There are 25% more black beads than purple beads in a bag. After Archie removed 40% of the black beads and increased the number of purple beads by 30%, there are now 198 fewer black beads than purple beads. Find the number of purple beads at first.

	Black	Purple
Before	5 u	4 u
Change	- 2 u	+ 1.2 u
After	3 u	5.2 u

Number of black beads in percentage
= 100% + 25%
= 125%

125% = ¹²⁵₁₀₀ = ⁵₄

Number of black beads that Archie removed
= 40% x 5 u
= ⁴⁰₁₀₀ x 5 u 
= 2 u

Number of purple beads that Archie increased 
= 30% x 4 u
= ³⁰₁₀₀  x 4 u
= 1.2 u

Number of black beads in the end
= 5 u - 2 u
= 3 u

Number of purple beads in the end
= 4 u + 1.2 u
= 5.2 u

Number of fewer black beads than purple beads in the end
= 5.2 u - 3 u 
= 2.2 u 

2.2 u = 198

1 u = 198 ÷ 2.2 = 90

Number of purple beads at first
= 4 u
= 4 x 90
= 360

Answer(s): 360