If the cost price of 15 articles is equal to the selling price... | Mathematics MCQ | Examoogle

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If the cost price of 15 articles is equal to the selling price of 12 articles, find the profit percentage.

$20\%$

$25\%$

$30\%$

$33.33\%$

Correct Answer

⚙️ TE • Technical Ratio MethodMathematicsProfit-Loss

Option B

$25\%$

Quick Summary:

Use the quantity ratio shortcut: Profit % = $\frac{ \text{CP quantity} - \text{SP quantity}}{ \text{SP quantity}}$ imes 100 = $\frac{15 - 12}{12}$ imes 100 = 25%.

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📐MAMath SolutionRatio Method

📋 Given

Cost price of 15 articles equals the selling price of 12 articles.

🔢 Formula Used

extProfit%=SP−CPCPimes100ext{\text{Profit} } \% = \frac{SP - CP}{CP} imes 100extProfit%=CPSP−CP​imes100

⚡ Exam Hall Shortcut / Speed Trick

Use the quantity ratio shortcut: Profit % = $\frac{\text{CP quantity} - \text{SP quantity}}{\text{SP quantity}}$ imes 100 = $\frac{15 - 12}{12}$ imes 100 = 25%.

⚠️ Common Student Trap / Pitfall

Students frequently calculate the profit percentage relative to the selling quantity's cost or use the wrong base by dividing by 15 instead of 12.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Set up the equation

Translate the problem statement into a direct algebraic equation where $15 \text{imes CP} = 12 imes SP$ .

15imes CP=12imes SP15 \text{imes CP} = 12 \text{imes SP}15imes CP=12imes SP

Find the price ratio

Rearrange the terms to find the ratio of Selling Price to Cost Price, which simplifies to $\frac{5}{4}$ .

racSPCP=1512=54rac{SP}{CP} = \frac{15}{12} = \frac{5}{4}racSPCP=1215​=45​

Calculate profit percentage

Let $CP = 4$ units and $SP = 5$ units. Compute the percentage gain to arrive at the final answer.

extProfit%=5−44imes100=25%ext{\text{Profit} } \% = \frac{5 - 4}{4} imes 100 = 25\%extProfit%=45−4​imes100=25%

✅

B is correct because the calculated profit percentage is 25%.

Core Concepts Used

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Cost Price and Selling Price Profit Percentage Ratio Method

💡 EXAM TIP

Mastering article-based profit-loss shortcuts drastically reduces calculation time in competitive aptitude sections.

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