PSLE The number of girls and boys taking part in a test are in the ratio 7 : 4. These pupils are put into two groups. 60% of the girls and 10% of the boys are in Group M. The rest of the pupils are in Group N.
- What is the ratio of the number of pupils in Group N to Group M? Give your answer in the simplest form.
- The number of boys in Group M is more than 70. What is the smallest possible total number of pupils taking part in the test?
Girls |
Boys |
70 u |
40 u |
Group M |
Group N |
Group M |
Group N |
42 u |
28 u |
4 u |
36 u |
(a)
Girls : Boys
7 : 4
70 : 40
Number of girls in Group M
= 60% x 70 u
=
60100 x 70 u
= 42 u
Number of girls in Group N
= 70 u - 42 u
= 28 u
Number of boys in Group M
= 10% x 40 u
=
10100 x 40 u
= 4 u
Number of boys in Group N
= 40 u - 4 u
= 36 u
Group M : Group N
28 + 36 : 42 + 4
64 : 46
(÷2)32 : 23
(b)
Number of boys in Group M = 4 u
Since the number of boys in Group M is 4 u, it must be multiple of 4.
Number of sets of 4
= 70 ÷ 4
= 17 r 2
Since the number of boys in Group M is more than 70, the number of sets must be 1 more than 17.
1 u = 17 + 1 = 18
Smallest possible number of pupils
= 70 u + 40 u
= 110 u
= 110 x 18
= 1980
Answer(s): (a) 32 : 23; (b) 1980