PSLE The number of girls and boys taking part in a quiz are in the ratio 4 : 7. These students are put into two groups. 20% of the girls and 40% of the boys are in Group V. The rest of the students are in Group W.
- What is the ratio of the number of students in Group W to Group V? Give your answer in the simplest form.
- The number of girls in Group W is fewer than 90. What is the largest possible total number of students taking part in the quiz?
Girls |
Boys |
40 u |
70 u |
Group V |
Group W |
Group V |
Group W |
8 u |
32 u |
28 u |
42 u |
(a)
Girls : Boys
4 : 7
40 : 70
Number of girls in Group V
= 20% x 40 u
=
20100 x 40 u
= 8 u
Number of girls in Group W
= 40 u - 8 u
= 32 u
Number of boys in Group V
= 40% x 70 u
=
40100 x 70 u
= 28 u
Number of boys in Group W
= 70 u - 28 u
= 42 u
Group W : Group V
32 + 42 : 8 + 28
74 : 36
(÷2)37 : 18
(b)
Number of girls in Group W = 32 u
Since the number of girls in Group W is 32 u, it must be multiple of 32.
Number of sets of 32
= 90 ÷ 32
= 2 r 26
Since the number of girls in Group W is less than 90, the number of sets must be 2.
1 u = 2
Largest possible number of students
= 40 u + 70 u
= 110 u
= 110 x 2
= 220
Answer(s): (a) 37 : 18; (b) 220