Understanding the Profit and Loss Scenario

This problem involves a shopkeeper who conducts two separate transactions. The outcome of the first transaction (selling at a loss) determines the cost price for the second transaction (selling at a profit). We need to calculate the final profit or loss across both transactions compared to the initial cost.

Step-by-Step Calculation of Overall Profit

Let's break down the problem into two parts based on the transactions:

Transaction 1: Selling the first item at a loss

• The initial cost price (CP) of the first item is given as Rs. 4,500.
• The item was sold at a loss of 5%.

First, we calculate the amount of loss:

$\text{Loss Amount} = \frac{\text{Loss Percentage}}{100} \times \text{CP}$

$\text{Loss Amount} = \frac{5}{100} \times 4500$

$\text{Loss Amount} = 0.05 \times 4500$

$\text{Loss Amount} = \text{Rs. } 225$

Now, we find the selling price (SP) of the first item. Since it was sold at a loss, the selling price is the cost price minus the loss amount.

$\text{SP}_1 = \text{CP}_1 - \text{Loss Amount}$

$\text{SP}_1 = 4500 - 225$

$\text{SP}_1 = \text{Rs. } 4275$

This amount (Rs. 4275) is the money the shopkeeper received after selling the first item.

Transaction 2: Selling the second item at a profit

• The shopkeeper used the money from the first sale (Rs. 4275) to buy another item.
• So, the cost price (CP) of the second item is Rs. 4275.
• This item was sold at a profit of 10%.

Next, we calculate the amount of profit on the second item:

$\text{Profit Amount} = \frac{\text{Profit Percentage}}{100} \times \text{CP}_2$

$\text{Profit Amount} = \frac{10}{100} \times 4275$

$\text{Profit Amount} = 0.10 \times 4275$

$\text{Profit Amount} = \text{Rs. } 427.50$

Now, we find the selling price (SP) of the second item. Since it was sold at a profit, the selling price is the cost price plus the profit amount.

$\text{SP}_2 = \text{CP}_2 + \text{Profit Amount}$

$\text{SP}_2 = 4275 + 427.50$

$\text{SP}_2 = \text{Rs. } 4702.50$

This is the final amount of money the shopkeeper has after the second transaction.

Calculating the Overall Profit or Loss

The overall profit or loss is the difference between the final amount the shopkeeper has (final selling price) and the initial amount he spent (initial cost price).

• Initial Cost (CP of first item) = Rs. 4500
• Final Amount (SP of second item) = Rs. 4702.50

Overall Profit/Loss = Final Amount - Initial Cost

Overall Profit/Loss = $4702.50 - 4500$

Overall Profit/Loss = Rs. 202.50

Since the result is positive, it represents an overall profit.

Summary of Transactions

Overall Profit = Final SP - Initial CP = Rs. 4702.50 - Rs. 4500 = Rs. 202.50

Conclusion on Shopkeeper's Overall Profit

After completing both transactions, the shopkeeper started with Rs. 4,500 and ended with Rs. 4,702.50. Therefore, his overall profit is Rs. 202.50.

Revision Table: Key Profit and Loss Formulas

Additional Information on Consecutive Transactions

When dealing with consecutive profit and loss transactions where the selling price of the first transaction becomes the cost price of the second, it's crucial to calculate each step sequentially. You cannot simply add or subtract the percentages directly. The base value for calculating the percentage changes is different in each step.

• In the first transaction, the percentage loss is calculated on the initial cost price (Rs. 4500).
• In the second transaction, the percentage profit is calculated on the new cost price (Rs. 4275), which was the selling price of the first item.

This step-by-step method ensures the correct calculation of the final amount and thus the overall profit or loss.