Understanding Profit and Loss Concepts

This question involves calculating the original cost price of an item when a loss percentage is known and then determining the required selling price to achieve a specific profit percentage. Finally, we need to find the difference between the desired selling price and the original selling price.

Step-by-Step Solution to the Problem

Step 1: Calculate the Cost Price (CP) of the Item

We are given that selling the item for Rs. 696 resulted in a loss of 13%. This means that the selling price (SP) is 13% less than the cost price (CP). In other words, the selling price is \(100\% - 13\% = 87\%\) of the cost price.

We can write this relationship as:

\(\text{Selling Price} = \text{Cost Price} \times (1 - \text{Loss Percentage})\)

Plugging in the given values:

\(696 = \text{CP} \times (1 - 0.13)\)

\(696 = \text{CP} \times 0.87\)

To find the Cost Price, we rearrange the formula:

\(\text{CP} = \frac{696}{0.87}\)

Performing the division:

\(\text{CP} = 800\)

So, the cost price of the item was Rs. 800.

Step 2: Calculate the Selling Price (SP) for a 10% Profit

Now that we know the cost price (CP = Rs. 800), we want to find the selling price required to gain a profit of 10%. A 10% profit means the selling price should be 10% more than the cost price. In other words, the selling price should be \(100\% + 10\% = 110\%\) of the cost price.

We can write this relationship as:

\(\text{New Selling Price} = \text{CP} \times (1 + \text{Profit Percentage})\)

Plugging in the values:

\(\text{New Selling Price} = 800 \times (1 + 0.10)\)

\(\text{New Selling Price} = 800 \times 1.10\)

Performing the multiplication:

\(\text{New Selling Price} = 880\)

To gain a profit of 10%, Unnati should have sold the item for Rs. 880.

Step 3: Determine How Much the Price Should Have Been Raised

The original selling price was Rs. 696. The new desired selling price for a 10% profit is Rs. 880. The question asks by how much the price should have been raised. This is the difference between the new selling price and the original selling price.

\(\text{Amount to Raise Price} = \text{New Selling Price} - \text{Original Selling Price}\)

\(\text{Amount to Raise Price} = 880 - 696\)

\(\text{Amount to Raise Price} = 184\)

Therefore, Unnati should have raised the price by Rs. 184 to gain a profit of 10%.

Summary of Calculations

Revision Table: Key Formulas in Profit and Loss

Understanding the basic formulas is crucial for solving profit and loss problems.

Additional Information: Solving Percentage-Based Problems

Problems involving profit and loss are essentially applications of percentages. Here are some points to remember when tackling such questions:

• Always identify the base for the percentage calculation. In profit and loss, percentages are usually calculated on the Cost Price (CP), unless otherwise stated.
• A loss means the selling price is less than the cost price. A profit means the selling price is more than the cost price.
• If an item is sold at an X% loss, the selling price is \((100 - X)\%\) of the cost price.
• If an item is sold at an Y% profit, the selling price is \((100 + Y)\%\) of the cost price.
• Be careful with consecutive percentages or discounts/markups.

These concepts help in quickly setting up the equations needed to find unknown values like CP or SP.