There are 25% more gold beads than black beads in a bag. After Vincent removed 20% of the gold beads and increased the number of black beads by 10%, there are now 32 fewer gold beads than black beads. Find the number of black beads at first.

	Gold	Black
Before	5 u	4 u
Change	- 1 u	+ 0.4 u
After	4 u	4.4 u

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

125% = ¹²⁵₁₀₀ = ⁵₄

Number of gold beads that Vincent removed
= 20% x 5 u
= ²⁰₁₀₀ x 5 u 
= 1 u

Number of black beads that Vincent increased 
= 10% x 4 u
= ¹⁰₁₀₀  x 4 u
= 0.4 u

Number of gold beads in the end
= 5 u - 1 u
= 4 u

Number of black beads in the end
= 4 u + 0.4 u
= 4.4 u

Number of fewer gold beads than black beads in the end
= 4.4 u - 4 u 
= 0.4 u 

0.4 u = 32

1 u = 32 ÷ 0.4 = 80

Number of black beads at first
= 4 u
= 4 x 80
= 320

Answer(s): 320