On selling an article for Rs. 264 a man loses 4%. In order to gain 12%, for how much he must sell the article?

Options

A. Rs.283.85
B. Rs.308
C. Rs.285
D. Rs.298.50

Answer

To solve the problem step by step, we need to find out the selling price required to gain a profit of 12% after knowing that selling the article for Rs. 264 results in a loss of 4%.

### Step 1: Determine the Cost Price (CP)
We know that selling the article for Rs. 264 results in a loss of 4%. This means that the selling price (SP) is 96% of the cost price (CP).

Let the cost price be \( CP \).

Since he is losing 4%, we can express this as:
\[ SP = CP - 0.04 \times CP = 0.96 \times CP \]

Given that \( SP = 264 \):
\[ 0.96 \times CP = 264 \]

To find the cost price, we rearrange the equation:
\[ CP = \frac{264}{0.96} \]

Calculating this gives:
\[ CP = 275 \]

### Step 2: Calculate the Selling Price for a 12% Gain
To find the selling price that would give a 12% gain, we need to calculate 112% of the cost price (since a gain of 12% means selling at 112% of the cost price).

\[ SP_{12\%} = CP + 0.12 \times CP = 1.12 \times CP \]

Substituting the cost price we found:
\[ SP_{12\%} = 1.12 \times 275 \]

Calculating this gives:
\[ SP_{12\%} = 308 \]

### Final Answer
Therefore, in order to gain 12%, the article must be sold for Rs. 308.

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