Apples are bought at 25 for Rs. 250 and sold at 30 for Rs. 390. What is the profit/loss percentage in this transaction?
30% Profit
Understanding the Profit and Loss Problem
This question asks us to determine the profit or loss percentage when buying apples at one price and selling them at another. To do this, we first need to figure out the cost price and selling price per apple. Comparing the price for a large quantity can be confusing, so breaking it down to a single unit is helpful.
Calculating the Cost Price (CP) per Apple
We are told that 25 apples are bought for Rs. 250. To find the cost of one apple, we divide the total cost by the number of apples.
- Total Cost Price for 25 apples = Rs. 250
- Number of apples bought = 25
Cost Price (CP) per apple = \(\frac{\text{Total Cost Price}}{\text{Number of apples}} = \frac{250}{25}\)
CP per apple = Rs. 10
Calculating the Selling Price (SP) per Apple
We are told that 30 apples are sold for Rs. 390. To find the selling price of one apple, we divide the total sales amount by the number of apples sold.
- Total Selling Price for 30 apples = Rs. 390
- Number of apples sold = 30
Selling Price (SP) per apple = \(\frac{\text{Total Selling Price}}{\text{Number of apples}} = \frac{390}{30}\)
SP per apple = Rs. 13
Determining Profit or Loss on Apples
Now we compare the Cost Price (CP) and Selling Price (SP) per apple:
- CP per apple = Rs. 10
- SP per apple = Rs. 13
Since the Selling Price (Rs. 13) is greater than the Cost Price (Rs. 10), there is a profit in this transaction.
Profit per apple = SP per apple - CP per apple
Profit per apple = Rs. 13 - Rs. 10 = Rs. 3
Calculating the Profit Percentage
The profit percentage is calculated on the Cost Price. The formula for profit percentage is:
\(\text{Profit percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100\)
Using the values we calculated:
\(\text{Profit percentage} = \left( \frac{\text{Rs. 3}}{\text{Rs. 10}} \right) \times 100\)
\(\text{Profit percentage} = \left( 0.3 \right) \times 100\)
\(\text{Profit percentage} = 30\%\)
So, there is a 30% profit in this transaction.
| Item | Quantity | Total Price (Rs.) | Price per Unit (Rs.) |
|---|---|---|---|
| Bought (CP) | 25 | 250 | \(\frac{250}{25} = 10\) |
| Sold (SP) | 30 | 390 | \(\frac{390}{30} = 13\) |
Comparing CP per apple (Rs. 10) and SP per apple (Rs. 13), we see a profit of Rs. 3 per apple.
Profit % = \(\left( \frac{3}{10} \right) \times 100 = 30\%\)
Revision Table: Key Concepts in Profit & Loss
| Concept | Formula | Description |
|---|---|---|
| Profit | SP > CP | Selling Price is greater than Cost Price. Profit = SP - CP. |
| Loss | SP < CP | Selling Price is less than Cost Price. Loss = CP - SP. |
| Profit % | \(\left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\) | Profit calculated as a percentage of the Cost Price. |
| Loss % | \(\left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\) | Loss calculated as a percentage of the Cost Price. |
Additional Information: Why Calculate Per Unit?
In profit and loss problems where different quantities are bought and sold, it is essential to calculate the cost and selling price per unit (per apple in this case). This allows for a direct comparison and accurate calculation of the profit or loss on each item, which is then used to find the overall percentage. Trying to compare the cost of 25 apples with the selling price of 30 apples directly would be incorrect because the quantities are different.
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?
