25 men can reap a field in 20 days. when should 15 men leave the work, if the whole field is to be reaped in 37 1/ 2 days after they leave the work?

Let 15 men work for m days.
Work done in 1 days = m/20
Remaining work = (1 - m/20)
25 men's 1 days work = 1/20
1 man's 1 days work = (1/20) x (1/25) = 1/500
10 men's 1 days work = 10/500 = 1/50
10 men's 75/2 days work = (1/50) x (75/2) = 75/100 = 3/4
∴ (1 - m/20) = 3/4
⇒ m/20 = 1/4
⇒ m = (1/4) x 20 = 5
Clearly, 15 men leave after 5 days.