PSLE The number of girls and boys taking part in a quiz are in the ratio 1 : 7. These pupils are put into two groups. 20% of the girls and 40% of the boys are in Group E. The rest of the pupils are in Group F.
- What is the ratio of the number of pupils in Group F to Group E? Give your answer in the simplest form.
- The number of boys in Group E is more than 70. What is the smallest possible total number of pupils taking part in the quiz?
Girls |
Boys |
10 u |
70 u |
Group E |
Group F |
Group E |
Group F |
2 u |
8 u |
28 u |
42 u |
(a)
Girls : Boys
1 : 7
10 : 70
Number of girls in Group E
= 20% x 10 u
=
20100 x 10 u
= 2 u
Number of girls in Group F
= 10 u - 2 u
= 8 u
Number of boys in Group E
= 40% x 70 u
=
40100 x 70 u
= 28 u
Number of boys in Group F
= 70 u - 28 u
= 42 u
Group E : Group F
8 + 42 : 2 + 28
50 : 30
(÷10)5 : 3
(b)
Number of boys in Group E = 28 u
Since the number of boys in Group E is 28 u, it must be multiple of 28.
Number of sets of 28
= 70 ÷ 28
= 2 r 14
Since the number of boys in Group E is more than 70, 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) 5 : 3; (b) 240