PSLE The number of boys and girls taking part in a test are in the ratio 1 : 4. These pupils are put into two groups. 70% of the boys and 20% of the girls 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 K is fewer than 50. What is the largest possible total number of pupils taking part in the test?
Boys |
Girls |
10 u |
40 u |
Group J |
Group K |
Group J |
Group K |
7 u |
3 u |
8 u |
32 u |
(a)
Boys : Girls
1 : 4
10 : 40
Number of boys in Group J
= 70% x 10 u
=
70100 x 10 u
= 7 u
Number of boys in Group K
= 10 u - 7 u
= 3 u
Number of girls in Group J
= 20% x 40 u
=
20100 x 40 u
= 8 u
Number of girls in Group K
= 40 u - 8 u
= 32 u
Group K : Group J
3 + 32 : 7 + 8
35 : 15
(÷5)7 : 3
(b)
Number of boys in Group K = 3 u
Since the number of boys in Group K is 3 u, it must be multiple of 3.
Number of sets of 3
= 50 ÷ 3
= 16 r 2
Since the number of boys in Group K is less than 50, the number of sets must be 16.
1 u = 16
Largest possible number of pupils
= 10 u + 40 u
= 50 u
= 50 x 16
= 800
Answer(s): (a) 7 : 3; (b) 800