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
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
A man sells a car to his friend at the loss of 10 %; who in return sells it for Rs. 54000 making a profit of 20 %. What was the initial value of the car?
An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
