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

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If the cost price of 15 pens is equal to the selling price of 12 pens, what is the profit percentage?

$20\%$

$25\%$

$30\%$

$15\%$

Correct Answer

📐 MA • Math Ratio MethodMathematicsMathematics

Option B

$25\%$

Quick Summary:

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

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📐MAMath SolutionRatio Method

📋 Given

Cost price of 15 pens is equal to the selling price of 12 pens.

🔢 Formula Used

Profit %=(SP−CPCP)×100\text{Profit } \% = \left(\frac{SP - CP}{CP}\right) \times 100Profit %=(CPSP−CP​)×100

⚡ Exam Hall Shortcut / Speed Trick

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

⚠️ Common Student Trap / Pitfall

Students often mistakenly calculate the profit percentage using the selling price quantity denominator instead of the cost price or vice versa.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Set up the basic equation

Let the cost price of one pen be $CP$ and the selling price of one pen be $SP$ . We are given that $15 \times CP = 12 \times SP$ .

15×CP=12×SP15 \times CP = 12 \times SP15×CP=12×SP

Find the ratio of CP to SP

Rearranging the terms gives the ratio of cost price to selling price: $\frac{CP}{SP} = \frac{12}{15} = \frac{4}{5}$ .

CPSP=45\frac{CP}{SP} = \frac{4}{5}SPCP​=54​

Calculate the profit percentage

Let $CP = 4$ units and $SP = 5$ units. The profit is $5 - 4 = 1$ unit. Thus, Profit % = $\frac{1}{4} \times 100 = 25\%$ .

Profit %=(5−44)×100=25%\text{Profit } \% = \left(\frac{5 - 4}{4}\right) \times 100 = 25\%Profit %=(45−4​)×100=25%

✅

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

Core Concepts Used

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Profit and Loss Cost Price and Selling Price Ratio and Proportion

💡 EXAM TIP

This inverse ratio technique is broadly useful in quantitative aptitude problems involving articles bought and sold at varying quantities.

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