5% of a number is what percentage of 2% of the same number? | Stage I (CBT I) MCQ | Examoogle

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Stage I (CBT I)RRB ALP CBT-I 11 Mar, 2026 Shift 1

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5% of a number is what percentage of 2% of the same number?

$71.43\%$

$35.71\%$

$250\%$

$40\%$

Correct Answer

📚 GK • GK Ratio MethodStage I (CBT I)RRB ALP CBT-I 11 Mar, 2026 Shift 1

Option C

$250\%$

Quick Summary:

Given: Compare $5\%$ of a number with $2\%$ of the same number.

📐MAMath SolutionRatio Method

📋 Given

Compare $5\%$ of a number with $2\%$ of the same number.

🔢 Formula Used

Required Percentage=(Given ValueReference Value)×100\text{Required Percentage} = \left( \frac{\text{Given Value}}{\text{Reference Value}} \right) \times 100Required Percentage=(Reference ValueGiven Value​)×100

⚡ Exam Hall Shortcut / Speed Trick

Since both percentages apply to the same number $x$ , cancel $x$ and $100$ directly: $\frac{5}{2} \times 100 = 250\%$ .

⚠️ Common Student Trap / Pitfall

Taking $2\%$ over $5\%$ instead of $5\%$ over $2\%$ , which yields $\frac{2}{5} \times 100 = 40\%$ (Option D).

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define the Variable

Let the given number be $x$ .

Base Number=x\text{Base Number} = xBase Number=x

Express the Percentages mathematically

The two given quantities are $5\%$ of $x$ and $2\%$ of $x$ .

5% of x=5100⋅x=0.05x5\% \text{ of } x = \frac{5}{100} \cdot x = 0.05x5% of x=1005​⋅x=0.05x

Write the Reference Value

The second quantity is $2\%$ of $x$ .

2% of x=2100⋅x=0.02x2\% \text{ of } x = \frac{2}{100} \cdot x = 0.02x2% of x=1002​⋅x=0.02x

Apply Percentage Formula

We need to find what percentage $0.05x$ is of $0.02x$ .

Required %=(0.05x0.02x)×100\text{Required } \% = \left( \frac{0.05x}{0.02x} \right) \times 100Required %=(0.02x0.05x​)×100

Simplify and Calculate

Cancel $x$ from numerator and denominator and simplify the ratio.

Required %=(52)×100=2.5×100=250%\text{Required } \% = \left( \frac{5}{2} \right) \times 100 = 2.5 \times 100 = 250\%Required %=(25​)×100=2.5×100=250%

✅

C is correct because $5\%$ of a number divided by $2\%$ of the same number yields $2.5$ , which corresponds to $250\%$ .

Core Concepts Used

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Percentage Comparison Relative Ratios Base Value Identification

💡 EXAM TIP

When comparing two percentages of the same quantity $x$ , the base $x$ cancels out completely, allowing you to work directly with the numbers themselves.

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