There are 25% more purple coins than gold coins in a bag. After Charlie removed 40% of the purple coins and increased the number of gold coins by 10%, there are now 112 fewer purple coins than gold coins. Find the number of gold coins at first.

	Purple	Gold
Before	5 u	4 u
Change	- 2 u	+ 0.4 u
After	3 u	4.4 u

Number of purple coins in percentage
= 100% + 25%
= 125%

125% = ¹²⁵₁₀₀ = ⁵₄

Number of purple coins that Charlie removed
= 40% x 5 u
= ⁴⁰₁₀₀ x 5 u 
= 2 u

Number of gold coins that Charlie increased 
= 10% x 4 u
= ¹⁰₁₀₀  x 4 u
= 0.4 u

Number of purple coins in the end
= 5 u - 2 u
= 3 u

Number of gold coins in the end
= 4 u + 0.4 u
= 4.4 u

Number of fewer purple coins than gold coins in the end
= 4.4 u - 3 u 
= 1.4 u 

1.4 u = 112

1 u = 112 ÷ 1.4 = 80

Number of gold coins at first
= 4 u
= 4 x 80
= 320

Answer(s): 320