At first, the ratio of the number of boys to the number of girls at a bird park was 3 : 5. When 42 girls and some boys entered the bird park, the number of girls increased by 12% and the total number of children at the bird park increased by 20%.

1. How many boys were there at first?
2. What percentage of the children at the bird park were boys in the end? Express your answer as a mixed number.

(a)

Boys	Girls	Total
3 u	5 u	8 u
(+ 70)	+ 0.6 u (+ 42)	+ 1.6 u (+ 112)
3 u + 70	5.6 u	9.6 u

Number of girls that entered the bird park
= 12% x 5 u
= ¹²₁₀₀ x 5 u
= 0.6 u

0.6 u = 42

1 u = 42 ÷ 0.6 = 70

Number of boys at first
= 3 u
= 3 x 70
= 210

(b)
Increase in the number of children
= 20% x 8 u
= ²⁰₁₀₀ x 8 u
= 1.6 u

Total number of children at the bird park in the end
= 8 u + 1.6 u
= 9.6 u
= 9.6 x 70
= 672

Increase in the number of boys
= 112 - 42
= 70

Total number of boys in the end
= 3 u + 70
= 3 x 70 + 70
= 280

Percentage of children who were boys
= ²⁸⁰₆₇₂ x 100
= 41²₃%

Answer(s): (a) 210; (b) 41²₃%