An article was sold for Rs. 642 when the cost price was Rs. 600. What is the profit percent earned?
7%
Understanding Profit Calculation
This question asks us to find the profit percentage when an article is sold for a price higher than its cost price. To do this, we first need to determine the amount of profit earned and then express that profit as a percentage of the original cost price.
Key Concepts: Cost Price and Selling Price
- Cost Price (CP): This is the amount of money spent to buy or produce an article. In this problem, the cost price is Rs. 600.
- Selling Price (SP): This is the amount of money for which the article is sold. In this problem, the selling price is Rs. 642.
Calculating the Profit Amount
Profit is earned when the Selling Price is greater than the Cost Price. The profit amount is calculated using the formula:
\(\text{Profit} = \text{Selling Price} - \text{Cost Price}\)
Let's plug in the values from the question:
\(\text{Profit} = \text{Rs. } 642 - \text{Rs. } 600\)
\(\text{Profit} = \text{Rs. } 42\)
So, the profit earned from selling the article is Rs. 42.
Calculating the Profit Percentage
The profit percentage is the profit expressed as a percentage of the Cost Price. The formula for profit percentage is:
\(\text{Profit Percent} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100\)
Now, let's substitute the calculated profit and the given cost price into this formula:
\(\text{Profit Percent} = \left( \frac{42}{600} \right) \times 100\)
We can simplify the fraction:
\(\text{Profit Percent} = \left( \frac{42}{6} \times \frac{1}{100} \right) \times 100\)
\(\text{Profit Percent} = \left( 7 \times \frac{1}{100} \right) \times 100\)
\(\text{Profit Percent} = \frac{7}{100} \times 100\)
\(\text{Profit Percent} = 7\)
Therefore, the profit percent earned is 7%.
Step-by-Step Calculation Summary
| Step | Description | Calculation | Result |
|---|---|---|---|
| 1 | Identify Cost Price (CP) | Given | Rs. 600 |
| 2 | Identify Selling Price (SP) | Given | Rs. 642 |
| 3 | Calculate Profit | SP - CP | Rs. 642 - Rs. 600 = Rs. 42 |
| 4 | Calculate Profit Percent | (Profit / CP) \(\times\) 100 | (42 / 600) \(\times\) 100 |
| 5 | Simplify and Final Result | \(\frac{42}{600} \times 100 = \frac{42}{6} = 7\) | 7% |
Revision Table: Profit and Loss Basics
| Term | 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 (Gain) | When SP > CP. | Profit = SP - CP |
| Loss | When CP > SP. | Loss = CP - SP |
| Profit Percent (Gain Percent) | Profit calculated on CP. | \(\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\) |
| Loss Percent | Loss calculated on CP. | \(\left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\) |
Additional Information on Profit and Loss
Understanding profit and loss concepts is fundamental in business mathematics. Profit indicates a gain from a transaction, while loss indicates a deficit. These are typically calculated based on the initial cost price to determine the percentage gain or loss on the investment.
- Profit percent and Loss percent are always calculated on the Cost Price unless specifically mentioned otherwise.
- A higher selling price compared to the cost price results in profit.
- A lower selling price compared to the cost price results in loss.
Similar Questions
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Important Questions from Discount and MP
If a trader marks the price of an article 50 percent more than the cost price and allows a discount of 30 percent, then what is his profit percentage?
What will be the selling price of an article if two successive discounts of 15% and 12% are offered on its marked price of Rs. 25,500?
Printed price of a mobile is Rs. 6,400. It is sold in Rs. 2,560 with two consecutive discount. If first discount is 20%, then what is the second discount?
Lekhana saves Rs. 15 on the purchase of a book when a discount of 20% is given. How much did she pay for the book?
What will be the selling price if three successive discounts of 10% is applied on an item marked at Rs 3000?
