There were 8 more girls than boys in the canteen. Excluding 10 boys, the number of boys was ⁴₅ of the number of girls. When another 12 girls joined, what fraction of the students were girls in the end? Give your answer in its simplest form.

	Girls	Boys
Comparing girls  and boys at first	8 more
Before	5 u	4 u + 10
Change	+ 12
After	5 u + 12	4 u + 10

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

5 u = 4 u + 10 + 8 
5 u - 4 u = 10 + 8

1 u = 18

Total number of girls in the end
= 5 u + 12
= 5 x 18 + 12
= 90 + 12
= 102

Total number of students in the end
= 5 u + 12 + 4 u + 10
= 9 u + 22
= 9 x 18 + 22
= 184

Fraction of the students who were girls in the end
= ¹⁰²₁₈₄
= ⁵¹₉₂

Answer(s): ⁵¹₉₂