A dealer sells an article at ₹850 after offering a cash discount of 15% on its marked price. Without discount, he would have earned a profit of 25%. What is the cost price of the article (in ₹)?

Let the marked price of the article be $\text{MP}$.The selling price after a 15% discount is ₹850.
$$850=\text{MP}\times \left(1-\frac{15}{100}\right)$$
$$850=\text{MP}\times \frac{85}{100}$$
$$\text{MP}=\frac{850\times 100}{85}=1000$$
If no discount is given, the selling price becomes equal to the marked price ($\text{SP}=\text{MP}=1000$).In this case, the profit earned is 25%. Let the cost price be $\text{CP}$.
$$\text{CP}\times \left(1+\frac{25}{100}\right)=1000$$
$$\text{CP}\times \frac{125}{100}=1000$$
$$\text{CP}\times \frac{5}{4}=1000$$
$$\text{CP}=\frac{1000\times 4}{5}=800$$
Therefore, the cost price of the article is ₹800.