The number of boys to the number of girls in Primary 5 Gentleness was 2 : 5. The number of boys to the number of girls in Primary 5 Patience was 4 : 5. Both classes had the same number of boys. When 10 girls from Primary 5 Gentleness joined Primary 5 Patience, the ratio of the number of boys to the number of girls in Primary 5 Gentleness became 1 : 2. Find the total enrolment of both classes.

Primary 5 Gentleness		Primary 5 Patience
Boys	Girls	Boys	Girls
2x2	5x2	4x1	5x1
1x4		1x4
4 u	10 u	4 u	5 u

The number of boys in both classes is the same.  Make the number of boys the same.  LCM of 2 and 4 is 4.

	Primary 5 Gentleness		Primary 5 Patience
	Boys	Girls	Boys	Girls
Before	4 u	10 u	4 u	5 u
Change		- 10		+ 10
After	1x4 = 4 u	2x4 = 8 u	4 u	5 u + 10

The number of boys in Primary 5 Gentleness remains unchanged.  Make the number of boys in Primary 5 the same.  LCM of 4 and 1 is 4.

Number of girls from Primary 5 Gentleness that joined Primary 5 Patience
= 10 u - 8 u
= 2 u

2 u = 10

1 u = 10 ÷ 2 = 5

Total enrolment of both classes
= 4 u + 10 u + 4 u + 5 u
= 23 u
= 23 x 5
= 115

Answer(s): 115