Shivam purchased two watches, first for Rs. 12000 and the second for Rs. 10000. He sold both the watches, first one at the profit of 10 percent and the second at a loss of 10 percent. What is the overall profit or loss?
0.909 percent profit
Understanding Profit and Loss on Multiple Items
This problem involves calculating the overall profit or loss when two items are bought and sold at different prices and different profit/loss percentages. We need to find the cost price and selling price for each item and then calculate the total cost price and total selling price to determine the overall gain or loss.
Calculating Selling Price for Each Watch
Let's first calculate the selling price for the first watch and the second watch individually.
First Watch Calculation
- Cost Price (CP\(_1\)) = Rs. 12000
- Profit Percentage = 10%
- Profit Amount = 10% of Rs. 12000
- Profit Amount = $\frac{10}{100} \times 12000 = 0.10 \times 12000 = 1200$
- Selling Price (SP\(_1\)) = CP\(_1\) + Profit Amount
- SP\(_1\) = $12000 + 1200 = 13200$
- So, the selling price of the first watch is Rs. 13200.
Second Watch Calculation
- Cost Price (CP\(_2\)) = Rs. 10000
- Loss Percentage = 10%
- Loss Amount = 10% of Rs. 10000
- Loss Amount = $\frac{10}{100} \times 10000 = 0.10 \times 10000 = 1000$
- Selling Price (SP\(_2\)) = CP\(_2\) - Loss Amount
- SP\(_2\) = $10000 - 1000 = 9000$
- So, the selling price of the second watch is Rs. 9000.
Calculating Overall Profit or Loss
Now, we need to find the total cost price and the total selling price for both watches combined.
- Total Cost Price (Total CP) = CP\(_1\) + CP\(_2\)
- Total CP = $12000 + 10000 = 22000$
- Total Selling Price (Total SP) = SP\(_1\) + SP\(_2\)
- Total SP = $13200 + 9000 = 22200$
Comparing the Total Selling Price and Total Cost Price:
- Total SP (Rs. 22200) is greater than Total CP (Rs. 22000).
- This means there is an overall profit.
- Overall Profit Amount = Total SP - Total CP
- Overall Profit Amount = $22200 - 22000 = 200$
- The overall profit is Rs. 200.
Calculating Overall Profit Percentage
To find the overall profit percentage, we use the formula:
Overall Profit Percentage = $\left(\frac{\text{Overall Profit Amount}}{\text{Total Cost Price}}\right) \times 100$
Plugging in the values:
Overall Profit Percentage = $\left(\frac{200}{22000}\right) \times 100$
Overall Profit Percentage = $\frac{200}{220} = \frac{20}{22} = \frac{10}{11}$
Now, we convert the fraction to a decimal percentage:
$\frac{10}{11} \approx 0.90909...$ percent
Rounded to three decimal places, the overall profit is 0.909 percent.
| Item | Cost Price (CP) | Profit/Loss % | Profit/Loss Amount | Selling Price (SP) |
|---|---|---|---|---|
| Watch 1 | Rs. 12000 | 10% Profit | Rs. 1200 | Rs. 13200 |
| Watch 2 | Rs. 10000 | 10% Loss | Rs. 1000 | Rs. 9000 |
| Total | Rs. 22000 | Rs. 22200 |
Total SP (Rs. 22200) > Total CP (Rs. 22000), indicating a profit.
Overall Profit = Rs. 22200 - Rs. 22000 = Rs. 200
Overall Profit Percentage = $\left(\frac{200}{22000}\right) \times 100 = \frac{200}{220} \approx 0.909\%$
The overall result is a profit of approximately 0.909 percent.
Revision Table: Key Concepts in Profit and Loss
| Concept | Formula | Description |
|---|---|---|
| Profit | SP > CP | Selling Price is more than Cost Price. |
| Loss | SP < CP | Selling Price is less than Cost Price. |
| Profit Amount | SP - CP | The difference between Selling Price and Cost Price when there is a profit. |
| Loss Amount | CP - SP | The difference between Cost Price and Selling Price when there is a loss. |
| Profit Percentage | $\left(\frac{\text{Profit Amount}}{\text{CP}}\right) \times 100$ | Profit expressed as a percentage of the Cost Price. |
| Loss Percentage | $\left(\frac{\text{Loss Amount}}{\text{CP}}\right) \times 100$ | Loss expressed as a percentage of the Cost Price. |
| Selling Price (Profit) | CP $\times \left(1 + \frac{\text{Profit \%}}{100}\right)$ | Calculating SP when Profit % is known. |
| Selling Price (Loss) | CP $\times \left(1 - \frac{\text{Loss \%}}{100}\right)$ | Calculating SP when Loss % is known. |
Additional Information on Profit and Loss Problems
When dealing with profit and loss for multiple items, it's crucial to calculate the total cost price and total selling price for all items combined before determining the overall profit or loss. You cannot simply average the individual profit/loss percentages unless the cost prices are the same.
In this problem, Shivam's two watches had different cost prices (Rs. 12000 and Rs. 10000). Even though one was sold at a 10% profit and the other at a 10% loss, the net result is not zero percent profit or loss because the profit and loss percentages are applied to different base amounts (the cost prices).
- A 10% profit on Rs. 12000 is Rs. 1200.
- A 10% loss on Rs. 10000 is Rs. 1000.
Since the profit amount (Rs. 1200) is greater than the loss amount (Rs. 1000), the overall transaction results in a net profit of Rs. 200. This net profit is then calculated as a percentage of the total cost price (Rs. 22000) to find the overall percentage profit.
Important Questions from Profit and Loss
Ram bought a chair at 35% discount on its market price, Had Ram got no discount, he would have had to pay ₹245 more. How much did Ram pay for the chair?
A shopkeeper bought an item for Rs. 4,500 and sold it at a loss of 5%. From this money, he bought another item and sold it at a profit of 10%. What is his overall profit?
A man sells two articles at Rs. 9,180 each. He gains 8% on one article and loses 15% on the other. His overall profit or loss is:
A shopkeeper selling an article for ₹46 loses 8%. In order to gain 6%, what should be the selling price of the article?
Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?
