A book-seller bought 200 textbooks for 12,000. He wanted to sell them at a profit so that he got 20 books free. At what profit percent should he sell them?

Options

A. 0.1
B. 0.11
C. 0.115
D. 0.12

Answer

To solve the problem, we need to determine the profit percentage at which the book-seller should sell the textbooks to effectively get 20 books for free. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the Cost Price (CP) of One Textbook
The total cost for 200 textbooks is 12,000. To find the cost price per textbook, we divide the total cost by the number of textbooks.

\[ \text{Cost Price (CP) per textbook} = \frac{\text{Total Cost}}{\text{Number of Textbooks}} = \frac{12000}{200} = 60 \]

**Hint:** Remember that the cost price per item is found by dividing the total cost by the total number of items.

### Step 2: Calculate the Total Number of Textbooks After Getting 20 Free
The book-seller wants to sell the textbooks such that he gets 20 textbooks free. Therefore, the total number of textbooks he will have to sell is:

\[ \text{Total Textbooks} = 200 + 20 = 220 \]

**Hint:** When calculating total items after getting some free, simply add the free items to the original quantity.

### Step 3: Determine the Selling Price (SP) Required to Achieve the Goal
To find out how much he needs to sell all 220 textbooks for, we first calculate the total cost of the 200 textbooks, which is 12,000. He wants to cover this cost and also make a profit.

Let’s denote the selling price per textbook as \( SP \). The total selling price for 220 textbooks will be:

\[ \text{Total Selling Price (SP)} = SP \times 220 \]

**Hint:** The total selling price is the price per item multiplied by the total number of items sold.

### Step 4: Set Up the Equation for Profit
To find the profit percentage, we need to establish the relationship between selling price and cost price. The profit is given by:

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

Substituting the values we have:

\[ \text{Profit} = (SP \times 220) - 12000 \]

**Hint:** Profit is the difference between total selling price and total cost.

### Step 5: Calculate the Selling Price to Achieve a Profit
Since we want to find the selling price that includes a profit, we can set the profit to be equal to the cost of the 20 free textbooks:

\[ \text{Profit} = 20 \times 60 = 1200 \]

Now we can set up the equation:

\[ (SP \times 220) - 12000 = 1200 \]

### Step 6: Solve for Selling Price (SP)
Rearranging the equation gives:

\[ SP \times 220 = 12000 + 1200 \]
\[ SP \times 220 = 13200 \]
\[ SP = \frac{13200}{220} = 60 \]

**Hint:** To isolate \( SP \), divide both sides of the equation by the number of textbooks.

### Step 7: Calculate the Profit Percentage
Now we can find the profit percentage using the formula:

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

Substituting the values we found:

\[ \text{Profit Percentage} = \left( \frac{60 - 60}{60} \right) \times 100 = 0\% \]

Since the selling price equals the cost price, there is no profit percentage.

**Hint:** Profit percentage is calculated based on the difference between selling price and cost price relative to the cost price.

### Conclusion
The book-seller should sell the textbooks at a selling price equal to the cost price to achieve the desired outcome of getting 20 books free, which results in a profit percentage of 0%.