On selling a fan for Rs. 4700, a shopkeeper loses 6%. At what price must he sell it gain 6%?

Answer

To solve the problem step by step, we will first determine the cost price of the fan based on the information provided about the selling price and the loss percentage. Then, we will calculate the selling price required to achieve a gain of 6%.

### Step 1: Identify the Selling Price and Loss Percentage
- The selling price (SP) of the fan is given as Rs. 4700.
- The loss percentage is 6%.

### Step 2: Calculate the Cost Price
Let the cost price (CP) be denoted as \( X \).

Since the shopkeeper incurs a loss of 6%, we can express the selling price in terms of the cost price:
\[ SP = CP - \text{Loss} \]
The loss can be calculated as:
\[ \text{Loss} = \frac{6}{100} \times CP = \frac{6}{100} \times X \]

Substituting this into the equation for selling price:
\[ 4700 = X - \frac{6}{100}X \]

This simplifies to:
\[ 4700 = X \left(1 - \frac{6}{100}\right) \]
\[ 4700 = X \left(\frac{94}{100}\right) \]

Now, we can solve for \( X \):
\[ X = \frac{4700 \times 100}{94} \]
\[ X = \frac{470000}{94} \]
\[ X = 5000 \]

So, the cost price of the fan is Rs. 5000.

### Step 3: Calculate the Selling Price for a Gain of 6%
To find the selling price for a gain of 6%, we again use the formula for selling price:
\[ SP = CP + \text{Gain} \]
The gain can be calculated as:
\[ \text{Gain} = \frac{6}{100} \times CP = \frac{6}{100} \times 5000 \]

Calculating the gain:
\[ \text{Gain} = \frac{6 \times 5000}{100} = 300 \]

Now substituting back into the selling price formula:
\[ SP = 5000 + 300 \]
\[ SP = 5300 \]

Thus, the selling price to gain 6% is Rs. 5300.

### Final Answer
The shopkeeper must sell the fan for Rs. 5300 to gain 6%.

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