An article is marked at ₹550. If it is sold at a discount of 40%, then the selling price becomes 10% more than its cost price. What is the cost price (in ₹)?

To find the cost price of the article, we can break down the problem into two main parts: calculating the selling price from the marked price and discount, and then finding the cost price from the selling price and the profit percentage.

Step 1: Calculate the Selling Price (SP)
The marked price (MP) of the article is given as ₹550, and it is sold at a discount of 40%.
The formula relating the Selling Price to the Marked Price and Discount is:

$\text{Selling Price (SP)}=\text{Marked Price (MP)}\times (1-\frac{\text{Discount \%}}{100})$

Substituting the given values into the formula:

$\text{SP}=550\times (1-\frac{40}{100})$

$\text{SP}=550\times 0.60$

$\text{SP}=₹330$

So, the selling price of the article is ₹330.

Step 2: Calculate the Cost Price (CP)
We are given that the selling price (₹330) is 10% more than the cost price (CP).
This means the relationship between SP and CP is:

$\text{SP}=\text{CP}\times (1+\frac{\text{Profit \%}}{100})$

Substituting the values of SP and the percentage increase:

$330=\text{CP}\times (1+\frac{10}{100})$

$330=\text{CP}\times 1.1$

Solving for CP:

$\text{CP}=\frac{330}{1.1}$

$\text{CP}=₹300$

Therefore, the cost price of the article is ₹300.