Team Size Changes Midway 14 men can complete a work in 12 days. After 4 days, 2 more men join. How many additional days are needed to complete the remaining work?

Introduction / Context:
Here, workforce changes partway through the project. The correct approach is to use man-days (men * days) to measure total work and calculate what remains after the first phase, adjusting for the new team size afterwards.

Given Data / Assumptions:

• Total with 14 men in 12 days ⇒ total work = 14*12 = 168 man-days.
• First 4 days with 14 men ⇒ 14*4 = 56 man-days completed.
• Then 2 more join ⇒ 16 men continue.

Concept / Approach:
Remaining work (in man-days) divided by the new daily capacity (men per day) gives remaining days.

Step-by-Step Solution:
Total work = 168 man-days.Done in first phase = 56 man-days.Remaining = 168 − 56 = 112 man-days.With 16 men: days needed = 112 / 16 = 7 days.

Verification / Alternative check:
Performing the calculation in fractional jobs gives the same answer; the man-day approach is clean and direct here.

Why Other Options Are Wrong:
5, 6, 8, or 9 days are not consistent with 112 man-days divided by 16 men.

Common Pitfalls:
Not converting to man-days first or assuming proportionality without accounting for the first phase’s contribution.

Final Answer:
7 days