Trip by bus

The 80 students of a school go on field trips. Since the course is made up of 40 boys and 40 girls, the teachers decide that in one coach the 40 boys travel and in the other the 40 girls since both buses have 40 seats.

Halfway, the bus drivers stop to refuel and 10 of the boys take the opportunity to get on the girls' coach. When they resume the march, the drivers realize that in one of the buses there are more passengers than seats and they lower the students who do not have a seat without noticing if they are boys or girls so that 10 of them change buses.

At this point, we have some boys in the girls coach and some girls in the boys coach.

How can we know if there are more boys in the girls coach or more girls in the boys coach?

Solution

The proportion will be the same in both coaches, that is, regardless of the number of girls or boys that will change buses, we will have the same number of boys in the girls 'coach as girls in the boys' coach. The explanation is simple and is that the boys who finally remain in the girls 'coach leave the same number of free places that the girls who remain in the boys' coach must necessarily occupy.