A merchant bought 60 items at ₹20 each. He sold 40 items at a ... | Mathematics MCQ | Examoogle

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MathematicsProfit and Loss

A merchant bought 60 items at ₹20 each. He sold 40 items at a profit of 25% and the remaining 20 items at a loss of 10%. What is the overall profit or loss percentage?

13.33% profit

15% profit

12% profit

10% profit

Correct Answer

⚙️ TE • Technical Ratio MethodMathematicsProfit and Loss

Option A

13.33% profit

Quick Summary:

Use the ratio of items 40:20, which is 2:1. The overall percentage is the weighted average of the profit/loss: $\frac{2 \times 25 + 1 \times (-10)}{2+1} = \frac{50-10}{3} = \frac{40}{3} = 13.33\%$ .

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📐MAMath SolutionRatio Method

📋 Given

Total items = 60, cost per item = ₹20, 40 items sold at 25% profit, remaining 20 items sold at 10% loss.

🔢 Formula Used

Overall Percentage=∑(Weighti×Profiti)∑Weighti\text{Overall Percentage} = \frac{\sum (\text{Weight}_i \times \text{Profit}_i)}{\sum \text{Weight}_i}Overall Percentage=∑Weighti​∑(Weighti​×Profiti​)​

⚡ Exam Hall Shortcut / Speed Trick

Use the ratio of items 40:20, which is 2:1. The overall percentage is the weighted average of the profit/loss: $\frac{2 \times 25 + 1 \times (-10)}{2+1} = \frac{50-10}{3} = \frac{40}{3} = 13.33\%$ .

⚠️ Common Student Trap / Pitfall

Students often calculate the profit on the total cost of 60 items separately using absolute values, which is time-consuming and prone to arithmetic errors.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Simplify using Ratios

Since the cost price is the same for all items, we can work with the ratio of items. The ratio of items sold at profit to those sold at loss is $40:20 = 2:1$ .

Ratio=2:1\text{Ratio} = 2:1Ratio=2:1

Calculate Weighted Profit/Loss

Apply the weighted average formula where profits are positive and losses are negative: $(2 \times 25\%) + (1 \times -10\%)$ .

(2×25)+(1×−10)=50−10=40(2 \times 25) + (1 \times -10) = 50 - 10 = 40(2×25)+(1×−10)=50−10=40

Find Overall Percentage

Divide the weighted sum by the total number of parts, which is $2 + 1 = 3$ .

Overall Profit=403=13.33%\text{Overall Profit} = \frac{40}{3} = 13.33\%Overall Profit=340​=13.33%

✅

A is correct because the weighted average of the profit and loss percentages over the item ratio $2:1$ results in a value of $13.33\%$ profit.

Core Concepts Used

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Weighted Average Profit and Loss Ratio Analysis

💡 EXAM TIP

This weighted average technique is identical to calculating the average speed for different distances or the final average marks of a class where weights represent the number of students.

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