PSLE
Jack had a collection of highlighters, pencils and foolscaps. He had 19 highlighters. 30% of his collection was pencils. He had 13 fewer pencils than foolscaps.

1. How many pencils did Jack have?
2. Jack gave away some pencils. His total collection decreased by 20%. What percentage of his collection was pencils after that?

(a)
30% = ³⁰₁₀₀ = ³₁₀

Number of pencils = 3 u
Number of foolscaps = 3 u + 13
Number of highlighters = 19
Total number of items = 10 u

10 u = 3 u + 3 u + 13 + 19
10 u - 6 u = 32
4 u = 32

1 u = 32 ÷ 4 = 8

Number of pencils
= 3 u
= 3 x 8
= 24

(b)
Total number of items at first
= 10 u
= 10 x 8
= 80

Total collection in the end in percent
= 100% - 20%
= 80%

Number of items after giving away some pencils
= 80% x 80
= ⁸⁰₁₀₀ x 80
= 64

Number of foolscaps and highlighters
= 10 u - 3 u
= 7 u
= 7 x 8
= 56

Number of pencils left
= 64 - 56
= 8

Percentage of his collection that was pencils after that
= ⁸₆₄ x 100%
= 12.5%

Answer(s): (a) 24; (b) 12.5%