Sapna bought book at a sale for Rs. 573.18, she received 18% discount on the MRP. What is the MRP of the book?
Rs. 699
Understanding the Book Discount Problem
The question asks us to find the original price, also known as the Maximum Retail Price (MRP), of a book. We are given the sale price and the percentage discount received on the MRP.
Relating Sale Price, Discount, and MRP
When a discount is applied to the MRP, the sale price is what the customer pays. The discount is calculated as a percentage of the MRP. The relationship can be expressed as:
Sale Price = MRP - (Discount Percentage of MRP)
Alternatively, if the discount is 18%, it means the customer pays 100% - 18% = 82% of the original MRP.
Calculating the Original MRP
Let the MRP of the book be denoted by \(M\). We are given:
- Sale Price = Rs. 573.18
- Discount Percentage = 18%
The sale price is 82% of the MRP. We can write this as an equation:
\( \text{Sale Price} = (100\% - \text{Discount Percentage}) \times \text{MRP} \)
\( 573.18 = (100\% - 18\%) \times M \)
\( 573.18 = 82\% \times M \)
To use this in a calculation, we convert the percentage to a decimal by dividing by 100:
\( 82\% = \frac{82}{100} = 0.82 \)
So, the equation becomes:
\( 573.18 = 0.82 \times M \)
To find \(M\), we need to divide the sale price by 0.82:
\( M = \frac{573.18}{0.82} \)
Now, let's perform the division:
\( M = 699 \)
So, the MRP of the book is Rs. 699.
Summary of Calculation Steps
| Description | Value |
|---|---|
| Sale Price | Rs. 573.18 |
| Discount Percentage | 18% |
| Percentage paid (100% - Discount%) | \(100\% - 18\% = 82\%\) |
| Decimal equivalent of percentage paid | \(0.82\) |
| Equation: Sale Price = Percentage paid \( \times \) MRP | \(573.18 = 0.82 \times \text{MRP}\) |
| Calculate MRP: MRP = Sale Price / Percentage paid (decimal) | \( \text{MRP} = \frac{573.18}{0.82} = 699 \) |
The calculated MRP is Rs. 699.
Revision Table: Key Concepts
| Term | Definition | Relation to Problem |
|---|---|---|
| MRP (Maximum Retail Price) | The maximum price a product can be sold for. | The value we needed to find. |
| Discount | A reduction in price, usually a percentage of the original price. | Given as 18%. |
| Sale Price | The price after the discount is applied. | Given as Rs. 573.18. |
Additional Information: Related Price Concepts
Understanding pricing concepts is important in many problems like this one. Here are a few related terms:
- Cost Price (CP): The price at which an item is bought.
- Selling Price (SP): The price at which an item is sold. In this problem, the Sale Price is the Selling Price.
- Profit: When SP > CP. Profit = SP - CP. Profit percentage is usually calculated on CP.
- Loss: When CP > SP. Loss = CP - SP. Loss percentage is usually calculated on CP.
- Marked Price (MP): Often the same as MRP. This is the price before any discount is offered. Discount is usually calculated on MP/MRP.
In this specific problem, the focus was on the relationship between MRP, Discount, and Sale Price, which is a common scenario in retail mathematics.
Important Questions from Profit and Loss
Ram bought a chair at 35% discount on its market price, Had Ram got no discount, he would have had to pay ₹245 more. How much did Ram pay for the chair?
A shopkeeper bought an item for Rs. 4,500 and sold it at a loss of 5%. From this money, he bought another item and sold it at a profit of 10%. What is his overall profit?
A man sells two articles at Rs. 9,180 each. He gains 8% on one article and loses 15% on the other. His overall profit or loss is:
A shopkeeper selling an article for ₹46 loses 8%. In order to gain 6%, what should be the selling price of the article?
Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?
