Surbhi sold an article for Rs. 176 after giving 12% discount on its marked price. Had she not given any discount; she would have earned a profit of 25%. What is the cost price (in Rs.) of the article?
160
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.
| Metric | Value | Calculation |
|---|---|---|
| Selling Price (with discount) | Rs. 176 | Given |
| Discount Percentage | 12% | Given |
| Marked Price (MP) | Rs. 200 | \( \frac{176}{0.88} \) |
| Selling Price (without discount) | Rs. 200 | Equal to MP |
| Profit Percentage (without discount) | 25% | Given |
| Cost Price (CP) | Rs. 160 | \( \frac{200}{1.25} \) |
The cost price of the article is Rs. 160.
Revision Table: Profit and Loss Concepts
| Term | Abbreviation | Definition |
|---|---|---|
| Cost Price | CP | The price at which an article is bought. |
| Selling Price | SP | The price at which an article is sold. |
| Marked Price | MP | The price marked on the article. Also known as List Price. |
| Profit | When SP > CP. Calculated as SP - CP. | |
| Loss | When SP < CP. Calculated as CP - SP. | |
| Discount | A reduction given on the Marked Price. Discount = MP - SP. |
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: \( \frac{\text{Profit}}{\text{CP}} \times 100 \)
Important Questions from Discount and MP
The marked price of an article is Rs. 1500. A shopkeeper sells it by giving 20% discount on its marked price. If the cost price of the article is Rs. 991, then his profit (in Rs.) is:
The marked price of an article is Rs. 240. A shopkeeper sells it by allowing 18% discount on its marked price and still gains 23%. What is the cost price (in Rs.) of the article?
Three shopkeepers A, B and C marked on an identical article at Rs. 4820. A, B and C sold their article on successive discounts of 20% and 20%; 25% and 15%; 30% and 10% respectively. Which shopkeeper gives the maximum discount and how much (in Rs.)?
Find a single discount percentage equivalent to successive discounts of 10%, 20% and 25%.
A shopkeeper marks the price of the article in such a way that after allowing 28% discount, he wants a gain of 12%. If the marked price is Rs. 224, then the cost price of the article is:
