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

Answer

To solve the problem step by step, we will first find the cost price of the color TV and then determine the selling price that would yield an 8% profit.

### Step 1: Understand the given information
- Selling Price (SP) = Rs. 23,520
- Loss Percentage = 4%

### Step 2: Calculate the Cost Price (CP)
We can use the formula for cost price when there is a loss:
\[ \text{Cost Price (CP)} = \frac{100}{100 - \text{Loss Percentage}} \times \text{Selling Price (SP)} \]

Substituting the values:
\[ \text{CP} = \frac{100}{100 - 4} \times 23,520 \]
\[ \text{CP} = \frac{100}{96} \times 23,520 \]

### Step 3: Simplify the calculation
Calculating \(\frac{100}{96}\):
\[ \frac{100}{96} = 1.04167 \quad (\text{approximately}) \]

Now, multiplying this by the selling price:
\[ \text{CP} = 1.04167 \times 23,520 \]

Calculating:
\[ \text{CP} = 24,500 \]

### Step 4: Calculate the new Selling Price for an 8% profit
To find the new selling price (SP) that would yield an 8% profit, we use the formula:
\[ \text{New SP} = \text{CP} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]

Substituting the values:
\[ \text{New SP} = 24,500 \times \left(1 + \frac{8}{100}\right) \]
\[ \text{New SP} = 24,500 \times 1.08 \]

### Step 5: Calculate the new Selling Price
Calculating:
\[ \text{New SP} = 24,500 \times 1.08 = 26,460 \]

### Final Answers
- Cost Price of the color TV = Rs. 24,500
- Selling Price for an 8% profit = Rs. 26,460

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