PSLE The number of girls and boys taking part in a contest are in the ratio 4 : 7. These students are put into two groups. 40% of the girls and 20% of the boys are in Group C. The rest of the students are in Group D.
- What is the ratio of the number of students in Group D to Group C? Give your answer in the simplest form.
- The number of boys in Group C is more than 80. What is the smallest possible total number of students taking part in the contest?
Girls |
Boys |
40 u |
70 u |
Group C |
Group D |
Group C |
Group D |
16 u |
24 u |
14 u |
56 u |
(a)
Girls : Boys
4 : 7
40 : 70
Number of girls in Group C
= 40% x 40 u
=
40100 x 40 u
= 16 u
Number of girls in Group D
= 40 u - 16 u
= 24 u
Number of boys in Group C
= 20% x 70 u
=
20100 x 70 u
= 14 u
Number of boys in Group D
= 70 u - 14 u
= 56 u
Group C : Group D
24 + 56 : 16 + 14
80 : 30
(÷10)8 : 3
(b)
Number of boys in Group C = 14 u
Since the number of boys in Group C is 14 u, it must be multiple of 14.
Number of sets of 14
= 80 ÷ 14
= 5 r 10
Since the number of boys in Group C is more than 80, the number of sets must be 1 more than 5.
1 u = 5 + 1 = 6
Smallest possible number of students
= 40 u + 70 u
= 110 u
= 110 x 6
= 660
Answer(s): (a) 8 : 3; (b) 660