If a person sells a book for Rs. 1170 then there will be a 22% loss find the profit or loss when the book is sold for Rs. 1450.

Options

A. 8.33% profit
B. 6.67% loss
C. 8.33% loss
D. 3.33% loss

Answer

To solve the problem, we need to find the cost price of the book first, and then determine the profit or loss when the book is sold for Rs. 1450.

### Step 1: Find the Cost Price (CP)
Given that selling the book for Rs. 1170 results in a 22% loss, we can use the formula for loss:

\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} \]

Since the loss is 22%, we can express it as:

\[ \text{Loss} = 0.22 \times \text{Cost Price} \]

We know that:

\[ \text{Selling Price} = \text{Cost Price} - \text{Loss} \]

Substituting the loss formula into the selling price equation gives:

\[ 1170 = \text{Cost Price} - (0.22 \times \text{Cost Price}) \]

This simplifies to:

\[ 1170 = \text{Cost Price} \times (1 - 0.22) \]

\[ 1170 = \text{Cost Price} \times 0.78 \]

Now, we can solve for the Cost Price:

\[ \text{Cost Price} = \frac{1170}{0.78} \]

Calculating this gives:

\[ \text{Cost Price} = 1500 \]

### Step 2: Determine Profit or Loss when Sold for Rs. 1450
Now that we have the Cost Price, we can find out the profit or loss when the book is sold for Rs. 1450.

Using the profit/loss formula:

\[ \text{Profit or Loss} = \text{Selling Price} - \text{Cost Price} \]

Substituting the values we have:

\[ \text{Profit or Loss} = 1450 - 1500 \]

Calculating this gives:

\[ \text{Profit or Loss} = -50 \]

Since the result is negative, it indicates a loss.

### Step 3: Calculate the Percentage of Loss
To find the percentage of loss, we use the formula:

\[ \text{Percentage Loss} = \left(\frac{\text{Loss}}{\text{Cost Price}}\right) \times 100 \]

Substituting the values:

\[ \text{Percentage Loss} = \left(\frac{50}{1500}\right) \times 100 \]

Calculating this gives:

\[ \text{Percentage Loss} = \frac{50}{1500} \times 100 = 3.33\% \]

### Final Answer
The loss when the book is sold for Rs. 1450 is **3.33%**.

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