There were 4 more girls than boys in the school hall. Excluding 12 boys, the number of boys was ²₃ of the number of girls. When another 10 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	4 more
Before	3 u	2 u + 12
Change	+ 10
After	3 u + 10	2 u + 12

Number of girls at first was 4 more than the number of boys. If another 4 boys entered the school hall at first, the number of girls and boys at first would be the same.

3 u = 2 u + 12 + 4 
3 u - 2 u = 12 + 4

1 u = 16

Total number of girls in the end
= 3 u + 10
= 3 x 16 + 10
= 48 + 10
= 58

Total number of students in the end
= 3 u + 10 + 2 u + 12
= 5 u + 22
= 5 x 16 + 22
= 102

Fraction of the students who were girls in the end
= ⁵⁸₁₀₂
= ²⁹₅₁

Answer(s): ²⁹₅₁