Question : Sanjay and Rohan can complete a work in 8 days and 12 days, respectively. Starting with Sanjay, they work on alternate days. In how many days will the work be completed?
Option 1: $8 \frac{1}{2}$
Option 2: $9 \frac{1}{2}$
Option 3: $9 \frac{2}{3}$
Option 4: $9 \frac{1}{3}$
Correct Answer: $9 \frac{1}{2}$
Solution :
Time taken by Sanjay to complete the work = 8 days
Part of work done by Sanjay in a day = $\frac{1}{8}$
Time taken by Rohan to complete the work = 12 days
Part of work done by Rohan in a day = $\frac{1}{12}$
Part of the work done by Sanjay and Rohan in two days
= $\frac{1}{8}+\frac{1}{12}$
= $\frac{3+2}{24}$
= $\frac{5}{24}$
Part of the work done by Sanjay and Rohan in 8 days = $\frac{5×4}{24} = \frac{20}{24}$
Part of the work done by Sanjay in 9th day = $\frac{1}{8} = \frac{3}{24}$
Remaining work = $\frac{24-20-3}{24} = \frac{1}{24}$
Time taken by Rohan to complete the remaining work = $\frac{\frac{1}{24}}{\frac{1}{12}} = \frac{1}{2}$ day
Total time taken = $9+\frac{1}{2}= 9\frac{1}{2}$ days
Hence, the correct answer is $9\frac{1}{2}$.
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