PSLE
Nora had a total of 201 purple and black beads. She used 19 purple beads and 90% of the black beads. After that, the ratio of the number of purple beads to black beads Nora had was 3 : 1.

1. What fraction of her black beads was Nora left with? Give your answer in the simplest form.
2. How many more purple beads than black beads did Nora have in the end?

	Purple	Black	Total
Before	3 u + 19	10 u	13 u + 19
Change	- 19	- 9 u
After	3 u	1 u	4 u
Comparing purple beads and black beads in the end	3	1	4

(a)
90% = ⁹⁰₁₀₀ = ⁹₁₀

Fraction of her black beads that Nora used = ⁹₁₀

Fraction of her black beads that Nora was left with
= 1 - ⁹₁₀
= ¹₁₀

(b)
The number of black beads in the end is repeated.
Since the numbers are already the same, we do not need to use LCM to make them the same.

Number of black beads at first = 10 u
Number of purple beads at first = 3 u + 19

Total number of beads at first
= 10 u + 3 u + 19
= 13 u + 19

13 u + 19 = 201
13 u = 201 - 19
13 u = 182

1 u = 182 ÷ 13 = 14

Number of black beads in the end = 1 u
Number of purple beads in the end = 3 u

Number of more purple beads than black beads that Nora had in the end
= 3 u - 1 u
= 2 u
= 2 x 14
= 28

Answer(s): (a)¹₁₀; (b) 28