By selling an article for Rs. 450, a man loses 10%. The gain or loss per cent if he sells it for Rs. 540 is.
एक आदमी को Rs. 450 में एक वस्तु बेचने पर 10% की हानि होती है। यदि वह उसे Rs. 540 में बेचता है, तो उसे कितने प्रतिशत अभिलाभ या हानि होगी?

Options

A. 8% अभिलाभ
B. 8% हानि
C. 9% अभिलाभ
D. 9% हानि

Explanation

To solve the problem step by step, let's follow the reasoning based on the information given.

### Step 1: Determine the Cost Price (CP)
Let the cost price of the article be Rs. \( x \).

From the problem, we know that when the article is sold for Rs. 450, there is a loss of 10%. The formula for loss percentage is given by:

\[ \text{Loss Percentage} = \frac{\text{Loss}}{\text{Cost Price}} \times 100 \]

Given that the loss percentage is 10%, we can express the loss in terms of the cost price:

\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} = x - 450 \]

Setting up the equation using the loss percentage:

\[ 10 = \frac{x - 450}{x} \times 100 \]

### Step 2: Solve the Equation
Now, we can simplify and solve for \( x \):

\[ 10 = \frac{x - 450}{x} \times 100 \]

Dividing both sides by 100:

\[ 0.1 = \frac{x - 450}{x} \]

Cross-multiplying gives:

\[ 0.1x = x - 450 \]

Rearranging the equation:

\[ x - 0.1x = 450 \]

\[ 0.9x = 450 \]

Dividing both sides by 0.9:

\[ x = \frac{450}{0.9} = 500 \]

So, the cost price (CP) is Rs. 500.

### Step 3: Calculate Gain or Loss at Selling Price of Rs. 540
Now, we need to find the gain or loss when the selling price is Rs. 540.

\[ \text{Selling Price (SP)} = 540 \]

Calculating the gain:

\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} = 540 - 500 = 40 \]

### Step 4: Calculate Gain Percentage
Now, we can calculate the gain percentage using the formula:

\[ \text{Gain Percentage} = \frac{\text{Gain}}{\text{Cost Price}} \times 100 \]

Substituting the values:

\[ \text{Gain Percentage} = \frac{40}{500} \times 100 = 8\% \]

### Final Answer
Thus, if he sells the article for Rs. 540, he gains 8%.

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