By selling a refrigerator for Rs. 23520, a dealer suffers a loss of 4%. What is the cost price of the refrigerator? At what price should he sell it to gain 8%?

Answer

To solve the problem step by step, we need to find the cost price (CP) of the refrigerator and then determine the selling price (SP) required to gain an 8% profit.

### Step 1: Understand the given information
- Selling Price (SP) = Rs. 23520
- Loss Percentage = 4%

### Step 2: Set up the equation for cost price (CP)
Let the cost price be \( CP = X \).

Since there is a loss of 4%, the selling price can be expressed as:
\[ SP = CP - \text{Loss} \]
The loss can be calculated as:
\[ \text{Loss} = \frac{4}{100} \times CP = \frac{4}{100} \times X \]
Thus, we can rewrite the equation for selling price:
\[ SP = X - \frac{4}{100} \times X \]
This simplifies to:
\[ SP = X \left(1 - \frac{4}{100}\right) = X \left(\frac{96}{100}\right) = \frac{96X}{100} \]

### Step 3: Substitute the selling price into the equation
Now we can substitute the known selling price into the equation:
\[ 23520 = \frac{96X}{100} \]

### Step 4: Solve for X (the cost price)
To find \( X \), we can rearrange the equation:
\[ X = \frac{23520 \times 100}{96} \]
Calculating this:
\[ X = \frac{2352000}{96} = 24500 \]
So, the cost price (CP) of the refrigerator is Rs. 24500.

### Step 5: Calculate the selling price for an 8% gain
To find the new selling price for an 8% gain, we use the formula:
\[ \text{New SP} = CP + \text{Gain} \]
The gain can be calculated as:
\[ \text{Gain} = \frac{8}{100} \times CP = \frac{8}{100} \times 24500 \]
Calculating the gain:
\[ \text{Gain} = 1960 \]
Now, substituting back to find the new selling price:
\[ \text{New SP} = 24500 + 1960 = 26460 \]

### Final Answers
- Cost Price (CP) = Rs. 24500
- Selling Price for 8% gain = Rs. 26460