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 2 : 3. There are 5 times as many contestants in Group B as in Group A. There are 15 less boys in Group A than Group B. What is the total number of contestants in Group A?
Group A |
Group B |
4 u |
5x4 = 20 u |
Boys |
Girls |
Boys |
Girls |
3 u |
1 u |
2x4 = 8 u |
3x4 = 12 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 5 is 20.
Number of less boys in Group A than Group B
= 8 u - 3 u
= 5 u
5 u = 15
1 u = 15 ÷ 5 = 3
Total number of contestants in Group A
= 3 u + 1 u
= 4 u
= 4 x 3
= 12
Answer(s): 12