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.

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

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.