Understanding the Problem: Profit and Loss Calculation

The question asks us to determine how much higher the selling price should have been compared to the cost price to achieve a 10% profit, given that the item was initially sold at a 12% loss for Rs. 220.

To solve this, we first need to find the original cost price (CP) of the item. Then, we calculate the desired selling price (SP) for a 10% profit. Finally, we find the difference between this desired SP and the CP.

Step 1: Calculate the Cost Price (CP)

We are given the selling price (SP) and the loss percentage. The formula relating SP, CP, and loss percentage is:

\(\text{SP} = \text{CP} \times (1 - \text{Loss \% / 100})\)

We are given:

• Selling Price (SP) = Rs. 220
• Loss Percentage = 12%

Substituting the values into the formula:

\(220 = \text{CP} \times (1 - 12 / 100)\)

\(220 = \text{CP} \times (1 - 0.12)\)

\(220 = \text{CP} \times 0.88\)

Now, we solve for CP:

\(\text{CP} = \frac{220}{0.88}\)

\(\text{CP} = \frac{22000}{88}\)

\(\text{CP} = \text{Rs. } 250\)

So, the cost price of the item was Rs. 250.

Step 2: Calculate the Selling Price for 10% Profit

Now that we have the cost price, we need to find the selling price (let's call it SP') required to make a 10% profit. The formula relating SP', CP, and profit percentage is:

\(\text{SP'} = \text{CP} \times (1 + \text{Profit \% / 100})\)

We know:

• Cost Price (CP) = Rs. 250
• Desired Profit Percentage = 10%

Substituting the values:

\(\text{SP'} = 250 \times (1 + 10 / 100)\)

\(\text{SP'} = 250 \times (1 + 0.10)\)

\(\text{SP'} = 250 \times 1.10\)

\(\text{SP'} = \text{Rs. } 275\)

To make a profit of 10%, Junko should have sold the item for Rs. 275.

Step 3: Find the Difference Above Cost Price

The question asks by how much the selling price (for 10% profit) should have been raised above the cost price. This is the difference between the desired selling price (SP') and the cost price (CP).

Difference = SP' - CP

Difference = Rs. 275 - Rs. 250

Difference = Rs. 25

Therefore, Junko should have raised the selling price by Rs. 25 above the cost price to make a profit of 10%.

Summary of Calculations

The selling price should have been Rs. 25 above the cost price to achieve a 10% profit.

Revision Table: Key Concepts

Additional Information: Profit and Loss Fundamentals

Profit and loss calculations are fundamental concepts in business and mathematics. They help in understanding the financial outcome of selling an item.

• Cost Price (CP): This is the original price at which an item is bought or manufactured.
• Selling Price (SP): This is the price at which an item is sold.
• Profit: Occurs when SP > CP. The profit amount is SP - CP.
• Loss: Occurs when SP < CP. The loss amount is CP - SP.
• Percentage calculations: Both profit and loss percentages are typically calculated with respect to the Cost Price unless specified otherwise. Understanding how to work with percentages in these formulas is crucial for solving such problems.

This problem combined both a loss scenario and a profit scenario, requiring us to first find the common link (Cost Price) before calculating the desired outcome.