PSLE The number of girls and boys taking part in a quiz are in the ratio 4 : 5. These pupils are put into two groups. 20% of the girls and 60% of the boys are in Group L. The rest of the pupils are in Group M.
- What is the ratio of the number of pupils in Group M to Group L? Give your answer in the simplest form.
- The number of boys in Group L is more than 80. What is the smallest possible total number of pupils taking part in the quiz?
Girls |
Boys |
40 u |
50 u |
Group L |
Group M |
Group L |
Group M |
8 u |
32 u |
30 u |
20 u |
(a)
Girls : Boys
4 : 5
40 : 50
Number of girls in Group L
= 20% x 40 u
=
20100 x 40 u
= 8 u
Number of girls in Group M
= 40 u - 8 u
= 32 u
Number of boys in Group L
= 60% x 50 u
=
60100 x 50 u
= 30 u
Number of boys in Group M
= 50 u - 30 u
= 20 u
Group L : Group M
32 + 20 : 8 + 30
52 : 38
(÷2)26 : 19
(b)
Number of boys in Group L = 30 u
Since the number of boys in Group L is 30 u, it must be multiple of 30.
Number of sets of 30
= 80 ÷ 30
= 2 r 20
Since the number of boys in Group L is more than 80, the number of sets must be 1 more than 2.
1 u = 2 + 1 = 3
Smallest possible number of pupils
= 40 u + 50 u
= 90 u
= 90 x 3
= 270
Answer(s): (a) 26 : 19; (b) 270