There were 11 more boys than girls in the canteen. Excluding 10 girls, the number of girls was ²₃ of the number of boys. When another 7 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	11 more
Before	3 u	2 u + 10
Change	+ 7
After	3 u + 7	2 u + 10

Number of boys at first was 11 more than the number of girls. If another 11 girls entered the canteen at first, the number of boys and girls at first would be the same.

3 u = 2 u + 10 + 11 
3 u - 2 u = 10 + 11

1 u = 21

Total number of boys in the end
= 3 u + 7
= 3 x 21 + 7
= 63 + 7
= 70

Total number of students in the end
= 3 u + 7 + 2 u + 10
= 5 u + 17
= 5 x 21 + 17
= 122

Fraction of the students who were boys in the end
= ⁷⁰₁₂₂
= ³⁵₆₁

Answer(s): ³⁵₆₁