Initial units of work = $8$ units

Out of which, $7$ units are completed in $21$ days.

So, the number of days that man takes in completing one unit of work = $21/7 = 3$ days

Now, amount of new work = $8 + 50\%$ of $8 = 8 + 4 = 12$ units

Work remaining = $12 – 7 = 5$ units

So, the time taken by the man to complete the rest of the work = $5 \times 3 = 15$ days