Understanding the Profit and Loss Problem

This question involves calculating the selling price required to achieve a desired profit percentage after initially selling an item at a loss. We are given the initial selling price (SP1) and the percentage loss incurred. We need to find the selling price (SP2) that would yield a specific percentage profit.

Step-by-Step Solution to Find the New Selling Price

To solve this problem, we first need to determine the cost price (CP) of the apples. The cost price is the price at which the fruit seller bought the apples. Once we know the cost price, we can calculate the selling price needed to make a 10% profit.

1. Calculate the Cost Price (CP)

The fruit seller loses 15% when selling apples at Rs. 68 per kg. This means the selling price of Rs. 68 represents (100% - 15%) = 85% of the cost price.

Let CP be the cost price per kg.

The relationship between Selling Price (SP), Cost Price (CP), and Loss Percentage is:

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

We are given SP = Rs. 68 and Loss Percentage = 15%.

So, the equation becomes:

$68 = \text{CP} \times (1 - \frac{15}{100})$

$68 = \text{CP} \times (1 - 0.15)$

$68 = \text{CP} \times 0.85$

Now, we can find the CP:

$\text{CP} = \frac{68}{0.85}$

$\text{CP} = 80$

The cost price of the apples is Rs. 80 per kg.

2. Calculate the New Selling Price (SP2) for 10% Profit

Now that we know the cost price is Rs. 80 per kg, the fruit seller wants to sell the apples to make a profit of 10%. This means the new selling price (SP2) should be the cost price plus 10% of the cost price.

The relationship between Selling Price (SP), Cost Price (CP), and Profit Percentage is:

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

We know CP = Rs. 80 and the desired Profit Percentage = 10%.

So, the new selling price (SP2) will be:

$\text{SP2} = 80 \times (1 + \frac{10}{100})$

$\text{SP2} = 80 \times (1 + 0.10)$

$\text{SP2} = 80 \times 1.10$

$\text{SP2} = 88$

The fruit seller should sell the apples at Rs. 88 per kg to make a profit of 10%.

Summary of Calculations

Therefore, to make a profit of 10%, the fruit seller should sell the apples at Rs. 88 per kg.

Revision Table: Key Profit and Loss Formulas

Additional Information on Profit and Loss Concepts

Profit and Loss are fundamental concepts in business mathematics. They are used to determine how much gain or loss has been made in a transaction.

• Cost Price (CP): This is the original price at which an article is bought.
• Selling Price (SP): This is the price at which an article is sold.
• Profit: Occurs when the Selling Price (SP) is greater than the Cost Price (CP). Profit = SP - CP.
• Loss: Occurs when the Cost Price (CP) is greater than the Selling Price (SP). Loss = CP - SP.
• Profit Percentage: The profit expressed as a percentage of the Cost Price. It's always calculated on the CP unless specified otherwise.
• Loss Percentage: The loss expressed as a percentage of the Cost Price. It's also always calculated on the CP unless specified otherwise.

Understanding the relationship between CP, SP, and percentage profit/loss is crucial for solving problems like the one with the fruit seller and apples. The cost price acts as the base for calculating both profit and loss percentages.