A multiple-choice question containing percentage values as opt... | Mathematics MCQ

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A multiple-choice question containing percentage values as options.

45%

40.65%

42.86%

37.5%

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option C

42.86%

Quick Summary:

Use the formula $\frac{x}{100-x} \times 100$ where $x=30$ . Calculation: $30/70 \times 100 = 300/7 \approx 42.86\%$ .

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📐MAMath SolutionDirect Formula

📋 Given

Price of rice is 30% less than the price of wheat.

🔢 Formula Used

Percentage more=(x100−x)×100\text{Percentage more} = \left( \frac{x}{100 - x} \right) \times 100Percentage more=(100−xx​)×100

⚡ Exam Hall Shortcut / Speed Trick

Use the formula $\frac{x}{100-x} \times 100$ where $x=30$ . Calculation: $30/70 \times 100 = 300/7 \approx 42.86\%$ .

⚠️ Common Student Trap / Pitfall

Many students incorrectly assume the answer is 30% or calculate $30\%$ of the rice price, ignoring that the base has changed to the price of rice.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define Prices

Assume the price of wheat is 100. Since the price of rice is 30% less than wheat, the price of rice is $100 - 30 = 70$ .

Pwheat=100,Price=70P_{wheat} = 100, P_{rice} = 70Pwheat​=100,Price​=70

Calculate Absolute Difference

Find the difference between the price of wheat and rice.

Difference=100−70=30\text{Difference} = 100 - 70 = 30Difference=100−70=30

Calculate Percentage More

To find the percentage more, divide the difference by the base price (price of rice) and multiply by 100.

Percentage=(3070)×100=3007≈42.857%\text{Percentage} = \left( \frac{30}{70} \right) \times 100 = \frac{300}{7} \approx 42.857\%Percentage=(7030​)×100=7300​≈42.857%

✅

C is correct because the price of wheat is approximately 42.86% more than the price of rice.

Core Concepts Used

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Percentage change Base value conversion Ratio comparison

💡 EXAM TIP

This is a standard variation of the 'Price-Consumption' problem in economics, often appearing in speed math tests.

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