Qamar gained 14% on the resale of a used stereo. If he purchased the item for Rs. 1,500 then how much did he sell it for?
Rs. 1,710
Understanding Profit Calculation on Resale
This problem involves calculating the selling price of an item when the cost price and the profit percentage are known. Qamar purchased a used stereo and sold it for a profit. We need to find the price at which he sold it.
Key Concepts in Profit and Loss
- Cost Price (CP): The original price at which an item is bought. In this case, the cost price of the stereo is Rs. 1,500.
- Selling Price (SP): The price at which an item is sold. This is what we need to find.
- Profit: When the selling price is greater than the cost price. Profit = SP - CP.
- Profit Percentage: Profit expressed as a percentage of the cost price. Profit % = \(\frac{\text{Profit}}{\text{CP}} \times 100\).
Calculating the Selling Price Step-by-Step
Qamar gained a 14% profit on the resale of the stereo. This means the profit amount is 14% of the cost price (Rs. 1,500).
Step 1: Calculate the Profit Amount
The profit amount can be calculated using the profit percentage and the cost price:
Profit Amount = Profit Percentage of Cost Price
Profit Amount = \(14\% \text{ of } Rs. 1,500\)
To calculate 14% of 1,500, we can write 14% as a decimal (\(0.14\)) or a fraction (\(\frac{14}{100}\)).
Profit Amount = \(\frac{14}{100} \times 1500\)
Profit Amount = \(0.14 \times 1500\)
Profit Amount = \(Rs. 210\)
So, Qamar made a profit of Rs. 210 on the resale of the stereo.
Step 2: Calculate the Selling Price
The selling price is the cost price plus the profit amount:
Selling Price (SP) = Cost Price (CP) + Profit Amount
SP = \(Rs. 1,500 + Rs. 210\)
SP = \(Rs. 1,710\)
Alternatively, you can calculate the selling price directly using the formula:
SP = CP \(\times \left(1 + \frac{\text{Profit \%}}{100}\right)\)
SP = \(1500 \times \left(1 + \frac{14}{100}\right)\)
SP = \(1500 \times \left(1 + 0.14\right)\)
SP = \(1500 \times 1.14\)
SP = \(Rs. 1,710\)
Both methods give the same selling price.
Final Answer for Stereo Resale
Qamar sold the used stereo for Rs. 1,710.
| Item | Value |
|---|---|
| Cost Price (CP) | Rs. 1,500 |
| Profit Percentage | 14% |
| Profit Amount | Rs. 210 |
| Selling Price (SP) | Rs. 1,710 |
Revision Table: Profit and Loss Basics
| Term | Definition | Formula |
|---|---|---|
| Cost Price (CP) | Original price of an item | - |
| Selling Price (SP) | Price at which item is sold | - |
| Profit | SP > CP | Profit = SP - CP |
| Loss | SP < CP | Loss = CP - SP |
| Profit % | Profit as a percentage of CP | \(\frac{\text{Profit}}{\text{CP}} \times 100\) |
| Loss % | Loss as a percentage of CP | \(\frac{\text{Loss}}{\text{CP}} \times 100\) |
Additional Information: Applications of Profit and Loss
Understanding profit and loss calculations is essential for various real-world scenarios, including:
- Business operations (pricing products, calculating revenue)
- Personal finance (calculating returns on investments, understanding discounts)
- Retail and sales (determining sale prices, understanding margins)
- Economics (analyzing market trends and business performance)
These concepts help in making informed decisions regarding buying and selling goods and services. When a question mentions a 'gain' percentage, it directly refers to a profit percentage.
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