If I purchased 11 books for Rs. 10 and sold all the books at the rate of 10 books for Rs. 11, the profit per cent is-

Options

A. `10%`
B. `11%`
C. `21%`
D. `100%`

Answer

To solve the problem step by step, we will calculate the cost price (CP), selling price (SP), profit, and then the profit percentage.

### Step 1: Calculate the Cost Price (CP)
We purchased 11 books for Rs. 10.

\[ \text{Cost Price (CP)} = \text{Total Cost for 11 books} = Rs. 10 \]

### Step 2: Calculate the Selling Price (SP)
We are selling the books at the rate of 10 books for Rs. 11.

To find the selling price for 11 books, we first find the selling price for 10 books and then calculate for 11 books.

\[ \text{Selling Price for 10 books} = Rs. 11 \]

Now, to find the selling price for 11 books, we can set up a proportion based on the selling price for 10 books:

\[ \text{Selling Price (SP) for 11 books} = \frac{11}{10} \times 11 = Rs. 12.1 \]

### Step 3: Calculate Profit
Profit is calculated as the difference between the selling price and the cost price.

\[ \text{Profit} = \text{Selling Price (SP)} - \text{Cost Price (CP)} = 12.1 - 10 = Rs. 2.1 \]

### Step 4: Calculate Profit Percentage
Profit percentage is calculated using the formula:

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

Substituting the values we have:

\[ \text{Profit Percentage} = \left( \frac{2.1}{10} \right) \times 100 = 21\% \]

### Conclusion
The profit percentage is **21%**.