There were 12 more boys than girls in the tuck shop. Excluding 2 girls, the number of girls was ⁴₅ of the number of boys. When another 12 boys joined, what fraction of the students were boys in the end? Give your answer in its simplest form.

	Boys	Girls
Comparing boys  and girls at first	12 more
Before	5 u	4 u + 2
Change	+ 12
After	5 u + 12	4 u + 2

Number of boys at first was 12 more than the number of girls. If another 12 girls entered the tuck shop at first, the number of boys and girls at first would be the same.

5 u = 4 u + 2 + 12 
5 u - 4 u = 2 + 12

1 u = 14

Total number of boys in the end
= 5 u + 12
= 5 x 14 + 12
= 70 + 12
= 82

Total number of students in the end
= 5 u + 12 + 4 u + 2
= 9 u + 14
= 9 x 14 + 14
= 140

Fraction of the students who were boys in the end
= ⁸²₁₄₀
= ⁴¹₇₀

Answer(s): ⁴¹₇₀