Rima buys a chair for Rs. 1000 and sells it at a loss of 8%. What is the selling price of the chair?
Rs. 920
Calculating Selling Price After an 8% Loss
Let's break down how to find the selling price of the chair when sold at a loss. We are given the cost price and the percentage loss.
Given Information:
- Cost Price (CP) of the chair = Rs. 1000
- Loss percentage = 8%
We need to find the Selling Price (SP) of the chair.
Understanding Loss in Percentage
When an item is sold at a loss, it means the selling price is less than the cost price. The loss percentage is calculated on the cost price.
Calculating the Amount of Loss
The loss amount is 8% of the Cost Price (Rs. 1000).
We can calculate the loss amount using the formula:
\(\text{Loss Amount} = \text{Loss Percentage} \times \text{Cost Price}\)
Substituting the given values:
\(\text{Loss Amount} = 8\% \text{ of } \text{Rs. } 1000\)
\(\text{Loss Amount} = \frac{8}{100} \times 1000\)
\(\text{Loss Amount} = 8 \times \frac{1000}{100}\)
\(\text{Loss Amount} = 8 \times 10\)
\(\text{Loss Amount} = \text{Rs. } 80\)
So, the loss incurred on selling the chair is Rs. 80.
Calculating the Selling Price
The Selling Price (SP) is obtained by subtracting the loss amount from the Cost Price (CP).
The formula for selling price with loss is:
\(\text{Selling Price (SP)} = \text{Cost Price (CP)} - \text{Loss Amount}\)
Substituting the values we have:
\(\text{SP} = \text{Rs. } 1000 - \text{Rs. } 80\)
\(\text{SP} = \text{Rs. } 920\)
Therefore, the selling price of the chair is Rs. 920.
| Item | Value |
|---|---|
| Cost Price (CP) | Rs. 1000 |
| Loss Percentage | 8% |
| Loss Amount | Rs. 80 |
| Selling Price (SP) | Rs. 920 |
Summary of the Calculation Steps
- Identify the Cost Price (CP) and Loss Percentage.
- Calculate the Loss Amount by taking the loss percentage of the CP.
- Subtract the Loss Amount from the CP to get the Selling Price (SP).
Revision Table: Profit and Loss Basics
| 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 |
| Loss | When CP > SP. | Loss = CP - SP |
| Profit Percentage | Profit calculated as a percentage of CP. | \(\frac{\text{Profit}}{\text{CP}} \times 100\%\) |
| Loss Percentage | Loss calculated as a percentage of CP. | \(\frac{\text{Loss}}{\text{CP}} \times 100\%\) |
Additional Information: Calculating SP directly from Loss Percentage
Alternatively, you can calculate the selling price directly if you know the loss percentage.
If there is a loss of 8%, it means the selling price is (100 - 8)% of the cost price.
So, Selling Price (SP) = (100 - 8)% of CP
SP = 92% of CP
SP = \(\frac{92}{100} \times 1000\)
SP = \(92 \times 10\)
SP = Rs. 920
This method gives the same result and is a useful shortcut for profit and loss calculations.
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?
