An article was sold for Rs. 1,215 after giving a discount of 19%. If a discount of 17.5% is given, then for how much (in Rs.) should the article be sold?
1,237.50
Understanding the Discount Problem
The question asks us to find the selling price of an article if a different discount percentage is applied, given its selling price after an initial discount. To solve this, we first need to determine the original price of the article before any discount, which is known as the marked price.
Calculating the Marked Price of the Article
We are given that the article was sold for Rs. 1,215 after a 19% discount. The selling price (SP) is related to the marked price (MP) and the discount percentage (D%) by the formula:
Selling Price = Marked Price × (1 - Discount Percentage / 100)
In this case:
- Selling Price (SP1) = Rs. 1,215
- Discount Percentage (D1) = 19%
We can rearrange the formula to find the Marked Price:
Marked Price = Selling Price / (1 - Discount Percentage / 100)
Substituting the given values:
\( \text{MP} = \frac{1215}{1 - \frac{19}{100}} \)
\( \text{MP} = \frac{1215}{1 - 0.19} \)
\( \text{MP} = \frac{1215}{0.81} \)
Now, let's perform the division:
\( \text{MP} = 1500 \)
So, the marked price of the article is Rs. 1,500.
Finding the New Selling Price After 17.5% Discount
Now that we have the marked price (MP = Rs. 1,500), we can calculate the new selling price (SP2) when a discount of 17.5% (D2 = 17.5%) is given.
Using the same formula:
New Selling Price = Marked Price × (1 - New Discount Percentage / 100)
Substituting the values:
\( \text{SP2} = 1500 \times \left(1 - \frac{17.5}{100}\right) \)
\( \text{SP2} = 1500 \times (1 - 0.175) \)
\( \text{SP2} = 1500 \times 0.825 \)
Performing the multiplication:
\( \text{SP2} = 1237.50 \)
So, if a discount of 17.5% is given, the article should be sold for Rs. 1,237.50.
Summary of Discount Calculation Steps
Here is a summary of the steps taken to find the new selling price:
- Identify the given selling price (SP1) and the initial discount percentage (D1).
- Use SP1 and D1 to calculate the marked price (MP) using the formula: \( \text{MP} = \text{SP1} / (1 - \text{D1} / 100) \).
- Identify the new discount percentage (D2).
- Use the calculated MP and the new discount percentage D2 to find the new selling price (SP2) using the formula: \( \text{SP2} = \text{MP} \times (1 - \text{D2} / 100) \).
| Item | Value |
|---|---|
| Initial Selling Price (SP1) | Rs. 1,215 |
| Initial Discount (D1) | 19% |
| Calculated Marked Price (MP) | Rs. 1,500 |
| New Discount (D2) | 17.5% |
| New Selling Price (SP2) | Rs. 1,237.50 |
Revision Table: Key Formulas for Discount and Selling Price
| Concept | Formula |
|---|---|
| Selling Price with Discount | \( \text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount}\%}{100}\right) \) |
| Marked Price from SP and Discount | \( \text{MP} = \frac{\text{SP}}{1 - \frac{\text{Discount}\%}{100}} \) |
| Discount Amount | \( \text{Discount Amount} = \text{MP} - \text{SP} \) or \( \text{MP} \times \frac{\text{Discount}\%}{100} \) |
Additional Information on Discounts and Pricing
In retail, the marked price (MP) is often the price displayed on the product tag. A discount is a reduction in this marked price. The selling price (SP) is the actual price paid by the customer after the discount is applied.
It's important to distinguish between cost price (CP), selling price (SP), and marked price (MP). Cost price is what the seller paid for the article. Selling price is what the seller sells it for. Marked price is the advertised price before any discounts.
Profit or loss is calculated based on the cost price and the selling price. If SP > CP, there is a profit. If SP < CP, there is a loss.
Discounts are always calculated on the marked price unless specified otherwise.
Important Questions from Discount and MP
A single discount equivalent to two successive discounts of 15% and 25% is:
Ramesh purchases 75 articles for ₹ 10800 and sells them at a loss equal to the selling price of 5 articles. What will be the selling price of one article?
A TV was available for Rs. 14,500. The price came down to Rs. 11,890 during the Diwali sale. What is the percentage discount?
A shopkeeper marks the marked price of an article 30% more than its real price and offers 10% discount. What is the gain percentage?
A chair is sold for Rs. 720 after giving a discount of 10% on its marked price. The cost price of the chair is Rs. 640. If it is sold at the marked price, then the profit percentage will be:
