28.57% of the total pages written by Q in July is in Hindi. Ho... | Mathematics MCQ | Examoogle

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28.57% of the total pages written by Q in July is in Hindi. How many English pages are written by Q in July?

200

284

268

232

None of the above

Correct Answer

📐 MA • Math Ratio MethodMathematicsPercentage

Option A

200

Quick Summary:

Recognize that $28.57\%$ is the fraction $2/7$ (since $1/7 \approx 14.28\%$ ). If $2/7$ are Hindi, then $5/7$ are English pages.

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📐MAMath SolutionRatio Method

📋 Given

Total pages written by Q in July = 280. Percentage of Hindi pages = 28.57%.

🔢 Formula Used

English Pages=Total Pages×(100%−Hindi Percentage)\text{English Pages} = \text{Total Pages} \times (100\% - \text{Hindi Percentage})English Pages=Total Pages×(100%−Hindi Percentage)

⚡ Exam Hall Shortcut / Speed Trick

Recognize that $28.57\%$ is the fraction $2/7$ (since $1/7 \approx 14.28\%$ ). If $2/7$ are Hindi, then $5/7$ are English pages.

⚠️ Common Student Trap / Pitfall

Students often try to calculate $28.57\%$ of 280 first, which is tedious; finding $5/7$ of 280 directly is much faster and less prone to arithmetic errors.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Convert percentage to fraction

Note that $28.57\% \approx \frac{2}{7}$ . Thus, the number of Hindi pages is $\frac{2}{7}$ of the total.

28.57100≈27\frac{28.57}{100} \approx \frac{2}{7}10028.57​≈72​

Calculate fraction of English pages

If $\frac{2}{7}$ of the pages are Hindi, the remaining fraction of English pages is $1 - \frac{2}{7} = \frac{5}{7}$ .

1−27=571 - \frac{2}{7} = \frac{5}{7}1−72​=75​

Determine total English pages

Multiply the fraction of English pages by the total number of pages in July, which is 280.

English Pages=280×57=40×5=200\text{English Pages} = 280 \times \frac{5}{7} = 40 \times 5 = 200English Pages=280×75​=40×5=200

✅

A is correct because $280 \times (1 - 0.2857) = 280 \times 0.7143 = 200$ .

Core Concepts Used

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Fractional Equivalents of Percentages Complementary Percentages Data Interpretation

💡 EXAM TIP

Memorizing common fraction-to-percentage conversions like $1/7 \approx 14.28\%$ and $1/9 \approx 11.11\%$ saves significant time in Competitive Aptitude exams.

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