PSLE The number of girls and boys taking part in a contest are in the ratio 5 : 7. These pupils are put into two groups. 30% of the girls and 60% of the boys are in Group U. The rest of the pupils are in Group V.
- What is the ratio of the number of pupils in Group V to Group U? Give your answer in the simplest form.
- The number of boys in Group U is more than 90. What is the smallest possible total number of pupils taking part in the contest?
Girls |
Boys |
50 u |
70 u |
Group U |
Group V |
Group U |
Group V |
15 u |
35 u |
42 u |
28 u |
(a)
Girls : Boys
5 : 7
50 : 70
Number of girls in Group U
= 30% x 50 u
=
30100 x 50 u
= 15 u
Number of girls in Group V
= 50 u - 15 u
= 35 u
Number of boys in Group U
= 60% x 70 u
=
60100 x 70 u
= 42 u
Number of boys in Group V
= 70 u - 42 u
= 28 u
Group U : Group V
35 + 28 : 15 + 42
63 : 57
(÷3)21 : 19
(b)
Number of boys in Group U = 42 u
Since the number of boys in Group U is 42 u, it must be multiple of 42.
Number of sets of 42
= 90 ÷ 42
= 2 r 6
Since the number of boys in Group U is more than 90, the number of sets must be 1 more than 2.
1 u = 2 + 1 = 3
Smallest possible number of pupils
= 50 u + 70 u
= 120 u
= 120 x 3
= 360
Answer(s): (a) 21 : 19; (b) 360