Twelve men can complete a piece of work in 14 days. They work together for 5 days, after which 3 more men join them. How many more days (correct to one decimal place) will the enlarged group take to finish the remaining work?

Introduction / Context:
This time and work question involves a change in the size of the workforce partway through the job. First, 12 men work together, and then 3 additional men join after a few days. We need to determine the extra number of days required to finish the remaining work once the additional men have joined. Such problems test understanding of man day concepts and proportional reasoning in aptitude exams.

Given Data / Assumptions:

• 12 men can complete the whole work in 14 days.
• These 12 men work for the first 5 days.
• After 5 days, 3 more men join, so a total of 15 men work for the remaining part.
• We must compute how many more days are needed after the 5th day to finish the remaining work.
• Work done is assumed to be directly proportional to the product of men and days, that is, man days.

Concept / Approach:
The main idea is to convert the entire job into man days. First we find the total man days needed to complete the work when 12 men do it in 14 days. Then we calculate how many man days are used during the first 5 days. The remaining man days are then divided by the new manpower of 15 men per day to get the remaining time in days. This systematic approach avoids confusion and matches how work allocation is handled in real situations.

Step-by-Step Solution:
Step 1: Total work in man days = number of men * days taken by them. Step 2: With 12 men taking 14 days, total work = 12 * 14 = 168 man days. Step 3: In the first 5 days, only 12 men work, so man days used = 12 * 5 = 60 man days. Step 4: Remaining work in man days = 168 - 60 = 108 man days. Step 5: After 5 days, 3 more men join, so total men now = 12 + 3 = 15 men. Step 6: Daily work capacity after joining = 15 man days per day. Step 7: Remaining time required = remaining man days / daily capacity = 108 / 15 days. Step 8: Simplify 108 / 15 = 7.2 days.

Verification / Alternative check:
To verify, calculate total effective days if we convert all work to fractions of the job. For example, 12 men in 1 day complete 12/168 = 1/14 of the work. In 5 days they complete 5/14. The remaining work is 1 - 5/14 = 9/14. Under 15 men, each day they complete 15/168 = 5/56 of the work. Time required = (9/14) / (5/56) = (9/14) * (56/5) = 36/5 = 7.2 days. This confirms our earlier man day calculation.

Why Other Options Are Wrong:
6.5 days and 7.5 days are close but incorrect and arise from rounding mistakes or arithmetic slips. 8.4 days and 9 days are much too large and would overshoot the required work, causing the team to perform more work than necessary. Only 7.2 days exactly satisfies the man day requirements and matches the fraction based verification.

Common Pitfalls:
Some learners mistakenly treat 12 men and 15 men as completing the same work in the same number of days, which ignores the increase in capacity. Others forget to convert the whole job to man days first and try to directly compare fractions without a consistent base. Careful tracking of total work, work already done, and remaining man days is essential for accuracy in such mixed workforce problems.

Final Answer:
After the first 5 days, the enlarged group of 15 men will take 7.2 more days to finish the remaining work.