Finding the Cost Price When There is a Loss

This question asks us to determine the original cost price of an article given its selling price and the percentage of loss incurred during the sale. Understanding the relationship between Cost Price (CP), Selling Price (SP), and Loss Percentage is crucial for solving such problems.

Understanding Loss Percentage

Loss occurs when the Selling Price (SP) of an article is less than its Cost Price (CP). The loss percentage is calculated based on the Cost Price. If there is a loss of 5%, it means the selling price is 5% less than the cost price.

Given Information

• Selling Price (SP) = Rs. 760
• Loss Percentage = 5%

Calculating the Cost Price (CP)

The formula relating Selling Price, Cost Price, and Loss Percentage is:

\( \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss Percentage}}{100}\right) \)

We are given the SP and the Loss Percentage, and we need to find the CP. We can rearrange the formula to solve for CP:

\( \text{CP} = \frac{\text{SP}}{1 - \frac{\text{Loss Percentage}}{100}} \)

Now, let's substitute the given values into the formula:

\( \text{CP} = \frac{760}{1 - \frac{5}{100}} \)

First, calculate the value inside the bracket:

\( 1 - \frac{5}{100} = 1 - 0.05 = 0.95 \)

Now, substitute this back into the formula for CP:

\( \text{CP} = \frac{760}{0.95} \)

To perform this division, we can remove the decimal from the denominator by multiplying both the numerator and the denominator by 100:

\( \text{CP} = \frac{760 \times 100}{0.95 \times 100} = \frac{76000}{95} \)

Now, divide 76000 by 95:

\( \frac{76000}{95} = 800 \)

So, the Cost Price (CP) of the article is Rs. 800.

Verification

Let's verify the answer. If the Cost Price is Rs. 800 and there is a 5% loss, the loss amount would be:

\( \text{Loss Amount} = 5\% \text{ of } 800 = \frac{5}{100} \times 800 = 5 \times 8 = 40 \)

The Selling Price would then be:

\( \text{SP} = \text{CP} - \text{Loss Amount} = 800 - 40 = 760 \)

This matches the given Selling Price, confirming that our calculated Cost Price of Rs. 800 is correct.

Revision Table: Key Formulas for Profit and Loss

Additional Information: Related Concepts

• Profit: When the Selling Price (SP) is greater than the Cost Price (CP). Profit = SP - CP.
• Profit Percentage: Calculated as \( \frac{\text{Profit}}{\text{CP}} \times 100 \).
• Loss: When the Selling Price (SP) is less than the Cost Price (CP). Loss = CP - SP.
• Trade Discount: A reduction in the list price given by the seller to the buyer at the time of sale. It is usually expressed as a percentage.
• Cash Discount: A reduction in the amount to be paid, offered for prompt payment.

Problems involving cost price, selling price, profit, and loss are common in commercial arithmetic and are important for understanding basic business calculations.