PSLE The number of boys and girls taking part in a test are in the ratio 1 : 2. These students are put into two teams. 60% of the boys and 20% of the girls are in Team P. The rest of the students are in Team Q.
- What is the ratio of the number of students in Team Q to Team P? Give your answer in the simplest form.
- The number of girls in Team P is more than 70. What is the smallest possible total number of students taking part in the test?
Boys |
Girls |
10 u |
20 u |
Team P |
Team Q |
Team P |
Team Q |
6 u |
4 u |
4 u |
16 u |
(a)
Boys : Girls
1 : 2
10 : 20
Number of boys in Team P
= 60% x 10 u
=
60100 x 10 u
= 6 u
Number of boys in Team Q
= 10 u - 6 u
= 4 u
Number of girls in Team P
= 20% x 20 u
=
20100 x 20 u
= 4 u
Number of girls in Team Q
= 20 u - 4 u
= 16 u
Team P : Team Q
4 + 16 : 6 + 4
20 : 10
(÷10)2 : 1
(b)
Number of girls in Team P = 4 u
Since the number of girls in Team P is 4 u, it must be multiple of 4.
Number of sets of 4
= 70 ÷ 4
= 17 r 2
Since the number of girls in Team P is more than 70, the number of sets must be 1 more than 17.
1 u = 17 + 1 = 18
Smallest possible number of students
= 10 u + 20 u
= 30 u
= 30 x 18
= 540
Answer(s): (a) 2 : 1; (b) 540