A trader claims to sell goods at a 10% profit but uses a weigh... | Mathematics MCQ | Examoogle

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MathematicsProfit and Loss

A trader claims to sell goods at a 10% profit but uses a weight that is 20% less than the actual weight. Find the total percentage of profit earned.

30%

35%

37.5%

40%

Correct Answer

⚙️ TE • Technical Ratio MethodMathematicsProfit and Loss

Option C

37.5%

Quick Summary:

Use the ratio of selling price to cost price: $(\frac{110}{100}) \times (\frac{100}{80}) = \frac{11}{8}$ . The profit is $(\frac{11-8}{8}) \times 100 = 37.5\%$ .

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📐MAMath SolutionRatio Method

📋 Given

Claimed profit = 10%, Weight used = 20% less than actual weight.

🔢 Formula Used

Total Profit=(1+Profit11−Loss2−1)×100%\text{Total Profit} = \left( \frac{1 + \text{Profit}_1}{1 - \text{Loss}_2} - 1 \right) \times 100\%Total Profit=(1−Loss2​1+Profit1​​−1)×100%

⚡ Exam Hall Shortcut / Speed Trick

Use the ratio of selling price to cost price: $(\frac{110}{100}) \times (\frac{100}{80}) = \frac{11}{8}$ . The profit is $(\frac{11-8}{8}) \times 100 = 37.5\%$ .

⚠️ Common Student Trap / Pitfall

Students often add the percentages (10% + 20% = 30%) without accounting for the fact that the cost price of the goods sold is reduced due to the underweight.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define the reference base

Assume the actual cost price of 100 units of weight is 100.

Actual weight=100,Cost=100\text{Actual weight} = 100, \quad \text{Cost} = 100Actual weight=100,Cost=100

Calculate the Selling Price

The trader claims a 10% profit on the original cost, so the selling price is $100 + 10 = 110$ .

Selling Price (SP)=110\text{Selling Price (SP)} = 110Selling Price (SP)=110

Calculate the effective Cost Price

Since the trader uses 20% less weight, they are only supplying 80 units for the cost of 80.

Effective Cost Price (CP)=100−20=80\text{Effective Cost Price (CP)} = 100 - 20 = 80Effective Cost Price (CP)=100−20=80

Calculate percentage profit

Profit is the difference between SP and effective CP relative to the effective CP: $\frac{110 - 80}{80} \times 100$ .

Profit=3080×100=37.5%\text{Profit} = \frac{30}{80} \times 100 = 37.5\%Profit=8030​×100=37.5%

✅

C is correct because the ratio of the effective selling price to the effective cost price leads to a total profit of 37.5%.

Core Concepts Used

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Profit and Loss Effective Cost Price Dishonest Dealer problems

💡 EXAM TIP

This concept of effective pricing is similar to 'Successive Percentage Changes' and 'Mixture & Alligation' problems involving volume or mass substitution.

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