Profit,Loss and Discount

Question

I want to solve this problem by the shortcut method taught in my class. So it will be highly helpful if somebody knows this method and would resolve my doubt in the shortcut method I have used here.

Q.A shopkieeper sells an article at 12% discount on the marked price and makes a profit of 10%.If he gives a discount of 4% he will earn a profit of Rupees 40. Find the marked price of the article. Correct answer :Rs 250. Where might have I gone wrong?

My Attempt:

CP=Cost Price, SP=Selling Price, MP=Marked Price

Answer 1

I found your mistake.

96 - 80 = 16. Not 6.

Then you get correct result.

Answer 2

The value of the article is $v$, and the price of the article (before any discounts) is $p$.

Then,

A shopkeeper sells an article at 12% discount on the marked price and makes a profit of 10%

tells you that $0.88\cdot p = 1.1\cdot c$

and

If he gives a discount of 4% he will earn a profit of Rupees 40

Tells you that $0.96 \cdot p = c + 40$

This should be all you need.