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. 80% of the girls and 40% of the boys are in Group J. The rest of the pupils are in Group K.
- What is the ratio of the number of pupils in Group K to Group J? Give your answer in the simplest form.
- The number of boys in Group J is more than 50. What is the smallest possible total number of pupils taking part in the test?
Girls |
Boys |
10 u |
40 u |
Group J |
Group K |
Group J |
Group K |
8 u |
2 u |
16 u |
24 u |
(a)
Girls : Boys
1 : 4
10 : 40
Number of girls in Group J
= 80% x 10 u
=
80100 x 10 u
= 8 u
Number of girls in Group K
= 10 u - 8 u
= 2 u
Number of boys in Group J
= 40% x 40 u
=
40100 x 40 u
= 16 u
Number of boys in Group K
= 40 u - 16 u
= 24 u
Group J : Group K
2 + 24 : 8 + 16
26 : 24
(÷2)13 : 12
(b)
Number of boys in Group J = 16 u
Since the number of boys in Group J is 16 u, it must be multiple of 16.
Number of sets of 16
= 50 ÷ 16
= 3 r 2
Since the number of boys in Group J is more than 50, the number of sets must be 1 more than 3.
1 u = 3 + 1 = 4
Smallest possible number of pupils
= 10 u + 40 u
= 50 u
= 50 x 4
= 200
Answer(s): (a) 13 : 12; (b) 200