Two lots of onions with equal quantity, one costing Tk. 10 per kg and the other costing Tk. 15 per kg are mixed together and whole lot is sold at Tk. 15 per kg . What is the profit or loss?
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Two lots of onions with equal quantity, one costing Tk. 10 per kg and the other costing Tk. 15 per kg are mixed together and the whole lot is sold at Tk. 15 per kg. What is the profit or loss?
Choices: ['10% loss', '20% loss', '10 % profit', '20% profit']
<h2>Correct Answer: '20% profit'</h2><h2>Explanation:</h2>To understand why the answer is '20% profit', we need to calculate the cost price and the selling price of the mixed lot of onions.
<h3>Step-by-Step Calculation</h3><h4>1. Determine the total cost price</h4>Let's assume the quantity of each lot of onions is $Q$ kg.
Cost of first lot: $Q$ kg at Tk. 10 per kg = $10Q$ Tk.
Cost of second lot: $Q$ kg at Tk. 15 per kg = $15Q$ Tk.
Total cost price (CP): \[ CP = 10Q + 15Q = 25Q \text{ Tk.} \]
<h4>2. Determine the total selling price</h4>The entire mixed lot weighs $2Q$ kg and is sold at Tk. 15 per kg.
Total selling price (SP): \[ SP = 2Q \times 15 = 30Q \text{ Tk.} \]
<h4>3. Calculate the profit</h4>Profit is the difference between the selling price and the cost price.
Profit: \[ \text{Profit} = SP - CP = 30Q - 25Q = 5Q \text{ Tk.} \]
<h4>4. Calculate the profit percentage</h4>Profit percentage is calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{5Q}{25Q}\right) \times 100 \] \[ = 0.2 \times 100 = 20\% \]
Therefore, the profit percentage is 20%. Hence, the correct answer is '20% profit'.
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