I'm surely no expert on business mathematics (I can't even balance my check book!) but here is what I think it means:
The cost for some item was 19.25 and it is marked up to selling price P. The amount of the "mark up" is P- 19.25 and that is 35% of the selling price. That is, we have P- 19.25= .35P and can solve that for P: (1- .35)P= .65P= 19.25 so P= 19.25/.65= 29.62 (rounded to the nearest penny).
Now we can calculate that the mark up itself was 29.62- 19.25= 10.37.
Now what percentage of the cost is that? 10.37/19.25= 0.54 (rounded to the nearest hundredth) so the markup of the cost is 54%.
25% of the price is .25(29.62)= 7.41 so after a 25% markdown the reduced price would be 29.62- 7.41= 22.21 (which is still (22.21- 19.25)/19.25= 15% above the cost).