# 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

1. 2400
2. 2450
3. 2500
4. 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?

Going exactly by the questions framed,
answer to the first one is wrong, and that to the second one is right.

For the answer to the first to be right, the question needs to be:

"When a shopkeeper reduces the selling price of a article from 1080 to 1026,
his loss increases by 4% of C.P. . What is the cost price of article?

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

• Please have a look at edited part of question. Commented Oct 6, 2015 at 12:48
• But the problem doesn't say "the loss changed by a specified percent of the Cost." If it did, then the method would be correct. The way the problem reads it says "the loss changed by a specified percent of itself"
– lulu
Commented Oct 6, 2015 at 12:54
• aaah now you cleared my confusion :) Thanks :) Commented Oct 6, 2015 at 12:56
• Please help me with question , similar to above: A man sold an article at a gain of 5%. Had he sold it for Rs 40 more, he would have gained 8%. Then the cost price of the article is? Commented Oct 18, 2015 at 14:59
• My answer is coming 4000/3, but actual answer is 10000 :( . Thanks Commented Oct 18, 2015 at 15:00