Qamar gained 12.5% on the resale of a used stereo. If he purchased the item for Rs. 1680, how much did he sell it for?
Calculating Selling Price with Profit Percentage
The question asks us to find the selling price of a used stereo after a profit was made on its resale. We are given the cost price and the percentage of profit gained.
Here's the information provided:
- Cost Price (CP) of the stereo = Rs. 1680
- Profit Percentage = 12.5%
To find the selling price, we first need to calculate the actual amount of profit gained. The profit is 12.5% of the cost price.
Step-by-Step Profit Calculation
The profit amount can be calculated using the formula:
\(\text{Profit} = \text{Profit Percentage} \times \text{Cost Price}\)
Given Profit Percentage = 12.5%, we can write this as a decimal or a fraction:
- As a decimal: \(12.5\% = \frac{12.5}{100} = 0.125\)
- As a fraction: \(12.5\% = \frac{12.5}{100} = \frac{125}{1000} = \frac{1}{8}\)
Using the decimal form:
\(\text{Profit} = 0.125 \times 1680\)
Let's perform the multiplication:
\(0.125 \times 1680 = \frac{1}{8} \times 1680\)
Now, divide 1680 by 8:
\(\frac{1680}{8} = 210\)
So, the profit gained on the resale is Rs. 210.
Calculating the Selling Price
The selling price (SP) is the cost price plus the profit.
\(\text{Selling Price} = \text{Cost Price} + \text{Profit}\)
Substitute the values:
\(\text{Selling Price} = 1680 + 210\)
\(\text{Selling Price} = 1890\)
Therefore, Qamar sold the stereo for Rs. 1890.
Summary of Calculations
| Item | Value |
|---|---|
| Cost Price (CP) | Rs. 1680 |
| Profit Percentage | 12.5% |
| Profit Amount | Rs. 210 |
| Selling Price (SP) | Rs. 1890 |
Revision Table: Key Profit and Loss Concepts
| Concept | Formula | Description |
|---|---|---|
| Cost Price (CP) | - | The price at which an item is purchased. |
| Selling Price (SP) | - | The price at which an item is sold. |
| Profit | SP - CP (if SP > CP) | The gain made when SP is greater than CP. |
| Loss | CP - SP (if CP > SP) | The reduction incurred when CP is greater than SP. |
| Profit Percentage | \(\left(\frac{\text{Profit}}{\text{CP}} \times 100\right)\%\) | Profit expressed as a percentage of the Cost Price. |
| Loss Percentage | \(\left(\frac{\text{Loss}}{\text{CP}} \times 100\right)\%\) | Loss expressed as a percentage of the Cost Price. |
Additional Information on Percentage Gain
When an item is sold at a profit percentage, the selling price can also be directly calculated using the formula:
\(\text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right)\)
Using this formula for the given problem:
\(\text{Selling Price} = 1680 \times \left(1 + \frac{12.5}{100}\right)\)
\(\text{Selling Price} = 1680 \times \left(1 + 0.125\right)\)
\(\text{Selling Price} = 1680 \times 1.125\)
Let's perform the multiplication:
\(1680 \times 1.125 = 1680 \times \frac{9}{8}\) (since \(1.125 = 1 + 0.125 = 1 + \frac{1}{8} = \frac{9}{8}\))
\(\frac{1680 \times 9}{8} = 210 \times 9 = 1890\)
This method gives the same selling price, Rs. 1890, and can be quicker for direct calculation.
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