25 workers completed half the work in 10 days.
Therefore total work = 25 people for 20 days = 500 "person-days" of work.
(To explain, a "person-day" is the unit of work 1 person can complete in 1 day.
So if you have more people, you can complete more person-days of work. If you
have less people, you need to work longer (more "days") to complete the same
person-days" of work.)
Another 250 person-days of work needs to be completed.
But since it needs to be completed in 15 days totally, and 10 days are already
over, this remaining work needs to be completed in 5 days.
i.e. 250 person-days of work needs to be completed in 5 days.
So how many persons do you need? 250 person-days/5 days = 50 people.
Need to add 25 more workers.
Hope you got it :)