PSLE The number of girls and boys taking part in a quiz are in the ratio 8 : 7. These students are put into two groups. 10% of the girls and 60% of the boys are in Group P. The rest of the students are in Group Q.
- What is the ratio of the number of students in Group Q to Group P? Give your answer in the simplest form.
- The number of boys in Group P is more than 90. What is the smallest possible total number of students taking part in the quiz?
Girls |
Boys |
80 u |
70 u |
Group P |
Group Q |
Group P |
Group Q |
8 u |
72 u |
42 u |
28 u |
(a)
Girls : Boys
8 : 7
80 : 70
Number of girls in Group P
= 10% x 80 u
=
10100 x 80 u
= 8 u
Number of girls in Group Q
= 80 u - 8 u
= 72 u
Number of boys in Group P
= 60% x 70 u
=
60100 x 70 u
= 42 u
Number of boys in Group Q
= 70 u - 42 u
= 28 u
Group P : Group Q
72 + 28 : 8 + 42
100 : 50
(÷50)2 : 1
(b)
Number of boys in Group P = 42 u
Since the number of boys in Group P is 42 u, it must be multiple of 42.
Number of sets of 42
= 90 ÷ 42
= 2 r 6
Since the number of boys in Group P is more than 90, the number of sets must be 1 more than 2.
1 u = 2 + 1 = 3
Smallest possible number of students
= 80 u + 70 u
= 150 u
= 150 x 3
= 450
Answer(s): (a) 2 : 1; (b) 450