If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
Understanding Percentage Loss Calculation
Let's analyze the problem concerning the selling price and cost price of articles to find the percentage loss. The question states that the selling price (SP) of 7 articles is equal to the cost price (CP) of 6 articles.
We can write this relationship as an equation:
\(7 \times \text{SP} = 6 \times \text{CP}\)
To find the percentage loss, we need to compare the SP of one article with the CP of one article. From the equation, we can find the ratio of SP to CP:
\(\frac{\text{SP}}{\text{CP}} = \frac{6}{7}\)
This ratio tells us that if the cost price of an article is 7 units, its selling price is 6 units. Since the selling price is less than the cost price, there is a loss.
The loss per article can be calculated as:
\(\text{Loss} = \text{CP} - \text{SP}\)
Using the ratio, if CP = 7 and SP = 6, then:
\(\text{Loss} = 7 - 6 = 1\) unit
Now, we can calculate the percentage loss. The percentage loss is always calculated on the cost price.
\(\text{Percentage Loss} = \left(\frac{\text{Loss}}{\text{CP}}\right) \times 100\%\)
Substituting the values based on our ratio:
\(\text{Percentage Loss} = \left(\frac{1}{7}\right) \times 100\%\)
\(\text{Percentage Loss} = \frac{100}{7}\%\)
To express this fraction as a mixed number, we divide 100 by 7:
\(100 \div 7 = 14\) with a remainder of \(2\).
So, \(\frac{100}{7}\% = 14\frac{2}{7}\%\).
Therefore, the percentage loss in this scenario is \(14\frac{2}{7}\%\).
Let's summarize the key steps for calculating percentage loss:
- Set up an equation based on the given information relating selling price and cost price.
- Determine the ratio of SP to CP to understand the relationship between the cost and selling prices of individual articles.
- Calculate the loss amount (CP - SP).
- Use the loss amount and cost price to calculate the percentage loss using the formula: \((\text{Loss}/\text{CP}) \times 100\%\).
- Simplify the result if necessary.
This method provides a clear way to calculate the percentage loss when dealing with scenarios involving different numbers of articles having equal total cost and selling prices. Understanding percentage loss calculation is crucial for 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:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
