Profit and Loss Calculation Explained

This problem involves calculating the original cost price of a suitcase based on a series of transactions involving profits. We need to work backward from the final selling price to determine the initial cost price for 'A'.

Understanding Key Concepts: Cost Price, Selling Price, and Profit

• Cost Price (CP): The price at which an item is bought.
• Selling Price (SP): The price at which an item is sold.
• Profit: When the Selling Price is greater than the Cost Price (\(SP > CP\)). Profit is calculated as \(Profit = SP - CP\).
• Profit Percentage: Calculated as \( \frac{Profit}{CP} \times 100\% \). Alternatively, \(SP = CP \times (1 + \frac{Profit\%}{100})\).

Step-by-Step Solution to Find A's Cost Price

Let's denote the cost price for A as \(CP_A\), the cost price for B as \(CP_B\), and the selling price for B as \(SP_B\).

Step 1: Analyze B's Transaction

'B' sells the suitcase to 'C' for Rs. 2860. This is the selling price for B (\(SP_B\)). B earns a profit of 30% on their cost price (\(CP_B\)).

Using the profit percentage formula:

\(SP_B = CP_B \times (1 + \frac{30}{100})\)

\(2860 = CP_B \times (1 + 0.30)\)

\(2860 = CP_B \times 1.30\)

Step 2: Calculate B's Cost Price

From the equation above, we can find \(CP_B\):

\(CP_B = \frac{2860}{1.30}\)

\(CP_B = 2200\)

So, the cost price for B was Rs. 2200.

Step 3: Relate B's Cost Price to A's Transaction

'A' sells the suitcase to 'B' at a 10% profit. The price at which A sells it to B is the cost price for B. Therefore, \(CP_B\) is the selling price for A (\(SP_A\)).

\(SP_A = CP_B = 2200\)

A earned a 10% profit on their cost price (\(CP_A\)). Using the profit percentage formula for A's transaction:

\(SP_A = CP_A \times (1 + \frac{10}{100})\)

\(2200 = CP_A \times (1 + 0.10)\)

\(2200 = CP_A \times 1.10\)

Step 4: Calculate A's Cost Price

From the equation above, we can find \(CP_A\):

\(CP_A = \frac{2200}{1.10}\)

\(CP_A = 2000\)

Thus, the cost price of the suitcase for 'A' was Rs. 2000.

Summary of Transactions

Working backward:

\(CP_B = \frac{SP_B}{1.30} = \frac{2860}{1.30} = 2200\)

\(CP_A = \frac{SP_A}{1.10} = \frac{CP_B}{1.10} = \frac{2200}{1.10} = 2000\)

The cost price for 'A' is Rs. 2000.

Profit and Loss Revision Table

Additional Information on Profit Calculation

When solving profit and loss problems involving multiple transactions, it's important to correctly identify the cost price and selling price for each person in the chain. The selling price for one person becomes the cost price for the next person in the transaction sequence.

• A's SP = B's CP
• B's SP = C's CP (or final selling price in this case)

Profit or loss percentage is always calculated based on the cost price unless specified otherwise.

In this problem, working backward from the known final selling price (\(SP_B\)) allowed us to first find \(CP_B\), and then use that value to find \(CP_A\).