શુભ એક વસ્તુને તેની મૂળ કિંમત કરતાં 40% વધુ અંકિત કરે છે. તે અ... | Mathematics MCQ (ગુજરાતી) | Examoogle

MathematicsProfit, Loss and Discount

શુભ એક વસ્તુને તેની મૂળ કિંમત કરતાં 40% વધુ અંકિત કરે છે. તે અંકિત કિંમત પર d% નો એકલ ડિસ્કાઉન્ટ આપે છે અને તેમ છતાં મૂળ કિંમત પર 10% નફો કમાય છે. ડિસ્કાઉન્ટ d% શોધો.

22%

$21\frac{2}{7}\%$

$21\frac{3}{7}\%$

23%

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsProfit, Loss and Discount

22%

Quick Summary:

Use the formula: $(100 + \text{Markup}) \times (100 - d) = (100 + \text{Profit}) \times 100$ . With 140 and 110, we get $140(100-d) = 11000$ . Solving $140-1.4d = 110$ leads directly to $d = 30/1.4 = 21\frac{3}{7}$ . Wait, re-evaluating: $140(1-d/100) = 110 \implies 1-d/100 = 110/140 = 11/14 \implies d/100 = 3/14 \implies d = 300/14 = 150/7 = 21\frac{3}{7}$ .

📐MAMath SolutionDirect Formula

📋 Given

Marked price is 40% above cost price (Markup = 40%), Profit = 10%.

🔢 Formula Used

(1+Markup100)×(1−d100)=(1+Profit100)(1 + \frac{\text{Markup}}{100}) \times (1 - \frac{d}{100}) = (1 + \frac{\text{Profit}}{100})(1+100Markup​)×(1−100d​)=(1+100Profit​)

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often incorrectly calculate discount on the cost price or use addition/subtraction of percentages instead of multiplying the ratios (multiplicative nature of profit and discount).

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define Relationship

Let Cost Price be $CP = 100$ . Since Markup is $40\%$ , the Marked Price ( $MP$ ) is $100 \times 1.4 = 140$ .

MP=140MP = 140MP=140

Calculate Selling Price

Since Profit is $10\%$ , Selling Price ( $SP$ ) is $CP + 10\% \text{ of } CP = 110$ .

SP=110SP = 110SP=110

Solve for Discount Percentage

The discount is the difference between $MP$ and $SP$ on the $MP$ base. Discount $D = MP - SP = 140 - 110 = 30$ . Discount percent $d = (30 / 140) \times 100$ .

d=30140×100=1507=2137%d = \frac{30}{140} \times 100 = \frac{150}{7} = 21\frac{3}{7}\%d=14030​×100=7150​=2173​%

✅

C is correct because the calculated discount percentage $d = 21\frac{3}{7}\%$ matches option C.

Core Concepts Used

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Profit and Loss Markup Percentage Discount Calculation

💡 EXAM TIP

This concept of base-switching (Markup on CP, Discount on MP) is identical to compound interest growth/decay patterns; remember to always multiply the ratio factors.

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