Question

50 men can compete a work in 28 days. They started the work together, but at the end of each 10 day, 10 men left the job. The work was completed in how many days?

Answer 1

We need a total of `50 times 28=1400` man days. After 10 days we got `50 times 10=500` man days, then `400` more after ten more days, then `300,` then `200` for a total of `1400` man days over 40 days.

Explanation:

I'm not sure what to add for a more detailed explanation as requested.

50 men can complete all the work in 28 days. We assume a fully scalable task; 100 men would take 14 days. So we need a total of `50 times 28 = 1400` man-days to complete the project. That could be one man working for 1400 days or 1400 men working for one day or something in between.

We need 1400 man days. After 10 days of 50 men working, we've finished 500 man days. After 10 more days of 40 men working, we finish 400 man days. So we've done 900 man days of work the first 20 days.

For the third 10 day period, we have 30 men, so get 300 man days more completed. We're up to 1200 man days.

For the fourth 10 day period, we have 20 men, so 200 more man days, for a running total of 1400 man days. That happens to be exactly how many we needed, so we're done with the problem, and with the task in 40 days.