Calculating Profit Percentage: Cost Price vs. Selling Price

This problem asks us to find the profit percentage when the cost price (CP) of an article is 30% less than its selling price (SP). Understanding the relationship between CP, SP, and profit percentage is key to solving this problem.

Understanding the Relationship

The problem states that the cost price is 30% less than the selling price. We can express this mathematically.

Given:

• Cost Price (CP)
• Selling Price (SP)

According to the question:

$\text{CP} = \text{SP} - 30\% \text{ of SP}$

This can be written as:

$\text{CP} = \text{SP} - \left(\frac{30}{100} \times \text{SP}\right)$

$\text{CP} = \text{SP} \left(1 - \frac{30}{100}\right)$

$\text{CP} = \text{SP} \left(\frac{100 - 30}{100}\right)$

$\text{CP} = \text{SP} \left(\frac{70}{100}\right)$

$\text{CP} = 0.7 \times \text{SP}$

Calculating the Profit Percentage

To make calculations easier, let's assume a value for the selling price (SP). A convenient value is 100.

Let $\text{SP} = 100$ units.

Using the relationship derived above:

$\text{CP} = 0.7 \times \text{SP}$

$\text{CP} = 0.7 \times 100$

$\text{CP} = 70$ units.

Now, we can calculate the profit. Profit is the difference between the selling price and the cost price:

$\text{Profit} = \text{SP} - \text{CP}$

$\text{Profit} = 100 - 70$

$\text{Profit} = 30$ units.

The profit percentage is calculated with respect to the cost price (CP). The formula for profit percentage is:

$\text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100\%$

Substitute the values we found:

$\text{Profit Percentage} = \left(\frac{30}{70}\right) \times 100\%$

$\text{Profit Percentage} = \left(\frac{3}{7}\right) \times 100\%$

$\text{Profit Percentage} \approx 0.42857 \times 100\%$

$\text{Profit Percentage} \approx 42.857\%$

Rounding to two decimal places, we get approximately 42.86%.

Step-by-Step Calculation

1. Assume Selling Price (SP) = 100.
2. Calculate Cost Price (CP): CP is 30% less than SP. $\text{CP} = 100 - (30/100)*100 = 100 - 30 = 70$.
3. Calculate Profit: Profit = SP - CP = $100 - 70 = 30$.
4. Calculate Profit Percentage: Profit Percentage = (Profit / CP) * 100. Profit Percentage = $(30 / 70) * 100$.
5. Simplify: $(3/7) * 100 \approx 42.86\%$.

Therefore, the profit percentage is approximately 42.86%.

Revision Table: Profit and Loss Concepts

Additional Information: Percentage Calculations

Understanding percentage calculations is vital for profit and loss problems. A percentage represents a part of a whole, expressed as a fraction of 100.

• Percentage Increase: To find a value that is X% more than Y, calculate $Y + (X/100) \times Y = Y(1 + X/100)$.
• Percentage Decrease: To find a value that is X% less than Y, calculate $Y - (X/100) \times Y = Y(1 - X/100)$.
• In this problem, CP is 30% less than SP. So, $\text{CP} = \text{SP} \times (1 - 30/100) = \text{SP} \times (70/100) = 0.7 \times \text{SP}$.
• The profit percentage is always calculated with respect to the cost price unless stated otherwise.