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
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
A man sells a car to his friend at the loss of 10 %; who in return sells it for Rs. 54000 making a profit of 20 %. What was the initial value of the car?
An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
