A merchant incurred a loss of 5% by selling a book for Rs 25.65. If he sells it for Rs 31,05. find his gain percent or loss percent.

Options

A. Gain 15%
B. Loss 15%
C. Gain 10%
D. Loss 10%

Answer

To solve the problem step by step, we need to find the cost price (CP) of the book first, and then determine the gain or loss percentage when the book is sold for Rs 31.05.

### Step 1: Find the Cost Price (CP)
The merchant incurred a loss of 5% when selling the book for Rs 25.65.

Using the formula for loss:
\[ \text{Loss} = \text{CP} - \text{SP} \]
Where:
- SP = Selling Price = Rs 25.65
- Loss = 5% of CP

Since the loss is 5%, we can express this as:
\[ \text{CP} = \text{SP} + \text{Loss} \]
\[ \text{Loss} = 0.05 \times \text{CP} \]

Substituting the values:
\[ \text{CP} = 25.65 + 0.05 \times \text{CP} \]

Rearranging the equation:
\[ \text{CP} - 0.05 \times \text{CP} = 25.65 \]
\[ 0.95 \times \text{CP} = 25.65 \]

Now, solving for CP:
\[ \text{CP} = \frac{25.65}{0.95} \]
\[ \text{CP} = 27 \]

### Step 2: Calculate the Gain when Selling at Rs 31.05
Now, we need to find the gain when the book is sold for Rs 31.05.

Gain can be calculated as:
\[ \text{Gain} = \text{SP} - \text{CP} \]
Where:
- SP = Selling Price = Rs 31.05
- CP = Cost Price = Rs 27

Substituting the values:
\[ \text{Gain} = 31.05 - 27 \]
\[ \text{Gain} = 4.05 \]

### Step 3: 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:
\[ \text{Gain Percentage} = \left( \frac{4.05}{27} \right) \times 100 \]

Calculating the gain percentage:
\[ \text{Gain Percentage} = \left( 0.15 \right) \times 100 \]
\[ \text{Gain Percentage} = 15\% \]

### Final Answer
The merchant has a gain of 15%.