There were 10 more boys than girls in the music room. Excluding 10 girls, the number of girls was ³₄ of the number of boys. When another 11 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	10 more
Before	4 u	3 u + 10
Change	+ 11
After	4 u + 11	3 u + 10

Number of boys at first was 10 more than the number of girls. If another 10 girls entered the music room at first, the number of boys and girls at first would be the same.

4 u = 3 u + 10 + 10 
4 u - 3 u = 10 + 10

1 u = 20

Total number of boys in the end
= 4 u + 11
= 4 x 20 + 11
= 80 + 11
= 91

Total number of pupils in the end
= 4 u + 11 + 3 u + 10
= 7 u + 21
= 7 x 20 + 21
= 161

Fraction of the pupils who were boys in the end
= ⁹¹₁₆₁
= ¹³₂₃

Answer(s): ¹³₂₃