PSLE
The number of girls and boys in a gymnasium were in the ratio 1 : 5. After 19.5 girls entered the gymnasium and half the number of boys left the gymnasium, the ratio of the number of girls to boys became 1 : 1. How many children were there in the gymnasium at first?

	girls	boys	Total
Before	1 u	5 u	6 u
Change	+ 19.5	- 2.5 u
After	1 u + 19.5	2.5 u

Number of boys who left the gymnasium
= 5 u ÷ 2
= 2.5 u

Number of girls in the end = 1 u + 19.5
Number of boys in the end = 2.5 u

Since the ratio of the number of girls to boys in the end is 1 : 1, the number of girls and boys in the end is equal.

2.5 u = 1 u + 19.5
2.5 u - 1 u = 19.5
1.5 u = 19.5

1 u = 19.5 ÷ 1.5 = 13

Total number of children in the gymnasium at first
= 1 u + 5 u
= 6 u
= 6 x 13
= 78

Answer(s): 78