A trader marks his goods 40% above cost price and allows a dis... | Mathematics MCQ | Examoogle

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A trader marks his goods 40% above cost price and allows a discount of 25%. What is his net profit percentage?

$5\%$

$10\%$

$15\%$

$20\%$

Correct Answer

📐 MA • Math Successive Percentage MethodMathematicsMathematics

Option A

$5\%$

Quick Summary:

Apply the net percentage change formula directly with $x = 40$ and $y = 25$ to save exam time.

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📐MAMath SolutionSuccessive Percentage Method

📋 Given

Markup percentage = 40%, Discount percentage = 25%

🔢 Formula Used

P=x−y−x×y100P = x - y - \frac{x \times y}{100}P=x−y−100x×y​

⚡ Exam Hall Shortcut / Speed Trick

Apply the net percentage change formula directly with $x = 40$ and $y = 25$ to save exam time.

⚠️ Common Student Trap / Pitfall

Students often directly subtract 25% from 40% to get 15%, forgetting that discount is applied on the marked price, not the cost price.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Assume Cost Price

Let the cost price of the goods be $100$ .

CP=100CP = 100CP=100

Calculate Marked Price

Since the goods are marked 40% above the cost price, the marked price becomes $140$ .

MP=100+(40100×100)=140MP = 100 + \left(\frac{40}{100} \times 100\right) = 140MP=100+(10040​×100)=140

Calculate Selling Price after Discount

A discount of 25% is allowed on the marked price of $140.

SP=140−(25100×140)=140−35=105SP = 140 - \left(\frac{25}{100} \times 140\right) = 140 - 35 = 105SP=140−(10025​×140)=140−35=105

Calculate Net Profit Percentage

Find the percentage increase from the cost price of 100 to the selling price of 105.

P=105−100100×100=5%P = \frac{105 - 100}{100} \times 100 = 5\%P=100105−100​×100=5%

✅

A is correct because the net profit percentage is calculated to be 5%.

Core Concepts Used

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Markup and Discount Successive Percentage Change Profit and Loss

💡 EXAM TIP

This successive percentage framework is also useful for solving problems involving successive discounts, population growth, and two-dimensional area changes.

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