24-20-2}{48} = \frac{2}{48}$
Time taken by X to do the remaining work = $\frac{ \frac{2}{48}}{\frac{1}{16}} = \frac{2}{3}$ day
Total time taken = $9 + \frac{2}{3} = \frac{29}{3}$ days
Hence, the correct answer is $\frac{29}{3}$ days.
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