A shopkeeper buys two books for Rs. 300. He sells the first book at a profit of 20% and the second book at a loss of 10%. What is the selling price of the first book if in the whole transaction there is no profit or no loss?

Options

A. Rs. 115
B. Rs. 125
C. Rs . 120
D. Rs. 110

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price (CP) of Each Book
The shopkeeper buys two books for a total of Rs. 300. Let's denote the cost price of the first book as \( CP_1 \) and the cost price of the second book as \( CP_2 \).

Given:
\[ CP_1 + CP_2 = 300 \]

### Step 2: Set Up the Profit and Loss Conditions
The first book is sold at a profit of 20%, and the second book is sold at a loss of 10%. The selling prices can be expressed as:
- Selling Price of the first book \( SP_1 = CP_1 + 20\% \text{ of } CP_1 = CP_1 + 0.2 \times CP_1 = 1.2 \times CP_1 \)
- Selling Price of the second book \( SP_2 = CP_2 - 10\% \text{ of } CP_2 = CP_2 - 0.1 \times CP_2 = 0.9 \times CP_2 \)

### Step 3: No Profit, No Loss Condition
Since the overall transaction results in no profit or loss, the total selling price must equal the total cost price:
\[ SP_1 + SP_2 = CP_1 + CP_2 \]
Substituting the expressions for \( SP_1 \) and \( SP_2 \):
\[ 1.2 \times CP_1 + 0.9 \times CP_2 = 300 \]

### Step 4: Substitute \( CP_2 \) in Terms of \( CP_1 \)
From Step 1, we have:
\[ CP_2 = 300 - CP_1 \]
Substituting \( CP_2 \) into the equation from Step 3:
\[ 1.2 \times CP_1 + 0.9 \times (300 - CP_1) = 300 \]

### Step 5: Simplify the Equation
Expanding the equation:
\[ 1.2 \times CP_1 + 270 - 0.9 \times CP_1 = 300 \]
Combining like terms:
\[ (1.2 - 0.9) \times CP_1 + 270 = 300 \]
\[ 0.3 \times CP_1 + 270 = 300 \]

### Step 6: Solve for \( CP_1 \)
Subtracting 270 from both sides:
\[ 0.3 \times CP_1 = 30 \]
Dividing both sides by 0.3:
\[ CP_1 = \frac{30}{0.3} = 100 \]

### Step 7: Calculate Selling Price of the First Book
Now that we have \( CP_1 \), we can find the selling price \( SP_1 \):
\[ SP_1 = 1.2 \times CP_1 = 1.2 \times 100 = 120 \]

### Final Answer
The selling price of the first book is Rs. 120.

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