PSLE
The contestants at a contest are divided in Group A and Group B. The ratio of the number of girls to boys in Group A is 3 : 1. The ratio of the number of girls to boys in Group B is 9 : 1. There are 5 times as many contestants in Group B as in Group A. There are 135 less girls in Group A than Group B. What is the total number of contestants in Group A?

Group A		Group B
4 u		10x2 = 20 u
Girls	Boys	Girls	Boys
3 u	1 u	9x2 = 18 u	1x2 = 2 u

Total number of contestants in Group A
= 3 u + 1 u
= 4 u

Total number of contestants in Group B
= 5 x 4 u
= 20 u

The total number of contestants in Group B is repeated.
Use LCM to make the total number of contestants in Group B the same.
LCM of 20 and 10 is 20.

Number of less girls in Group A than Group B
= 18 u - 3 u
= 15 u

15 u = 135

1 u = 135 ÷ 15 = 9

Total number of contestants in Group A
= 3 u + 1 u
= 4 u
= 4 x 9
= 36

Answer(s): 36