A person buys a radio for 1030 and he spent 50 on its repairs. If he sold it for 1200, find the profit percent

Options

A. 10 1/3
B. 11 1/9
C. 12 1/2
D. none of these

Answer

To solve the problem step by step, we will calculate the cost price, selling price, profit, and then the profit percentage.

### Step 1: Calculate the Total Cost Price (CP)
The person buys the radio for Rs. 1030 and spends Rs. 50 on repairs.
To find the total cost price, we add the purchase price and the repair cost:

\[ \text{Total CP} = \text{Cost Price} + \text{Repair Cost} = 1030 + 50 = 1080 \]

### Step 2: Identify the Selling Price (SP)
The selling price of the radio is given as Rs. 1200.

### Step 3: Calculate the Profit
Profit can be calculated by subtracting the total cost price from the selling price:

\[ \text{Profit} = \text{Selling Price} - \text{Total CP} = 1200 - 1080 = 120 \]

### Step 4: Calculate the Profit Percentage
Profit percentage is calculated using the formula:

\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Total CP}} \right) \times 100 \]

Substituting the values we have:

\[ \text{Profit Percentage} = \left( \frac{120}{1080} \right) \times 100 \]

Calculating this gives:

\[ \text{Profit Percentage} = \left( \frac{120 \times 100}{1080} \right) = \frac{12000}{1080} \approx 11.11\% \]

### Step 5: Express the Profit Percentage in Fraction
To express 11.11% as a fraction:

\[ 11.11\% = 11 \frac{1}{9}\% \]

### Final Answer
The profit percentage is \( 11 \frac{1}{9}\% \).

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