the cost price of 100 books is equal to the selling price of 60 books. The gain or loss percentage will be :

Options

A. `66 %`
B. `66 2/3 %`
C. `66 1/3 %`
D. `66 3/4 %`

Answer

To solve the problem, let's break it down step by step.

### Step 1: Define Variables
Let the cost price (CP) of one book be \( x \). Therefore, the cost price of 100 books will be:
\[ \text{CP of 100 books} = 100x \]

### Step 2: Selling Price Calculation
According to the question, the cost price of 100 books is equal to the selling price (SP) of 60 books. Thus, we can express this as:
\[ 100x = \text{SP of 60 books} \]
Let the selling price of one book be \( y \). Therefore, the selling price of 60 books will be:
\[ \text{SP of 60 books} = 60y \]
Setting these equal gives us:
\[ 100x = 60y \]

### Step 3: Solve for Selling Price
From the equation \( 100x = 60y \), we can solve for \( y \):
\[ y = \frac{100x}{60} = \frac{5x}{3} \]

### Step 4: Calculate Gain
The gain can be calculated using the formula:
\[ \text{Gain} = \text{SP} - \text{CP} \]
For one book, the gain will be:
\[ \text{Gain} = y - x = \frac{5x}{3} - x = \frac{5x}{3} - \frac{3x}{3} = \frac{2x}{3} \]

### Step 5: Calculate Gain Percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{\frac{2x}{3}}{x} \right) \times 100 = \left( \frac{2}{3} \right) \times 100 = \frac{200}{3} \approx 66.67\% \]

### Conclusion
The gain percentage is approximately \( 66.67\% \).

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