The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
Rs.7,482
Calculating Selling Price with Profit Percentage
The question asks us to find the selling price of an article given its cost price and the profit percentage at which it was sold. We are given the cost price and the profit percentage.
| Item | Value |
|---|---|
| Cost Price (CP) | Rs. 6,450 |
| Profit Percentage | 16% |
Understanding Profit and Selling Price
Profit is the amount by which the selling price is greater than the cost price. Profit percentage is calculated on the cost price.
The relationship between Cost Price (CP), Selling Price (SP), and Profit is:
Profit = Selling Price (SP) - Cost Price (CP)
The formula to calculate Selling Price when Profit Percentage is given is:
$\text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right)$
Step-by-Step Calculation of Selling Price
We are given:
- Cost Price (CP) = Rs. 6,450
- Profit Percentage = 16%
Substitute the given values into the formula:
$\text{SP} = 6450 \times \left(1 + \frac{16}{100}\right)$
First, simplify the term inside the parenthesis:
$\frac{16}{100} = 0.16$
$1 + 0.16 = 1.16$
Now, multiply the Cost Price by this value:
$\text{SP} = 6450 \times 1.16$
Perform the multiplication:
$6450 \times 1.16 = 7482$
So, the Selling Price (SP) is Rs. 7,482.
Final Selling Price
The selling price of the article, when sold at a profit of 16% on a cost price of Rs. 6,450, is Rs. 7,482.
Revision Table: Key Concepts
| Concept | Definition/Formula |
|---|---|
| Cost Price (CP) | The price at which an article is bought. |
| Selling Price (SP) | The price at which an article is sold. |
| Profit | When SP > CP. Profit = SP - CP. |
| Profit Percentage | $\frac{\text{Profit}}{\text{CP}} \times 100$. Calculated on CP. |
| SP with Profit % | $\text{SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right)$ |
Additional Information on Profit and Loss
Besides profit, there can also be a loss. Loss occurs when the Selling Price is less than the Cost Price.
- Loss = Cost Price (CP) - Selling Price (SP)
- Loss Percentage = $\frac{\text{Loss}}{\text{CP}} \times 100$ (also calculated on CP)
- Formula for SP with Loss %: $\text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss Percentage}}{100}\right)$
Understanding the difference between calculating percentage on CP vs. SP is crucial in profit and loss problems.
Important Questions from Profit and Loss
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
A man sells a car to his friend at the loss of 10 %; who in return sells it for Rs. 54000 making a profit of 20 %. What was the initial value of the car?
By selling a horse for Rs. 670, a tradesman would lose 5%. At what price must he sell it to gain 5%?
An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
