Solving Profit and Loss Percentage on Equal Priced Items

This question involves calculating the overall profit or loss percentage when two items, having the same initial cost price, are sold with different profit and loss percentages.

Step-by-Step Calculation Breakdown

To find the overall profit or loss percentage, we need to compare the total cost price (CP) with the total selling price (SP) after considering the profit on one item and the loss on the other.

Step 1: Assume a Cost Price (CP) for Each Item.

Since the problem states the two items have equal prices, let's assume the cost price for each item is $100. This assumption simplifies the calculation of percentages.

Cost Price of Item 1 = $ \text{CP}_1 = 100 $

Cost Price of Item 2 = $ \text{CP}_2 = 100 $

Step 2: Calculate the Selling Price (SP) of the First Item.

The first item is sold at a 12% profit. The formula for selling price with profit is:

$ \text{SP} = \text{CP} \times \left( 1 + \frac{\text{Profit Percentage}}{100} \right) $

So, for Item 1:

$ \text{SP}_1 = 100 \times \left( 1 + \frac{12}{100} \right) = 100 \times (1 + 0.12) = 100 \times 1.12 = 112 $

The selling price of the first item is $112.

Step 3: Calculate the Selling Price (SP) of the Second Item.

The second item is sold at an 8% loss. The formula for selling price with loss is:

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

So, for Item 2:

$ \text{SP}_2 = 100 \times \left( 1 - \frac{8}{100} \right) = 100 \times (1 - 0.08) = 100 \times 0.92 = 92 $

The selling price of the second item is $92.

Step 4: Calculate the Total Cost Price and Total Selling Price.

Total Cost Price = Cost of Item 1 + Cost of Item 2

$ \text{CP}_{\text{Total}} = \text{CP}_1 + \text{CP}_2 = 100 + 100 = 200 $

Total Selling Price = Selling Price of Item 1 + Selling Price of Item 2

$ \text{SP}_{\text{Total}} = \text{SP}_1 + \text{SP}_2 = 112 + 92 = 204 $

Step 5: Determine Overall Profit or Loss.

Compare the Total Selling Price ($ \text{SP}_{\text{Total}} $) with the Total Cost Price ($ \text{CP}_{\text{Total}} $).

Since $ \text{SP}_{\text{Total}} = 204 $ is greater than $ \text{CP}_{\text{Total}} = 200 $, there is an overall profit.

Overall Profit Amount = $ \text{SP}_{\text{Total}} - \text{CP}_{\text{Total}} = 204 - 200 = 4 $

Step 6: Calculate the Overall Profit Percentage.

The formula for overall profit percentage is:

$ \text{Overall Profit Percentage} = \left( \frac{\text{Overall Profit Amount}}{\text{Total Cost Price}} \right) \times 100\% $

$ \text{Overall Profit Percentage} = \left( \frac{4}{200} \right) \times 100\% $

$ \text{Overall Profit Percentage} = \left( \frac{1}{50} \right) \times 100\% = 2\% $

Therefore, T makes an overall profit of 2%.

Summary Table

The final result shows a total selling price ($204) greater than the total cost price ($200), resulting in a profit of 2%.