If 75 men can complete a piece of work in 20 days.  How much longer will it take to complete the work by 50 men? 

30 days.
Explanation:
With the 75 men case:
One day work = 1 / 20
One man’s one day work = 1 / ( 20 * 75)
Now with the 50 men case:
No. Of workers = 50
One day work = 50 * 1 / ( 20 * 75)

The total number of days required to complete the work = (75 * 20) / 50 = 30 days.