PSLE
Valen had a collection of punchers, folders and rulers. He had 48 punchers. 30% of his collection was folders. He had 32 fewer folders than rulers.

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

(a)
30% = ³⁰₁₀₀ = ³₁₀

Number of folders = 3 u
Number of rulers = 3 u + 32
Number of punchers = 48
Total number of items = 10 u

10 u = 3 u + 3 u + 32 + 48
10 u - 6 u = 80
4 u = 80

1 u = 80 ÷ 4 = 20

Number of folders
= 3 u
= 3 x 20
= 60

(b)
Total number of items at first
= 10 u
= 10 x 20
= 200

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

Number of items after giving away some folders
= 80% x 200
= ⁸⁰₁₀₀ x 200
= 160

Number of rulers and punchers
= 10 u - 3 u
= 7 u
= 7 x 20
= 140

Number of folders left
= 160 - 140
= 20

Percentage of his collection that was folders after that
= ²⁰₁₆₀ x 100%
= 12.5%

Answer(s): (a) 60; (b) 12.5%