A radio is sold for Rs. 3120 at a loss of 4%. What will be the gain or loss percent if it is sold for Rs. 3445?

Answer

To solve the problem step-by-step, we will first find the cost price (CP) of the radio based on the selling price (SP) and the loss percentage. Then, we will calculate the gain or loss percentage when the radio is sold for Rs. 3445.

### Step 1: Calculate the Cost Price (CP)

Given:
- Selling Price (SP) = Rs. 3120
- Loss Percentage = 4%

We know that:
\[ \text{Loss} = \text{CP} \times \frac{\text{Loss Percentage}}{100} \]
\[ \text{SP} = \text{CP} - \text{Loss} \]

Substituting the loss in terms of CP:
\[ \text{SP} = \text{CP} - \left(\text{CP} \times \frac{4}{100}\right) \]
\[ \text{SP} = \text{CP} \left(1 - \frac{4}{100}\right) \]
\[ \text{SP} = \text{CP} \left(\frac{96}{100}\right) \]
\[ \text{SP} = \text{CP} \times 0.96 \]

Now, rearranging to find CP:
\[ \text{CP} = \frac{\text{SP}}{0.96} \]
\[ \text{CP} = \frac{3120}{0.96} \]
\[ \text{CP} = 3250 \]

### Step 2: Calculate Gain or Loss when Sold for Rs. 3445

Now we will find the gain or loss when the radio is sold for Rs. 3445.

Given:
- New Selling Price (SP) = Rs. 3445
- Cost Price (CP) = Rs. 3250

Now, we calculate the gain:
\[ \text{Gain} = \text{SP} - \text{CP} \]
\[ \text{Gain} = 3445 - 3250 \]
\[ \text{Gain} = 195 \]

### Step 3: Calculate Gain Percentage

Now, we can find the gain percentage:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100 \]
\[ \text{Gain Percentage} = \left(\frac{195}{3250}\right) \times 100 \]
\[ \text{Gain Percentage} = 6 \]

### Final Answer

The gain percentage when the radio is sold for Rs. 3445 is **6%**.

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