There are 25% more yellow marbles than purple marbles in a bag. After Archie removed 40% of the yellow marbles and increased the number of purple marbles by 30%, there are now 220 fewer yellow marbles than purple marbles. Find the number of purple marbles at first.

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

Number of yellow marbles in percentage
= 100% + 25%
= 125%

125% = ¹²⁵₁₀₀ = ⁵₄

Number of yellow marbles that Archie removed
= 40% x 5 u
= ⁴⁰₁₀₀ x 5 u 
= 2 u

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

Number of yellow marbles in the end
= 5 u - 2 u
= 3 u

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

Number of fewer yellow marbles than purple marbles in the end
= 5.2 u - 3 u 
= 2.2 u 

2.2 u = 220

1 u = 220 ÷ 2.2 = 100

Number of purple marbles at first
= 4 u
= 4 x 100
= 400

Answer(s): 400