A person buys 80 kg of rice and sells it at a profit of as much money as he paid for 30 kg His profit per cent is :

Options

A. `27 3/11`
B. 35
C. 40
D. `37 1/2`

Answer

To solve the problem, let’s break it down step by step.

### Step 1: Define Variables
Let the cost price (CP) of 1 kg of rice be \( x \). Therefore, the cost price of 80 kg of rice is:
\[ \text{CP of 80 kg} = 80 \times x = 80x \]

### Step 2: Calculate the Profit
According to the problem, the profit made by selling the rice is equal to the amount paid for 30 kg of rice. Therefore, the profit (P) is:
\[ P = \text{CP of 30 kg} = 30 \times x = 30x \]

### Step 3: Calculate the Selling Price
The selling price (SP) can be calculated using the formula:
\[ \text{SP} = \text{CP} + \text{Profit} = 80x + 30x = 110x \]

### Step 4: Calculate Profit Percentage
The profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{30x}{80x} \right) \times 100 = \left( \frac{30}{80} \right) \times 100 \]
Simplifying this gives:
\[ \text{Profit Percentage} = \left( \frac{3}{8} \right) \times 100 = 37.5\% \]

### Conclusion
Thus, the profit percentage is \( 37.5\% \).