PSLE
The contestants at a contest are divided in Group A and Group B. The ratio of the number of boys to girls in Group A is 3 : 1. The ratio of the number of boys to girls in Group B is 7 : 1. There are 4 times as many contestants in Group B as in Group A. There are 165 more boys in Group B than Group A. What is the total number of girls?

Group A		Group B
4 u		8x2 = 16 u
Boys	Girls	Boys	Girls
3 u	1 u	7x2 = 14 u	1x2 = 2 u

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

Total number of contestants in Group B
= 4 x 4 u
= 16 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 16 and 8 is 16.

Number of more boys in Group B than Group A
= 14 u - 3 u
= 11 u

11 u = 165

1 u = 165 ÷ 11 = 15

Total number of girls
= 1 u + 2 u
= 3 u
= 3 x 15
= 45

Answer(s): 45