Calculate Cost Price of Bike Sold at a Loss

This solution demonstrates how to determine the original price (cost price) of an item when its selling price and the percentage of loss are known.

Understanding Key Concepts

• Selling Price (SP): The amount for which the bike was sold. Here, SP = ₹13,600.
• Loss Percentage: The reduction in price from the original cost, expressed as a percentage of the cost price. Here, Loss% = 20%.
• Cost Price (CP): The original price the seller paid for the bike. This is the value we need to find.

Formula for Calculating Selling Price with Loss

When an item is sold at a loss, the selling price is calculated using the cost price and the loss percentage. The formula is:

$SP = CP \times (1 - \frac{Loss\%}{100})$

Where:

• $SP$ is the Selling Price
• $CP$ is the Cost Price
• $Loss\%$ is the Loss Percentage

Step-by-Step Calculation to Find Cost Price

We are given the following information:

• Selling Price (SP) = ₹13,600
• Loss Percentage = 20%

Let's use the formula to find the Cost Price (CP):

1. Plug the known values into the formula:

   $₹13,600 = CP \times (1 - \frac{20}{100})$

2. Simplify the term inside the parenthesis:

   $1 - \frac{20}{100} = 1 - 0.20 = 0.80$

   The equation now looks like this:

   $₹13,600 = CP \times 0.80$

3. Rearrange the formula to solve for CP:

   To find CP, divide the SP by 0.80.

   $CP = \frac{₹13,600}{0.80}$

4. Perform the division:

   $CP = 17,000$

   Therefore, the Cost Price (CP) is ₹17,000.

Final Answer Explanation

The cost price of the bike was ₹17,000. The seller bought the bike for ₹17,000 and sold it for ₹13,600. The loss amount is ₹17,000 - ₹13,600 = ₹3,400. This loss of ₹3,400 is exactly 20% of the original cost price (₹17,000), confirming our calculation.