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%?

Correct Option (D)

Let the total initial work be represented by 8 units. The man completes 7/8 of the job, which corresponds to 7 units of work, in 21 days.

• The rate of work is determined by calculating the time taken to complete one unit of work: $\frac{21 \text{ days}}{7 \text{ units}} = 3$7 units21 days​=3 days per unit.
• The quantum of work is subsequently increased by 50%. The initial total work was 8 units.
• The new total work is calculated as: Original total work + 50% of Original total work = $8 + \frac{50}{100} \times 8 = 8 + 4 = 12$8+10050​×8=8+4=12 units.
• Since 7 units of work have already been completed, the remaining work to be finished is: New total work - Work already completed = $12 - 7 = 5$12−7=5 units.
• To complete these remaining 5 units of work, at a rate of 3 days per unit, the additional time required is $5 \times 3 = 15$5×3=15 days.

Incorrect Options:

Options A (22), B (21), and C (18) are incorrect. These outcomes would typically arise from misinterpretations of the problem's conditions, such as incorrectly calculating the additional quantum of work, misidentifying the remaining work after the increase, or applying the derived work rate inconsistently. For instance, selecting 21 days (Option B) overlooks the specified increase in the total quantum of work.