20 men can complete a task in 30 days. If one man leaves the site at the end of each day, then what fraction of work will be completed?

To find the fraction of work completed, we need to determine how many men are left on the site each day.

Initially, there are 20 men on the site, and they can complete the task in 30 days. This means that each man contributes 1/20th of the work per day.

On the first day, all 20 men are present, so they complete 20/20 or 1 whole unit of work.

On the second day, one man leaves, so there are 19 men remaining. Each man still contributes 1/20th of the work, so they complete 19/20th of the remaining work.

On the third day, another man leaves, leaving 18 men. They complete 18/20th of the remaining work.

This pattern continues until the 30th day, where only one man is left and he completes 1/20th of the remaining work.

To find the total fraction of work completed, we add up all the fractions from each day.

1/20 + 19/20 + 18/20 + ... + 1/20

This can be simplified to:

(1 + 19 + 18 + ... + 1) / 20

To find the sum of the numbers from 1 to 20, we can use the formula for the sum of an arithmetic series:

Sum = (n/2)(first term + last term)

In this case, the first term is 1, the last term is 20, and the number of terms is 20.

Sum = (20/2)(1 + 20) = 10(21) = 210

So the total fraction of work completed is:

210/20 = 21/2

Therefore, the fraction of work completed when one man leaves the site at the end of each day is 21/2.