A retailer bought 250 kg of a cereal and sold it at a profit to the extent of what he paid for 160 kg. What is his profit percentage?

Options

A. 32
B. 64
C. 36
D. 18

Answer

To solve the problem, we need to determine the profit percentage of the retailer based on the information provided. Let's break it down step by step.

### Step 1: Define Variables
Let the cost price (CP) of 1 kg of cereal be \( x \). Therefore, the cost price for 250 kg of cereal is:
\[ \text{Total Cost Price (CP)} = 250 \times x = 250x \]

### Step 2: Determine the Selling Price (SP)
According to the problem, the retailer sold the cereal at a profit equal to what he paid for 160 kg. The cost price for 160 kg of cereal is:
\[ \text{Cost Price for 160 kg} = 160 \times x = 160x \]
Thus, the selling price (SP) of the 250 kg of cereal is:
\[ \text{Selling Price (SP)} = \text{Total Cost Price} + \text{Profit} = 250x + 160x = 410x \]

### Step 3: Calculate Profit
Now, we can calculate the profit made by the retailer:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 410x - 250x = 160x \]

### Step 4: Calculate Profit Percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{160x}{250x} \right) \times 100 = \left( \frac{160}{250} \right) \times 100 \]
Simplifying this:
\[ \text{Profit Percentage} = \left( \frac{16}{25} \right) \times 100 = 64\% \]

### Final Answer
The profit percentage of the retailer is **64%**.

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