The ratio of selling price to the cost price is 8 ∶ 11. What is the loss percentage?
27.27 percent
Calculate Loss Percentage from SP:CP Ratio
Understanding the relationship between selling price (SP) and cost price (CP) is crucial for determining profit or loss.
The question provides the ratio of the selling price to the cost price as 8 ∶ 11. This means:
- Selling Price (SP) ∶ Cost Price (CP) = 8 ∶ 11
This ratio can be interpreted as: for every 11 units of cost price, the selling price is 8 units.
Identifying Profit or Loss
To determine if there is a profit or a loss, we compare the selling price and the cost price. In this ratio, the selling price (8 parts) is less than the cost price (11 parts). When the selling price is lower than the cost price, the transaction results in a loss.
Since SP (8 units) < CP (11 units), there is a loss.
Calculating the Loss Amount
The amount of loss is the difference between the cost price and the selling price.
Loss = Cost Price - Selling Price
From the given ratio, we can represent the cost price as 11x and the selling price as 8x, where 'x' is a common positive factor. However, for calculating the percentage based on the ratio, we can simply use the ratio values directly as proportional units.
Using the ratio values:
Loss = 11 units - 8 units = 3 units
Calculating the Loss Percentage
The loss percentage is always calculated with respect to the cost price. The formula for loss percentage is:
\text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) × 100\%
Now, we substitute the values (or ratio units) into the formula:
\text{Loss Percentage} = \left( \frac{3 \text{ units}}{11 \text{ units}} \right) × 100\%
\text{Loss Percentage} = \left( \frac{3}{11} \right) × 100\%
To calculate the percentage, we perform the division and multiplication:
\frac{3}{11} × 100 = \frac{300}{11}
Dividing 300 by 11:
300 ÷ 11 ≈ 27.2727...
Rounding to two decimal places, the loss percentage is approximately 27.27 percent.
Summary of Calculation Steps
| Step | Description | Calculation |
|---|---|---|
| 1 | Identify SP and CP from the ratio SP ∶ CP = 8 ∶ 11 | SP = 8 (units), CP = 11 (units) |
| 2 | Determine if it is profit or loss (Compare SP and CP) | SP < CP, so it is a Loss |
| 3 | Calculate the Loss amount | Loss = CP - SP = 11 - 8 = 3 (units) |
| 4 | Apply the Loss Percentage formula | \text{Loss %} = \left( \frac{\text{Loss}}{\text{CP}} \right) × 100 |
| 5 | Substitute values and calculate | \text{Loss %} = \left( \frac{3}{11} \right) × 100 = \frac{300}{11} \approx 27.27\% |
The loss percentage is 27.27 percent.
Revision Table: Key Profit and Loss Formulas
| Concept | Formula | Condition |
|---|---|---|
| Profit | SP - CP | If SP > CP |
| Loss | CP - SP | If SP < CP |
| Profit Percentage | \left( \frac{\text{Profit}}{\text{CP}} \right) × 100\% | Always calculated on CP |
| Loss Percentage | \left( \frac{\text{Loss}}{\text{CP}} \right) × 100\% | Always calculated on CP |
Additional Information on Ratio and Percentage
A ratio provides a comparison between two quantities. When dealing with profit and loss, the ratio of SP to CP directly tells us if SP is greater than, less than, or equal to CP, indicating profit, loss, or break-even respectively.
Converting fractions to percentages is a fundamental skill. To convert a fraction \frac{a}{b} to a percentage, you multiply it by 100 and add the percent symbol (\%). For example, \frac{1}{4} = \frac{1}{4} × 100\% = 25\%.
In profit and loss calculations, the cost price (CP) serves as the base for calculating both profit percentage and loss percentage unless the question specifically states otherwise (which is rare).
Important Questions from Profit and Loss
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
