A person sold an article at a loss of 7%. Had he sold it at a gain of 10.5%, he would have received 105 more. To gain 11%, he should have sold it (in) for:

Options

A. 600
B. 666
C. 636
D. 642

Answer

To solve the problem step by step, let's denote the Cost Price (CP) of the article as \( x \).

### Step 1: Determine the Selling Price at a Loss of 7%
When the article is sold at a loss of 7%, the Selling Price (SP) can be calculated as:
\[ SP = CP - (7\% \text{ of } CP) = x - 0.07x = 0.93x \]

**Hint:** Remember that a loss means the selling price is less than the cost price.

### Step 2: Determine the Selling Price at a Gain of 10.5%
If the article were sold at a gain of 10.5%, the Selling Price would be:
\[ SP = CP + (10.5\% \text{ of } CP) = x + 0.105x = 1.105x \]

**Hint:** A gain means the selling price is more than the cost price.

### Step 3: Set Up the Equation Based on the Given Information
According to the problem, selling at a gain of 10.5% would yield \( 105 \) more than selling at a loss of 7%. Therefore, we can set up the equation:
\[ 1.105x = 0.93x + 105 \]

**Hint:** This equation represents the relationship between the two selling prices.

### Step 4: Solve for Cost Price (CP)
Now, let's solve the equation:
\[ 1.105x - 0.93x = 105 \]
\[ 0.175x = 105 \]
\[ x = \frac{105}{0.175} = 600 \]

**Hint:** To isolate \( x \), divide both sides by \( 0.175 \).

### Step 5: Calculate the Selling Price for a Gain of 11%
Now that we have the Cost Price \( x = 600 \), we can find the Selling Price for a gain of 11%:
\[ SP = CP + (11\% \text{ of } CP) = 600 + 0.11 \times 600 = 600 + 66 = 666 \]

**Hint:** To find the selling price for a gain, add the gain to the cost price.

### Final Answer
Thus, to gain 11%, the person should have sold the article for:
\[ \boxed{666} \]