Fifty men can build a tank in 40 days. They all start the work together, but every 10 days, 5 men leave the job permanently. After how many total days will the tank be completely built?

Introduction / Context:
This question is a variation of time and work problems where the workforce is not constant over time. Instead, workers leave periodically, and hence the effective daily work done decreases in steps. You must carefully account for the work done in each period with a different number of workers and sum up their contributions until the total work is completed.

Given Data / Assumptions:

• Fifty men can complete the tank construction in 40 days if all remain.
• All 50 start together.
• Every 10 days, 5 men leave and do not return.
• All men have the same constant working efficiency.
• We must find the actual time required to finish the work with this decreasing workforce.

Concept / Approach:
First, calculate the total amount of work in man-days using the constant workforce scenario. Then, break the actual work period into segments of 10 days, during which the workforce is constant. For each segment, compute the work done using the number of men in that segment. Subtract these from the total work until the remaining work becomes zero. The sum of all segment lengths gives the total time required to complete the job.

Step-by-Step Solution:
Total work in man-days = 50 men * 40 days = 2000 man-days. First 10 days: 50 men work, so work done = 50 * 10 = 500 man-days. Men left = 50 − 5 = 45. Next 10 days: 45 men work, so work done = 45 * 10 = 450 man-days. Total = 950. Men left = 45 − 5 = 40. Next 10 days: 40 men work, so work done = 40 * 10 = 400 man-days. Total = 1350. Men left = 40 − 5 = 35. Next 10 days: 35 men work, so work done = 35 * 10 = 350 man-days. Total = 1700. Men left = 35 − 5 = 30. Remaining work = 2000 − 1700 = 300 man-days. With 30 men working, time = 300 / 30 = 10 days. Total time = 10 + 10 + 10 + 10 + 10 = 50 days.

Verification / Alternative check:
You can think of the pattern as five consecutive 10 day blocks with workforces 50, 45, 40, 35 and 30 men. The total man-days = 10 * (50 + 45 + 40 + 35 + 30) = 10 * 200 = 2000 man-days, exactly the required amount of work. This confirms that the work is completed right at the end of the fifth block, which is at 50 days.

Why Other Options Are Wrong:
48 or 49 days would produce fewer than 2000 man-days, so the tank would still be incomplete. 47.5 days is not even aligned with the 10 day step pattern and would require fractional days in the middle of a segment, which does not match the way men leave the work (exactly every 10 days).

Common Pitfalls:
A common mistake is to assume the average workforce and then divide total work by this average, which does not always produce the correct result when the pattern of leaving is in discrete steps. Another mistake is to stop one step too early by miscalculating the remaining work after each segment.

Final Answer:
The tank will be completely built in 50 days.