PSLE The number of girls and boys taking part in a test are in the ratio 1 : 4. These pupils are put into two groups. 60% of the girls and 20% of the boys are in Group N. The rest of the pupils are in Group P.
- What is the ratio of the number of pupils in Group P to Group N? Give your answer in the simplest form.
- The number of girls in Group P is fewer than 50. What is the largest possible total number of pupils taking part in the test?
Girls |
Boys |
10 u |
40 u |
Group N |
Group P |
Group N |
Group P |
6 u |
4 u |
8 u |
32 u |
(a)
Girls : Boys
1 : 4
10 : 40
Number of girls in Group N
= 60% x 10 u
=
60100 x 10 u
= 6 u
Number of girls in Group P
= 10 u - 6 u
= 4 u
Number of boys in Group N
= 20% x 40 u
=
20100 x 40 u
= 8 u
Number of boys in Group P
= 40 u - 8 u
= 32 u
Group P : Group N
4 + 32 : 6 + 8
36 : 14
(÷2)18 : 7
(b)
Number of girls in Group P = 4 u
Since the number of girls in Group P is 4 u, it must be multiple of 4.
Number of sets of 4
= 50 ÷ 4
= 12 r 2
Since the number of girls in Group P is less than 50, the number of sets must be 12.
1 u = 12
Largest possible number of pupils
= 10 u + 40 u
= 50 u
= 50 x 12
= 600
Answer(s): (a) 18 : 7; (b) 600