To solve this problem, we need to analyze how the work capacity changes each day as new men join and how this affects the completion of the job. Let's break it down step by step.
Understanding the Work Rate
Initially, we have one man working on the job. Let's assume this man's work capacity is represented as 1 unit of work per day. Now, on the second day, a new man joins, and according to the problem, the capacity of each man doubles. This means that on the second day, each man (the original and the new one) will work at a rate of 2 units per day.
Daily Work Calculation
Now, let's summarize the work done each day:
- Day 1: 1 man x 1 unit = 1 unit
- Day 2: 2 men x 2 units each = 4 units
- Day 3: 3 men x 4 units each = 12 units
- Day 4: 4 men x 8 units each = 32 units
- Day 5: 5 men x 16 units each = 80 units
- Day 6: 6 men x 32 units each = 192 units
How the Rate Changes with New Men
Now, if a new man joins on the second day and it results in each man working at thrice the rate of the previous day, the calculations change significantly:
- Day 1: 1 man x 1 unit = 1 unit
- Day 2: 2 men x 3 units each = 6 units
- Day 3: 3 men x 9 units each = 27 units
- Day 4: 4 men x 27 units each = 108 units
- Day 5: 5 men x 81 units each = 405 units
- Day 6: 6 men x 243 units each = 1458 units
Accumulating Total Work
With this new rate, we can accumulate the total work done over the days. Assuming the job requires a certain total of work units, we can see the exponential growth in the work capacity:
- Total work by Day 1: 1 unit
- Total work by Day 2: 1 + 6 = 7 units
- Total work by Day 3: 7 + 27 = 34 units
- Total work by Day 4: 34 + 108 = 142 units
- Total work by Day 5: 142 + 405 = 547 units
- Total work by Day 6: 547 + 1458 = 2005 units
Determining Job Completion
Given that the job was completed in 6 days under the initial doubling rule, we now want to find out when the work will be completed under the new condition where each man works at thrice the rate. Based on our calculations, we can conclude that the job will be completed well before the sixth day due to the rapid increase in productivity.
Hence, under the new work condition, the job will actually be completed by the end of Day 4, as the cumulative work will exceed the required amount. Therefore, the answer is:
4th Day
