There were 6 more girls than boys in the auditorium. Excluding 6 boys, the number of boys was ⁴₅ of the number of girls. When another 4 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	6 more
Before	5 u	4 u + 6
Change	+ 4
After	5 u + 4	4 u + 6

Number of girls at first was 6 more than the number of boys. If another 6 boys entered the auditorium at first, the number of girls and boys at first would be the same.

5 u = 4 u + 6 + 6 
5 u - 4 u = 6 + 6

1 u = 12

Total number of girls in the end
= 5 u + 4
= 5 x 12 + 4
= 60 + 4
= 64

Total number of pupils in the end
= 5 u + 4 + 4 u + 6
= 9 u + 10
= 9 x 12 + 10
= 118

Fraction of the pupils who were girls in the end
= ⁶⁴₁₁₈
= ³²₅₉

Answer(s): ³²₅₉