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?
18%
Calculating Percentage Discount on TV Price During Sale
The question asks us to find the percentage discount offered on a TV during a Diwali sale. We are given the original price and the sale price of the TV.
Understanding Discount and Percentage Discount
- Discount: This is the reduction in the original price of an item. It is the difference between the original price and the sale price.
- Percentage Discount: This is the discount expressed as a percentage of the original price. It tells us what fraction of the original price was reduced.
Step-by-Step Calculation of Percentage Discount
Let's break down the steps to find the percentage discount.
- Identify the Original Price:
The original price of the TV before the sale was Rs. 14,500.
Original Price = Rs. 14,500
- Identify the Sale Price:
The price of the TV during the Diwali sale was Rs. 11,890.
Sale Price = Rs. 11,890
- Calculate the Discount Amount:
The discount amount is the difference between the Original Price and the Sale Price.
Discount Amount = Original Price - Sale Price
Discount Amount = \( \text{Rs.} \, 14,500 - \text{Rs.} \, 11,890 \)
Discount Amount = \( \text{Rs.} \, 2,610 \)
The discount offered was Rs. 2,610.
- Calculate the Percentage Discount:
The percentage discount is calculated using the formula:
\( \text{Percentage Discount} = \left( \frac{\text{Discount Amount}}{\text{Original Price}} \right) \times 100\% \)
Substitute the calculated Discount Amount and the Original Price into the formula:
\( \text{Percentage Discount} = \left( \frac{2610}{14500} \right) \times 100\% \)
Now, perform the division:
\( \frac{2610}{14500} = \frac{261}{1450} \)
Dividing 261 by 1450 gives 0.18.
\( \text{Percentage Discount} = 0.18 \times 100\% \)
\( \text{Percentage Discount} = 18\% \)
The percentage discount offered on the TV is 18%.
Comparing with Options
Let's compare our calculated percentage discount with the given options:
- Option 1: 19.56%
- Option 2: 19%
- Option 3: 18%
- Option 4: 17.6%
Our calculated percentage discount of 18% matches Option 3.
| Item | Price/Amount |
|---|---|
| Original Price | Rs. 14,500 |
| Sale Price | Rs. 11,890 |
| Discount Amount | Rs. 2,610 |
| Percentage Discount | 18% |
Conclusion
The percentage discount on the TV during the Diwali sale was 18%.
Revision Table: Key Concepts in Pricing and Discounts
| Term | Definition | Calculation Example |
|---|---|---|
| Original Price | The initial price of an item before any discount. | Rs. 14,500 (in this problem) |
| Sale Price | The price of an item after a discount is applied. | Rs. 11,890 (in this problem) |
| Discount Amount | The amount of reduction from the original price. | Original Price - Sale Price = 14500 - 11890 = Rs. 2610 |
| Percentage Discount | Discount Amount expressed as a percentage of the Original Price. | \(\left( \frac{\text{Discount Amount}}{\text{Original Price}} \right) \times 100\%\) |
Additional Information: Related Retail Math Concepts
Understanding pricing often involves other related concepts:
- Cost Price (CP): The price at which a seller buys a product.
- Selling Price (SP): The price at which a seller sells a product to a customer. This can be the original price or a discounted price (Sale Price).
- Profit: When SP > CP. Profit = SP - CP.
- Loss: When SP < CP. Loss = CP - SP.
- Profit Percentage: \( \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\% \)
- Loss Percentage: \( \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\% \)
- Markup: The difference between the cost of a product and its selling price. Often expressed as a percentage of the cost price.
- Markdown: A reduction in the original selling price, often leading to a sale price (this is essentially a discount). Often expressed as a percentage of the original selling price.
In this problem, the Rs. 14,500 is the original selling price set by the retailer, and Rs. 11,890 is the markdown price or sale price.
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 shopkeeper marks the marked price of an article 30% more than its real price and offers 10% discount. What is the gain percentage?
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?
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:
