40 percent of the cost price of an article is equal to the 25 percent of its selling price. What is the profit percentage?
60 percent
Calculating Profit Percentage from Cost and Selling Price Relationship
The question provides a relationship between the cost price (CP) and the selling price (SP) of an article. We are told that 40 percent of the cost price is equal to 25 percent of its selling price. Our goal is to find the profit percentage based on this information.
Understanding the Relationship
Let's represent the cost price as \( \text{CP} \) and the selling price as \( \text{SP} \). The given condition can be written as an equation:
\( 40\% \text{ of } \text{CP} = 25\% \text{ of } \text{SP} \)
We can convert the percentages to decimals:
\( 0.40 \times \text{CP} = 0.25 \times \text{SP} \)
Finding the Ratio of SP to CP
To find the profit percentage, we need to relate the selling price to the cost price. We can rearrange the equation to find the ratio \( \frac{\text{SP}}{\text{CP}} \):
\( \frac{\text{SP}}{\text{CP}} = \frac{0.40}{0.25} \)
To simplify the fraction, we can multiply the numerator and denominator by 100:
\( \frac{\text{SP}}{\text{CP}} = \frac{40}{25} \)
We can simplify the fraction by dividing both 40 and 25 by their greatest common divisor, which is 5:
\( \frac{\text{SP}}{\text{CP}} = \frac{40 \div 5}{25 \div 5} = \frac{8}{5} \)
So, the selling price is \( \frac{8}{5} \) times the cost price:
\( \text{SP} = \frac{8}{5} \times \text{CP} \)
Calculating the Profit
Profit is the difference between the selling price and the cost price:
\( \text{Profit} = \text{SP} - \text{CP} \)
Substitute the expression for SP in terms of CP:
\( \text{Profit} = \frac{8}{5} \times \text{CP} - \text{CP} \)
To subtract, we can think of \( \text{CP} \) as \( 1 \times \text{CP} \) or \( \frac{5}{5} \times \text{CP} \):
\( \text{Profit} = \left(\frac{8}{5} - 1\right) \times \text{CP} \)
\( \text{Profit} = \left(\frac{8}{5} - \frac{5}{5}\right) \times \text{CP} \)
\( \text{Profit} = \frac{8 - 5}{5} \times \text{CP} \)
\( \text{Profit} = \frac{3}{5} \times \text{CP} \)
The profit is \( \frac{3}{5} \) of the cost price.
Determining the Profit Percentage
The profit percentage is calculated as the ratio of the profit to the cost price, multiplied by 100 percent:
\( \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\% \)
Substitute the value of Profit we found:
\( \text{Profit Percentage} = \left( \frac{\frac{3}{5} \times \text{CP}}{\text{CP}} \right) \times 100\% \)
The \( \text{CP} \) terms cancel out:
\( \text{Profit Percentage} = \frac{3}{5} \times 100\% \)
Now, we calculate the value:
\( \text{Profit Percentage} = 0.6 \times 100\% \)
\( \text{Profit Percentage} = 60\% \)
Thus, the profit percentage is 60 percent.
| Step | Description | Formula/Calculation |
|---|---|---|
| 1 | Write down the given relationship | \(0.40 \times \text{CP} = 0.25 \times \text{SP}\) |
| 2 | Find the ratio SP/CP | \( \frac{\text{SP}}{\text{CP}} = \frac{0.40}{0.25} = \frac{8}{5} \) |
| 3 | Express Profit in terms of CP | \( \text{Profit} = \text{SP} - \text{CP} = \frac{8}{5}\text{CP} - \text{CP} = \frac{3}{5}\text{CP} \) |
| 4 | Calculate Profit Percentage | \( \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\% = \left( \frac{3/5 \times \text{CP}}{\text{CP}} \right) \times 100\% = \frac{3}{5} \times 100\% = 60\% \) |
Revision Table: Cost Price, Selling Price, Profit Percentage
Let's quickly review the key terms involved in this profit percentage problem.
- Cost Price (CP): The price at which an article is purchased.
- Selling Price (SP): The price at which an article is sold.
- Profit: Occurs when SP > CP. Profit = SP - CP.
- Loss: Occurs when SP < CP. Loss = CP - SP.
- Profit Percentage: Calculated as \( \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\% \). Always based on CP unless specified otherwise.
- Loss Percentage: Calculated as \( \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\% \). Always based on CP unless specified otherwise.
Additional Information on Profit and Loss Concepts
Problems involving cost price, selling price, and profit percentage are common in quantitative aptitude. Understanding how percentages relate two quantities is crucial. In this specific problem, we were given a direct relationship between percentages of CP and SP, allowing us to find the ratio of SP to CP first, and then easily calculate the profit percentage.
- The relationship \( \text{SP} = \frac{8}{5} \times \text{CP} \) means that for every 5 units of cost price, the selling price is 8 units. The profit is the difference, \( 8 - 5 = 3 \) units.
- The profit percentage is then the profit (3 units) divided by the cost price (5 units), expressed as a percentage: \( \frac{3}{5} \times 100\% = 60\% \). This confirms our calculation.
- It is important to remember that profit or loss percentage is conventionally calculated with respect to the cost price.
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?
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:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
