A team of 14 persons can complete a job in 16 days (uniform productivity). Initially, 8 persons start the work and continue for 12 days. After 12 days, 8 more persons join (so the team becomes 16 persons). How many days will the team take to complete the remaining work after the new members join?

Introduction / Context:
This is a classic manpower–time problem with a change in crew size mid-project. We translate total work into person-days, account for work already done, and then compute the duration for the remainder with the increased team.

Given Data / Assumptions:

• 14 persons complete the work in 16 days ⇒ total work W = 14 * 16 person-days = 224 person-days.
• Phase 1: 8 persons work for 12 days.
• Phase 2: 8 more join ⇒ 16 persons for the remainder.
• Uniform productivity per person per day.

Concept / Approach:
Compute the total work in person-days. Subtract the contribution of the first phase (already completed). Divide leftover person-days by the new team size to get the additional days required after the joining event.

Step-by-Step Solution:

Verification / Alternative check:
Total elapsed time from the start would be 12 + 8 = 20 days. The question specifically asks for the time to complete the remaining work after the join, which is 8 days. Since 8 days is not among the listed numeric options, the correct choice is “None of these.”

Why Other Options Are Wrong:
12 days: Ignores increased manpower; would overshoot.

7 days: Underestimates the remaining person-days for 16 workers.

9 days: Overestimates remainder time compared with exact division (128/16).

Common Pitfalls:
Confusing total duration with post-joining duration; not converting to person-days; or rounding prematurely. Always calculate remainder precisely.

Final Answer:
None of these (the required time for the remainder is 8 days)