PSLE
The number of girls and boys taking part in a test are in the ratio 4 : 5. These students are put into two groups. 30% of the girls and 40% of the boys are in Group J. The rest of the students are in Group K.

1. What is the ratio of the number of students in Group K to Group J? Give your answer in the simplest form.
2. The number of boys in Group J is more than 70. What is the smallest possible total number of students taking part in the test?

Girls		Boys
40 u		50 u
Group J	Group K	Group J	Group K
12 u	28 u	20 u	30 u

(a)
Girls : Boys
4 : 5
40 : 50

Number of girls in Group J
= 30% x 40 u
= ³⁰₁₀₀ x 40 u
= 12 u

Number of girls in Group K
= 40 u - 12 u
= 28 u

Number of boys in Group J
= 40% x 50 u
= ⁴⁰₁₀₀ x 50 u
= 20 u

Number of boys in Group K
= 50 u - 20 u
= 30 u

Group J : Group K
28 + 30 : 12 + 20 
58 : 32 _(÷2)
29 : 16

(b)
Number of boys in Group J = 20 u

Since the number of boys in Group J is 20 u, it must be multiple of 20.

Number of sets of 20
= 70 ÷ 20
= 3 r 10

Since the number of boys in Group J is more than 70, the number of sets must be 1 more than 3.

1 u = 3 + 1 = 4

Smallest possible number of students
= 40 u + 50 u
= 90 u
= 90 x 4
= 360

Answer(s): (a) 29 : 16; (b) 360