There were 11 more girls than boys in the tuck shop. Excluding 12 boys, the number of boys was ⁴₅ of the number of girls. When another 5 girls joined, what fraction of the pupils were girls in the end? Give your answer in its simplest form.

	Girls	Boys
Comparing girls  and boys at first	11 more
Before	5 u	4 u + 12
Change	+ 5
After	5 u + 5	4 u + 12

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

5 u = 4 u + 12 + 11 
5 u - 4 u = 12 + 11

1 u = 23

Total number of girls in the end
= 5 u + 5
= 5 x 23 + 5
= 115 + 5
= 120

Total number of pupils in the end
= 5 u + 5 + 4 u + 12
= 9 u + 17
= 9 x 23 + 17
= 224

Fraction of the pupils who were girls in the end
= ¹²⁰₂₂₄
= ¹⁵₂₈

Answer(s): ¹⁵₂₈