Find the cost, given that reducing the selling price from 1080 to 1026 increased the loss by 4% 
When a shopkeeper reduces the selling price of an article from 1080 to
  1026 his loss increases by 4% . What is the cost price of article?

Solution of book : 
4% CP =  1080-1026
CP = 1350
Easy enough. Now see very similar question (came in exam):

If a man reduces the selling price of a fan from rs 1250 to Rs 1000,
  his loss increases by 20%. The cost price of the fan is

Answer Options : 


*

*2400

*2450

*2500

*2350


Now if we apply method which we had applied on first question , you wouldn't find your answer in one of the options even! . So let's try diff method
CP - 1250 = 5x //eq no. 1 //here 5x is total loss amount, since the old and new loss amounts are in the ratio 5:6 
CP - 1000 = 6x //eq no. 2
solving above two equations will produce x = 250 , put it in to eq no.1 , and CP = 2500, and we got solution.
Now if you apply just above method on to the first question you'll again find the diff answer oO
So please explain which method is correct and where is discrepancy occurring from.
Edit (trying to refute both answers) :

CP - SP(old) = x% of CP //eq 1
CP - SP(new) = y% of CP //eq 2
SP(old) - SP(new) = (y-x)% of CP //eq 2-1

Concrete example : 
let's CP = 100, and SP = 80 , hence loss = 20% of CP
now let's change SP = 70, hence loss = 30% of CP
now let's use SP(old) - SP(new) = (y-x)% of CP 
80-70 = 10% of CP
which gets CP =100 back
Hence above method shouldn't be wrong, is it?

If I have understood correctly, the first method is not correct. 
the word "loss" ought to refer to the difference between the cost price ($C$) and the sell price ($S$). For clarity, let's define $S$ to be the initial sell price, prior to any discounts. (So for the first problem $S=1080$ and for the second $S=1250$) Then, for the first one I'd write:
$$.04(S-C)=-1080+1026=-54\;\Rightarrow\;S-C=-1350$$ $$C=S+1350=1080+1350=2430$$
The second method follows this procedure
