PSLE
Billy had a collection of pencils, files and punchers. He had 16 pencils. 40% of his collection was files. He had 12 fewer files than punchers.

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

(a)
40% = ⁴⁰₁₀₀ = ²₅

Number of files = 2 u
Number of punchers = 2 u + 12
Number of pencils = 16
Total number of items = 5 u

5 u = 2 u + 2 u + 12 + 16
5 u - 4 u = 28
1 u = 28

Number of files
= 2 u
= 2 x 28
= 56

(b)
Total number of items at first
= 5 u
= 5 x 28
= 140

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

Number of items after giving away some files
= 80% x 140
= ⁸⁰₁₀₀ x 140
= 112

Number of punchers and pencils
= 5 u - 2 u
= 3 u
= 3 x 28
= 84

Number of files left
= 112 - 84
= 28

Percentage of his collection that was files after that
= ²⁸₁₁₂ x 100%
= 25%

Answer(s): (a) 56; (b) 25%