Finding the Cost Price with Discount and Profit

This problem involves calculating the original cost of an article given its selling price after a discount and the potential profit if no discount were applied. We need to work backwards from the selling price to the marked price, and then from the marked price (acting as a new selling price) to the cost price.

Step 1: Calculate the Marked Price (MP)

We are given that Surbhi sold the article for Rs. 176 after giving a 12% discount on the marked price. This means the selling price (SP) is 176.

The selling price represents the marked price minus the discount amount. If the discount is 12% of the marked price, then the selling price is $(100 - 12)\% = 88\%$ of the marked price.

Let MP be the marked price.

The relationship is:

\( \text{SP} = \text{MP} \times (1 - \text{Discount Percentage}) \)

\( 176 = \text{MP} \times (1 - 0.12) \)

\( 176 = \text{MP} \times 0.88 \)

To find the Marked Price, we rearrange the equation:

\( \text{MP} = \frac{176}{0.88} \)

\( \text{MP} = \frac{17600}{88} \)

\( \text{MP} = 200 \)

So, the marked price of the article was Rs. 200.

Step 2: Calculate the Cost Price (CP)

We are told that if Surbhi had not given any discount, she would have earned a profit of 25%. Not giving a discount means selling the article at its marked price.

In this scenario, the selling price (SP) would be equal to the marked price (MP), which is Rs. 200. The profit earned would be 25%.

The selling price with profit is calculated as the cost price plus the profit amount. If the profit is 25% of the cost price, then the selling price is $(100 + 25)\% = 125\%$ of the cost price.

Let CP be the cost price.

The relationship is:

\( \text{SP}_{\text{no discount}} = \text{CP} \times (1 + \text{Profit Percentage}) \)

Here, \( \text{SP}_{\text{no discount}} = \text{MP} = 200 \).

\( 200 = \text{CP} \times (1 + 0.25) \)

\( 200 = \text{CP} \times 1.25 \)

To find the Cost Price, we rearrange the equation:

\( \text{CP} = \frac{200}{1.25} \)

\( \text{CP} = \frac{20000}{125} \)

\( \text{CP} = 160 \)

Therefore, the cost price of the article is Rs. 160.

The cost price of the article is Rs. 160.

Revision Table: Profit and Loss Concepts

Additional Information: Formulae Used

• Selling Price after Discount: \( \text{SP} = \text{MP} \times (1 - \frac{\text{Discount \%}}{100}) \)
• Selling Price with Profit: \( \text{SP} = \text{CP} \times (1 + \frac{\text{Profit \%}}{100}) \)
• Selling Price with Loss: \( \text{SP} = \text{CP} \times (1 - \frac{\text{Loss \%}}{100}) \)
• Discount Percentage: \( \frac{\text{Discount}}{\text{MP}} \times 100 \)
• Profit Percentage: \( \frac{\text{Profit}}{\text{CP}} \times 100 \)