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 7 : 3. The ratio of the number of boys to girls in Group B is 7 : 8. There are 3 times as many contestants in Group B as in Group A. There are 84 more boys in Group B than Group A. What is the total number of contestants?

Group A		Group B
10 u		15x2 = 30 u
Boys	Girls	Boys	Girls
7 u	3 u	7x2 = 14 u	8x2 = 16 u

Total number of contestants in Group A
= 7 u + 3 u
= 10 u

Total number of contestants in Group B
= 3 x 10 u
= 30 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 30 and 15 is 30.

Number of more boys in Group B than Group A
= 14 u - 7 u
= 7 u

7 u = 84

1 u = 84 ÷ 7 = 12

Total number of contestants
= 7 u + 3 u + 14 u + 16 u
= 40 u
= 40 x 12
= 480

Answer(s): 480