PSLE The number of girls and boys taking part in a quiz are in the ratio 3 : 7. These pupils are put into two groups. 60% of the girls and 10% of the boys are in Group K. The rest of the pupils are in Group L.
- What is the ratio of the number of pupils in Group L to Group K? Give your answer in the simplest form.
- The number of boys in Group K is more than 50. What is the smallest possible total number of pupils taking part in the quiz?
Girls |
Boys |
30 u |
70 u |
Group K |
Group L |
Group K |
Group L |
18 u |
12 u |
7 u |
63 u |
(a)
Girls : Boys
3 : 7
30 : 70
Number of girls in Group K
= 60% x 30 u
=
60100 x 30 u
= 18 u
Number of girls in Group L
= 30 u - 18 u
= 12 u
Number of boys in Group K
= 10% x 70 u
=
10100 x 70 u
= 7 u
Number of boys in Group L
= 70 u - 7 u
= 63 u
Group K : Group L
12 + 63 : 18 + 7
75 : 25
(÷25)3 : 1
(b)
Number of boys in Group K = 7 u
Since the number of boys in Group K is 7 u, it must be multiple of 7.
Number of sets of 7
= 50 ÷ 7
= 7 r 1
Since the number of boys in Group K is more than 50, the number of sets must be 1 more than 7.
1 u = 7 + 1 = 8
Smallest possible number of pupils
= 30 u + 70 u
= 100 u
= 100 x 8
= 800
Answer(s): (a) 3 : 1; (b) 800