CTET Paper II (Mathematics and Science) 22 Dec 2021 Solved Paper

Concept:To compare fractions, multiply or divide numerator and denominator by powers of 10 to remove decimals.Explanation:We are given $\frac{547.527}{0.0082} = x$.Multiply numerator by 1000 to get 547527, and denominator by 10000 to get 82. So, $x = \frac{547527}{82} \times \frac{1000}{10000} = \frac{547527}{82} \times \frac{1}{10}$.Thus, $\frac{547527}{82} = 10x$? Wait, check: $x = \frac{547527}{82} \times \frac{1}{10}$ implies $\frac{547527}{82} = 10x$. But the original solution gave $x/10$. Let's re-evaluate carefully.Actually, $\frac{547.527}{0.0082} = \frac{547.527 \times 1000}{0.0082 \times 1000} = \frac{547527}{8.2}$ Not 82. To get denominator 82, multiply numerator and denominator by 10000: $\frac{547.527 \times 10000}{0.0082 \times 10000} = \frac{5475270}{82}$? No, 547.527 × 10000 = 5,475,270? That would be 5475270? Wait: 547.527 × 1000 = 547,527; × 10000 = 5,475,270. So that gives $\frac{5475270}{82}$? But we need $\frac{547527}{82}$. Let's do correctly: To get denominator 82 from 0.0082, multiply by 10000. Numerator becomes 547.527 × 10000 = 5,475,270. So $x = \frac{5475270}{82}$? That doesn't match. Better approach: Write $x = \frac{547.527}{0.0082}$. Multiply numerator and denominator by 10000: $x = \frac{547.527 \times 10000}{0.0082 \times 10000} = \frac{5475270}{82}$. Then $x = \frac{5475270}{82}$. But we need $\frac{547527}{82}$. That's ten times smaller. So $\frac{547527}{82} = \frac{x}{10}$. Yes, because $x = \frac{5475270}{82} = 10 \times \frac{547527}{82}$. So $\frac{547527}{82} = \frac{x}{10}$.Thus, the step: $x = \frac{547.527}{0.0082} = \frac{547527}{82} \times \frac{10000}{1000}$? That was original but confusing. Let's use clear step:First, note that $\frac{547.527}{0.0082} = \frac{547527 \times 10^{-3}}{82 \times 10^{-4}} = \frac{547527}{82} \times \frac{10^{-3}}{10^{-4}} = \frac{547527}{82} \times 10^{1} = \frac{547527}{82} \times 10$. So $x = 10 \times \frac{547527}{82}$. Hence $\frac{547527}{82} = \frac{x}{10}$.Answer:$\frac{547527}{82} = \frac{x}{10}$, so the correct option is D.