A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work is further increased by 50%?

The correct answer is 15.

Let's break down the problem step-by-step to find out how many more days will be required to finish the increased work.

Step 1: Calculate the total time required for the initial full job
The man completes $\frac{7}{8}$ of the job in 21 days.

Let the total initial work be represented as 1 unit.
Time taken to complete 1 full unit of initial work = $21\times \frac{8}{7}=24$ days.

Step 2: Determine the remaining work of the initial job
Remaining fraction of the initial work = $1-\frac{7}{8}=\frac{1}{8}$ unit.

Step 3: Calculate the extra work added
The total quantum of work is increased by 50%.
Extra work added = 50% of 1 unit = 0.5 units = $\frac{1}{2}$ unit.

Step 4: Calculate the total remaining work to be completed
Total remaining work = (Remaining fraction of initial work) + (Extra work added)
$\text{Total remaining work}=\frac{1}{8}+\frac{1}{2}=\frac{1}{8}+\frac{4}{8}=\frac{5}{8}$ units.

Step 5: Calculate the number of days required to finish the remaining work
Since 1 full unit of work takes 24 days, the time required to complete $\frac{5}{8}$ units of work is:
$\text{Days required}=24\times \frac{5}{8}=3\times 5=15$ days.

Thus, it will take him 15 more days to finish the job.