Question

25 men are employed to do a work in, which they could finish in 20 days but they drop off by 5 men at the end of every 10 days. In what time will the work be completed?

Answer 1

The work finishes on the 24th day.

Explanation:

We start with 25 men. They can do a job in 20 days. This means that the 25 men finish `1/20` of the job each day. This means that each man (using `m` to mean the work a man does each day) does:

`25m=1/20=>m=1/500` of the job each day.

At the end of 10 days, the 25 men will have finished:

`(1/500)(25)(10)=250/500=1/2` of the job.

And now we drop off 5 men, leaving 20 left. We have `1/2` of the job to do:

`(1/500)(20)(10)=200/500=2/5`

Now the job is `1/2+2/5=5/10+4/10=9/10` done, leaving `1/10` to do. We drop off 5 men, leaving 15. They should finish before the 10 days are up:

`(1/500)(15)(10)=150/500=3/10`

And they do. In fact, they can do the remaining work 3 times over. This means they'll finish on the 4th day:

`(1/500)(15)(3)=45/500<1/10`

`(1/500)(15)(4)=60/500>1/10`

Answer 2

The time taken will be `23 1/3` days, so the work will be completed by the `24th` day.

Explanation:

We are working with inverse proportion where, as the number of people decreases, the time taken to finish a task will increase.
Find the constant first.

`x xx y =k`

The total task requires `25 xx20 = 500` 'man-days'

In the first `10` days, `25xx10 = 250` 'man-days.', which means that the task is half completed.

For the next `10` days there are only `20` men.

The amount of work completed is: `20xx10 = 200` 'man-days'.

There are then `15` men left to complete the remaining amount of work.

`500-250-200 =50` 'man-days'

The work can be completed in:

`50/15 = 3 1/3` days

The total time taken is therefore `10+10+3 1/3` days

The work will be completed on the `24th` day.