A person have a loss of 10% on selling a radio in Rs 810. If he sells it in Rs 1035, then his profit percentage is

Options

A. `20%`
B. `18%`
C. `25%`
D. `15%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the given information
- Selling Price (SP) when there is a loss = Rs 810
- Loss percentage = 10%

### Step 2: Calculate the Cost Price (CP)
Since there is a loss of 10%, we can express this as:
\[ \text{Loss} = \text{CP} - \text{SP} \]
Given that the loss is 10% of the Cost Price (CP):
\[ 10\% \text{ of CP} = \text{CP} - 810 \]

This can be rewritten as:
\[ 0.10 \times \text{CP} = \text{CP} - 810 \]

### Step 3: Rearranging the equation
Rearranging the equation gives us:
\[ 0.10 \text{CP} + 810 = \text{CP} \]
\[ 810 = \text{CP} - 0.10 \text{CP} \]
\[ 810 = 0.90 \text{CP} \]

### Step 4: Solve for CP
To find CP, divide both sides by 0.90:
\[ \text{CP} = \frac{810}{0.90} \]
\[ \text{CP} = 900 \]

### Step 5: Calculate the new Selling Price (SP)
Now, if the person sells the radio for Rs 1035, we need to find the profit:
\[ \text{New SP} = Rs 1035 \]

### Step 6: Calculate the Profit
Profit is calculated as:
\[ \text{Profit} = \text{New SP} - \text{CP} \]
\[ \text{Profit} = 1035 - 900 \]
\[ \text{Profit} = 135 \]

### Step 7: Calculate the Profit Percentage
Profit percentage is calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 \]
\[ \text{Profit Percentage} = \left(\frac{135}{900}\right) \times 100 \]

### Step 8: Simplify the Profit Percentage
Calculating this gives:
\[ \text{Profit Percentage} = \frac{13500}{900} \]
\[ \text{Profit Percentage} = 15\% \]

### Final Answer
Thus, the profit percentage when the radio is sold for Rs 1035 is **15%**.

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