PSLE The number of girls and boys taking part in a test are in the ratio 1 : 7. These pupils are put into two groups. 50% of the girls and 30% of the boys are in Group X. The rest of the pupils are in Group Y.
- What is the ratio of the number of pupils in Group Y to Group X? Give your answer in the simplest form.
- The number of boys in Group X is more than 50. What is the smallest possible total number of pupils taking part in the test?
Girls |
Boys |
10 u |
70 u |
Group X |
Group Y |
Group X |
Group Y |
5 u |
5 u |
21 u |
49 u |
(a)
Girls : Boys
1 : 7
10 : 70
Number of girls in Group X
= 50% x 10 u
=
50100 x 10 u
= 5 u
Number of girls in Group Y
= 10 u - 5 u
= 5 u
Number of boys in Group X
= 30% x 70 u
=
30100 x 70 u
= 21 u
Number of boys in Group Y
= 70 u - 21 u
= 49 u
Group X : Group Y
5 + 49 : 5 + 21
54 : 26
(÷2)27 : 13
(b)
Number of boys in Group X = 21 u
Since the number of boys in Group X is 21 u, it must be multiple of 21.
Number of sets of 21
= 50 ÷ 21
= 2 r 8
Since the number of boys in Group X is more than 50, the number of sets must be 1 more than 2.
1 u = 2 + 1 = 3
Smallest possible number of pupils
= 10 u + 70 u
= 80 u
= 80 x 3
= 240
Answer(s): (a) 27 : 13; (b) 240