A merchant incurred a loss of 5% by selling a book for 25.65. If he sells it for 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 will follow these calculations:

### Step 1: Determine the Cost Price (CP)
The merchant incurred a loss of 5% when selling the book for Rs. 25.65. This means that the selling price (SP) is 95% of the cost price (CP).

Let’s denote the CP as \( CP \).

Since a loss of 5% implies:
\[ SP = CP - 5\% \text{ of } CP = 0.95 \times CP \]

Given that the SP is Rs. 25.65, we can set up the equation:
\[ 0.95 \times CP = 25.65 \]

### Step 2: Calculate the Cost Price (CP)
To find the CP, we rearrange the equation:
\[ CP = \frac{25.65}{0.95} \]

Calculating this gives:
\[ CP = 27 \]

### Step 3: Determine the New Selling Price (SP)
The new selling price is given as Rs. 31.05.

### Step 4: Calculate the Profit
Now, we will calculate the profit made when selling at the new SP:
\[ \text{Profit} = \text{New SP} - CP \]
\[ \text{Profit} = 31.05 - 27 = 4.05 \]

### Step 5: Calculate the Gain Percent
To find the gain percent, we use the formula:
\[ \text{Gain Percent} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
\[ \text{Gain Percent} = \left( \frac{4.05}{27} \right) \times 100 \]

Calculating this gives:
\[ \text{Gain Percent} = 15\% \]

### Final Answer
The merchant gains 15% when selling the book for Rs. 31.05.

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