You must first define what you mean by "markup". There are two prevailing versions and they are equally simple to implement so one really cannot be construed over the other.
1) Markup is a percentage of the Wholesale Price. Theoretical limits Example: Cost = $50, Markup = 60%; Retail Price: $50 + 0.60*$50 = $50 + $30 = $80
2) Markup is a percentage of the Retail Price. Theoretical limits [0,1] Example: Cost = $50, Retail Price = $80, Markup = (80-50)/80 = 30/80 = 37.5%
As far as the second part of your question, I am confused by it. How can a 60% markup result in a 25% profit?
Using C = Wholesale Cost
1) C + 0.6*C = 1.6*C = Retail Price, Profit = 60%. It's just the way this markup works.
2) Markup/(C + Markup) = 60% ==> Markup = 150%*C
Maybe I'm just not seeing it, but I'm not.