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. 40% of the girls and 30% of the boys are in Group T. The rest of the pupils are in Group U.

1. What is the ratio of the number of pupils in Group U to Group T? Give your answer in the simplest form.
2. The number of boys in Group T is more than 90. What is the smallest possible total number of pupils taking part in the test?

Girls		Boys
70 u		40 u
Group T	Group U	Group T	Group U
28 u	42 u	12 u	28 u

(a)
Girls : Boys
7 : 4
70 : 40

Number of girls in Group T
= 40% x 70 u
= ⁴⁰₁₀₀ x 70 u
= 28 u

Number of girls in Group U
= 70 u - 28 u
= 42 u

Number of boys in Group T
= 30% x 40 u
= ³⁰₁₀₀ x 40 u
= 12 u

Number of boys in Group U
= 40 u - 12 u
= 28 u

Group T : Group U
42 + 28 : 28 + 12 
70 : 40 _(÷10)
7 : 4

(b)
Number of boys in Group T = 12 u

Since the number of boys in Group T is 12 u, it must be multiple of 12.

Number of sets of 12
= 90 ÷ 12
= 7 r 6

Since the number of boys in Group T is more than 90, the number of sets must be 1 more than 7.

1 u = 7 + 1 = 8

Smallest possible number of pupils
= 70 u + 40 u
= 110 u
= 110 x 8
= 880

Answer(s): (a) 7 : 4; (b) 880