During a sale, 50% of the goods are sold at a profit of 20%. O... | Mathematics MCQ | Examoogle

MathematicsArithmetic

During a sale, 50% of the goods are sold at a profit of 20%. Of the remaining goods, 40% are sold at a profit of 10%, and the rest are sold at a loss of 10%. If the overall profit is x%, what is the value of x?

10%

11%

Correct Answer

⚙️ TE • Technical Weighted Average MethodMathematicsArithmetic

Option D

11%

Quick Summary:

Assume the total goods equal 100 units with cost price 1 unit each. Calculate total profit units: $(50 \times 0.20) + (20 \times 0.10) + (30 \times -0.10) = 10 + 2 - 3 = 9$ . Wait, recalculating: $50\% \times 20\% = 10$ , $20\% \times 10\% = 2$ , $30\% \times (-10\%) = -3$ . Result $10 + 2 - 3 = 9\%$ .

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📐MAMath SolutionWeighted Average Method

📋 Given

50% goods at 20% profit, 40% of the remaining at 10% profit, and the final rest at 10% loss.

🔢 Formula Used

Overall Profit=∑(wi×pi)\text{Overall Profit} = \sum (w_i \times p_i)Overall Profit=∑(wi​×pi​)

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often calculate 40% of total goods instead of 40% of the 'remaining' goods, and neglect the negative sign for the loss.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define Goods Distribution

Assume total goods = 100 units, each costing 1 unit. First part = 50 units. Remaining = 50 units. Second part = 40% of 50 = 20 units. Third part = 50 - 20 = 30 units.

Parts: P1=50,P2=20,P3=30\text{Parts: } P_1 = 50, P_2 = 20, P_3 = 30Parts: P1​=50,P2​=20,P3​=30

Calculate Profit/Loss per Section

Calculate the absolute profit or loss contribution of each section: $50 \times 20\% = 10$ , $20 \times 10\% = 2$ , and $30 \times (-10\%) = -3$ .

Profit=(50×0.20)+(20×0.10)+(30×−0.10)=10+2−3=9\text{Profit} = (50 \times 0.20) + (20 \times 0.10) + (30 \times -0.10) = 10 + 2 - 3 = 9Profit=(50×0.20)+(20×0.10)+(30×−0.10)=10+2−3=9

Determine Overall Percentage

Since total cost is 100 units and total profit is 9 units, the overall percentage is $\frac{9}{100} \times 100\% = 9\%$ .

x=9%\text{x} = 9\%x=9%

✅

B is correct because the weighted average calculation $(0.5 \times 20\%) + (0.2 \times 10\%) + (0.3 \times -10\%) = 10\% + 2\% - 3\% = 9\%$ .

Core Concepts Used

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Weighted Average Profit and Loss Percentage Allocation

💡 EXAM TIP

This concept of weighted averages is identical to calculating the combined mean in Statistics and the effective rate of interest in Compound Interest problems.

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