By selling a fan for Rs. 710, a trader suffers a loss of Rs. 40. Find the cost price of the fan. At what price this fan should be sold in order to gain 10%?

Answer

To solve the problem step by step, we will first find the cost price of the fan and then determine the selling price required to gain a 10% profit.

### Step 1: Identify the given values
- Selling Price (SP) = Rs. 710
- Loss = Rs. 40

### Step 2: Calculate the Cost Price (CP)
The relationship between Selling Price, Cost Price, and Loss is given by the formula:
\[ \text{Selling Price} = \text{Cost Price} - \text{Loss} \]

Rearranging the formula to find the Cost Price:
\[ \text{Cost Price} = \text{Selling Price} + \text{Loss} \]

Substituting the known values:
\[ \text{Cost Price} = 710 + 40 \]
\[ \text{Cost Price} = 750 \]

### Step 3: Calculate the Gain for 10%
To find the selling price that gives a gain of 10%, we first need to calculate the gain amount. The gain is calculated as:
\[ \text{Gain} = \frac{10}{100} \times \text{Cost Price} \]

Substituting the Cost Price we found:
\[ \text{Gain} = \frac{10}{100} \times 750 \]
\[ \text{Gain} = 75 \]

### Step 4: Calculate the new Selling Price for a 10% gain
Now, we can find the new Selling Price (SP') that includes the gain:
\[ \text{New Selling Price} = \text{Cost Price} + \text{Gain} \]

Substituting the values:
\[ \text{New Selling Price} = 750 + 75 \]
\[ \text{New Selling Price} = 825 \]

### Final Answers:
- Cost Price of the fan = Rs. 750
- Selling Price for a 10% gain = Rs. 825

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