Fifteen people working at the same rate would complete some work in 10 days. How many days would 6 people need to complete the same work?

so you need 15(10) or 150 man-days to do the job

so with 6 men you would need 150/6 or 25 days

or

use a ratio

15/6 = x/10
6x = 150
x = 25