A retailer sets the list price of a product 25% higher than its purchase price. After offering a discount of 12% on the list price, the retailer earns a profit of ₹240. Find the purchase price of the product.

The correct answer is ₹2,400.

Let's break down the problem step-by-step to find the purchase price (Cost Price) of the product.

Step 1: Define the variables and understand the given relationships.
Let the purchase price (Cost Price, CP) of the product be $x$.

The retailer sets the list price (Marked Price, MP) 25% higher than the purchase price.
$\text{List Price (MP)}=x+0.25x=1.25x$

Step 2: Calculate the Selling Price (SP) after the discount.
A discount of 12% is offered on the list price.
$\text{Discount Amount}=12\%\text{of MP}=0.12\times 1.25x=0.15x$

Therefore, the Selling Price (SP) is:
$\text{Selling Price (SP)}=\text{MP}-\text{Discount}$
$\text{SP}=1.25x-0.15x=1.10x$

Step 3: Relate the Profit to the Cost Price and Selling Price.
Profit is given by the formula:
$\text{Profit}=\text{Selling Price (SP)}-\text{Purchase Price (CP)}$

We are given that the profit earned by the retailer is ₹240.
$240=1.10x-x$
$240=0.10x$

Step 4: Solve for the Purchase Price ($x$).
$x=\frac{240}{0.10}$
$x=2400$

Thus, the purchase price of the product is ₹2,400.