There were 8 more boys than girls in the classroom. Excluding 12 girls, the number of girls was ⁴₅ of the number of boys. When another 8 boys joined, what fraction of the pupils were boys in the end? Give your answer in its simplest form.

	Boys	Girls
Comparing boys  and girls at first	8 more
Before	5 u	4 u + 12
Change	+ 8
After	5 u + 8	4 u + 12

Number of boys at first was 8 more than the number of girls. If another 8 girls entered the classroom at first, the number of boys and girls at first would be the same.

5 u = 4 u + 12 + 8 
5 u - 4 u = 12 + 8

1 u = 20

Total number of boys in the end
= 5 u + 8
= 5 x 20 + 8
= 100 + 8
= 108

Total number of pupils in the end
= 5 u + 8 + 4 u + 12
= 9 u + 20
= 9 x 20 + 20
= 200

Fraction of the pupils who were boys in the end
= ¹⁰⁸₂₀₀
= ²⁷₅₀

Answer(s): ²⁷₅₀