Harry School had 450 students and Tim School had 10% more students. When an equal number of students left each school, the ratio of the students in Tim School to that in Harry School became 5 : 4. How many students were there in both schools in the end?

	Harry School	Tim School	Difference
Before	450		45
Change	- ?	- ?
After	5 u	4 u	1 u

Since an equal number of students left each school, the difference in the number of students at first and in the end between the 2 schools remains the same.  Make the difference between the number of students in Harry School and Tim School at first and in the end the same. 

Difference between the number of students in both schools at first
= 10% x 450
= ¹⁰₁₀₀ x 450
= 45

Difference between the number of students in both schools in the end
= 5 u - 4 u
= 1 u

1 u = 45

Total number of students in both schools in the end
= 5 u + 4 u
= 9 u
= 9 x 45
= 405

Answer(s): 405