Subtracting 35% of X from X is equivalent to multiplying X by: | Mathematics MCQ | Examoogle

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MathematicsPercentage

Subtracting 35% of X from X is equivalent to multiplying X by:

0.35

0.65

1.35

0.75

Correct Answer

📐 MA • Math Direct FormulaMathematicsPercentage

Option B

0.65

Quick Summary:

Given: Subtract 35% of X from X

📐MAMath SolutionDirect Formula

📋 Given

Subtract 35% of X from X

🔢 Formula Used

X−35100X=(1−35100)X=65100X=0.65XX - \frac{35}{100}X = \left(1-\frac{35}{100}\right)X = \frac{65}{100}X = 0.65XX−10035​X=(1−10035​)X=10065​X=0.65X

⚡ Exam Hall Shortcut / Speed Trick

Remember subtracting p% leaves (100‑p)% → 100‑35=65 → write as 0.65

⚠️ Common Student Trap / Pitfall

Many think the result is 0.35 instead of the remaining 0.65

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Interpret the statement

The problem asks for X minus 35 % of X, i.e. $X-0.35X$

X−0.35XX - 0.35XX−0.35X

Convert percentage to decimal

35% = $\frac{35}{100}=0.35$

0.35=351000.35 = \frac{35}{100}0.35=10035​

Perform the subtraction

$X-0.35X = (1-0.35)X = 0.65X$

(1−0.35)X=0.65X(1-0.35)X = 0.65X(1−0.35)X=0.65X

Identify the multiplier

Thus the operation is equivalent to multiplying X by 0.65

Multiplier=0.65\text{Multiplier}=0.65Multiplier=0.65

✅

B is correct because $X-35\%\text{ of }X = X-0.35X = 0.65X$ , so the factor is 0.65

Core Concepts Used

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💡 EXAM TIP

The same idea is used in discount problems: a 35 % discount leaves you paying 65 % of the marked price.

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