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
- Veer bought some sharpeners at the rate of ₹180/dozen. He sold them for ₹23 each. His profit percentage is ____ % (rounded off to two decimal places).
- A shopkeeper lists the price of a fan at 60% above its cost price and offers a 15% discount on its list price. If he earns a profit of ₹117, then what is the list price (in ₹) of the fan?
- The marked price of an article is ₹800. It is sold at two successive discounts of 24% and 15%, respectively. Find the selling price of the article.
- A discount of 13% on the marked price of an article is allowed and then the article is sold for ₹348. The marked price of the article is:
- A trader claims to sell grains at a profit of 29%, but also dishonestly uses a weight which is 13% less than what is mentioned on it. Find the total percentage of profit earned by the trader. (Round off the answer to the nearest whole number.)
