Final answer:
The number of workers during the fourth year was approximately 8,736.
Step-by-step explanation:
To determine the number of workers during the fourth year, we need to calculate the number of workers employed at the end of each year based on the given information. Let's start:
- At the end of the first year, 5% of the workers were retrenched. So the number of workers remaining = 8,000 - (5% of 8,000) = 8,000 - (0.05 * 8,000) = 8,000 - 400 = 7,600 workers.
- At the end of the second year, 5% of the workers at that time were retrenched. So the number of workers remaining = 7,600 - (5% of 7,600) = 7,600 - (0.05 * 7,600) = 7,600 - 380 = 7,220 workers.
- To complete the job in time, the number of workers was increased by 10% of those working at the end of the third year. So the number of workers at the end of the third year = 7,220 + (10% of 7,220) = 7,220 + (0.1 * 7,220) = 7,220 + 722 = 7,942 workers.
- Finally, to find the number of workers during the fourth year, we need to consider the previous year's number of workers plus the increased 10%. So the number of workers during the fourth year = 7,942 + (10% of 7,942) = 7,942 + (0.1 * 7,942) = 7,942 + 794.2 ≈ 8,736 workers.
Therefore, there were approximately 8,736 workers during the fourth year.