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

The loss percentage is 27.27 percent.

Revision Table: Key Profit and Loss Formulas

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).