By selling a radio for Rs. 950, a man loses 5%. What per cent shall he gain by selling it for Rs,1040 ?

Options

A. 0.04
B. 0.045
C. 0.05
D. 0.09

Answer

To solve the problem step by step, we will first find the cost price of the radio using the information about the selling price and the loss percentage. Then, we will calculate the gain percentage when the radio is sold for Rs. 1040.

### Step 1: Find the Cost Price (CP) of the Radio

Given:
- Selling Price (SP) = Rs. 950
- Loss Percentage = 5%

We know that:
\[ \text{Loss} = \frac{\text{Loss Percentage}}{100} \times \text{Cost Price} \]

From the loss, we can express the relationship between SP, CP, and Loss:
\[ \text{SP} = \text{CP} - \text{Loss} \]

Substituting the loss in terms of CP:
\[ \text{SP} = \text{CP} - \left(\frac{5}{100} \times \text{CP}\right) \]
\[ \text{SP} = \text{CP} \left(1 - \frac{5}{100}\right) \]
\[ \text{SP} = \text{CP} \left(\frac{95}{100}\right) \]

Now, we can rearrange this to find CP:
\[ \text{CP} = \text{SP} \times \frac{100}{95} \]

Substituting the value of SP:
\[ \text{CP} = 950 \times \frac{100}{95} \]
\[ \text{CP} = 950 \times \frac{20}{19} \]
\[ \text{CP} = 1000 \]

### Step 2: Calculate the Gain when Selling for Rs. 1040

Now that we have the cost price, we can find the gain when the radio is sold for Rs. 1040.

Given:
- New Selling Price (SP) = Rs. 1040

Gain can be calculated as:
\[ \text{Gain} = \text{SP} - \text{CP} \]
\[ \text{Gain} = 1040 - 1000 \]
\[ \text{Gain} = 40 \]

### Step 3: Calculate the Gain Percentage

Gain Percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100 \]
\[ \text{Gain Percentage} = \left(\frac{40}{1000}\right) \times 100 \]
\[ \text{Gain Percentage} = 4\% \]

### Final Answer

The man shall gain **4%** by selling the radio for Rs. 1040.

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