There are 25% more white cards than purple cards in a bag. After Carl removed 40% of the white cards and increased the number of purple cards by 20%, there are now 162 fewer white cards than purple cards. Find the number of purple cards at first.

	White	Purple
Before	5 u	4 u
Change	- 2 u	+ 0.8 u
After	3 u	4.8 u

Number of white cards in percentage
= 100% + 25%
= 125%

125% = ¹²⁵₁₀₀ = ⁵₄

Number of white cards that Carl removed
= 40% x 5 u
= ⁴⁰₁₀₀ x 5 u 
= 2 u

Number of purple cards that Carl increased 
= 20% x 4 u
= ²⁰₁₀₀  x 4 u
= 0.8 u

Number of white cards in the end
= 5 u - 2 u
= 3 u

Number of purple cards in the end
= 4 u + 0.8 u
= 4.8 u

Number of fewer white cards than purple cards in the end
= 4.8 u - 3 u 
= 1.8 u 

1.8 u = 162

1 u = 162 ÷ 1.8 = 90

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

Answer(s): 360