Final Answer:
If all 20 labourers work at the same pace as the first 16 workers, the field will be harvested in 24 days.
Step-by-step explanation:
Let's solve the problem step by step:
We are given that 16 workers can reap a field in 30 days. To determine the number of workers needed to reap the field in 24 days, we can use the concept of worker-days. A worker-day represents the amount of work one worker can complete in one day.
First, let's determine the total amount of worker-days it takes to reap the field:
Total worker-days to reap the field = Number of workers × Number of days they work
Total worker-days to reap the field = 16 workers × 30 days
Total worker-days to reap the field = 480 worker-days
This means that reaping the field requires 480 worker-days of effort.
Now, let's assume we want this same field to be reaped in fewer days, specifically in 24 days. The total amount of work remains the same, but we want it to be completed in 24 days, not 30.
So, we have to figure out how many workers would be needed to complete the same 480 worker-days of effort in only 24 days:
Workers needed for 24 days = Total worker-days to reap the field / Number of days to reap the field
Workers needed for 24 days = 480 worker-days / 24 days
Workers needed for 24 days = 20 workers
Therefore, 20 workers must be engaged to reap the field in 24 days, assuming they all work at the same rate as the initial 16 workers.