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
- Veer bought some sharpeners at the rate of ₹180/dozen. He sold them for ₹23 each. His profit percentage is ____ % (rounded off to two decimal places).
- A shopkeeper lists the price of a fan at 60% above its cost price and offers a 15% discount on its list price. If he earns a profit of ₹117, then what is the list price (in ₹) of the fan?
- The marked price of an article is ₹800. It is sold at two successive discounts of 24% and 15%, respectively. Find the selling price of the article.
- A discount of 13% on the marked price of an article is allowed and then the article is sold for ₹348. The marked price of the article is:
- A trader claims to sell grains at a profit of 29%, but also dishonestly uses a weight which is 13% less than what is mentioned on it. Find the total percentage of profit earned by the trader. (Round off the answer to the nearest whole number.)
