I purchase 100 kg of tea and sell it for a profit to the extent of what I would have paid for 40 kg. What is my profit percentage?

Options

A. 0.4
B. 0.25
C. 0.3
D. 0.2

Answer

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

### Step 1: Define the Variables
Let the cost price (CP) of 100 kg of tea be \( CP_{100} \).

### Step 2: Determine the Selling Price (SP)
According to the problem, the profit made from selling 100 kg of tea is equivalent to the cost price of 40 kg of tea. Therefore, if we denote the cost price of 1 kg of tea as \( CP_{1} \), we have:
\[ CP_{1} = \frac{CP_{100}}{100} \]
Thus, the cost price of 40 kg of tea is:
\[ CP_{40} = 40 \times CP_{1} = 40 \times \frac{CP_{100}}{100} = \frac{40 \times CP_{100}}{100} = \frac{CP_{100}}{2.5} \]

### Step 3: Relate Selling Price to Cost Price
The selling price of 100 kg of tea can be expressed as:
\[ SP_{100} = CP_{100} + \text{Profit} \]
From the previous step, we know:
\[ \text{Profit} = CP_{40} = \frac{CP_{100}}{2.5} \]
Thus, we can write:
\[ SP_{100} = CP_{100} + \frac{CP_{100}}{2.5} \]

### Step 4: Simplify the Selling Price
To combine these terms, we can express \( \frac{CP_{100}}{2.5} \) as:
\[ \frac{CP_{100}}{2.5} = \frac{CP_{100}}{2.5} = 0.4 \times CP_{100} \]
Now, substituting this back into the equation gives:
\[ SP_{100} = CP_{100} + 0.4 \times CP_{100} = 1.4 \times CP_{100} \]

### Step 5: Calculate Profit
Now we can find the profit:
\[ \text{Profit} = SP_{100} - CP_{100} = 1.4 \times CP_{100} - CP_{100} = 0.4 \times CP_{100} \]

### Step 6: Calculate Profit Percentage
Profit percentage is given by the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP_{100}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{0.4 \times CP_{100}}{CP_{100}} \right) \times 100 = 0.4 \times 100 = 40\% \]

### Final Answer
The profit percentage is **40%**.

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