If $\frac{155}{0.155} = \frac{15.5}{K}$, then the value of $ K... | Mathematics MCQ | Examoogle

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If $\frac{155}{0.155} = \frac{15.5}{K}$ , then the value of $K$ is:

$1.55$

$15.51$

$0.0155$

$155$

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsArithmetic

Option C

$0.0155$

Quick Summary:

Shift the decimal points by balancing both sides or use scale factors: $0.155 = \frac{155}{1000}$ , so $\frac{155}{0.155} = 1000$ . Then $\frac{15.5}{K} = 1000 \implies K = \frac{15.5}{1000} = 0.0155$ .

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📐MAMath SolutionDirect Formula

📋 Given

Given equation: $\frac{155}{0.155}$ = $\frac{15.5}{K}$

🔢 Formula Used

ab=cK  ⟹  K=b×ca\frac{a}{b} = \frac{c}{K} \implies K = \frac{b \times c}{a}ba​=Kc​⟹K=ab×c​

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Confusing decimal place shifts between numerator and denominator leading to $1.55$ or $155$ instead of $0.0155$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Step 1: Write down the given equation

We are given the proportional equation involving decimals: $\frac{155}{0.155} = \frac{15.5}{K}$

1550.155=15.5K\frac{155}{0.155} = \frac{15.5}{K}0.155155​=K15.5​

Step 2: Cross-multiply to isolate K

Rearranging the equation to solve for $K$ , we get $K = \frac{15.5 \times 0.155}{155}$

K=15.5×0.155155K = \frac{15.5 \times 0.155}{155}K=15515.5×0.155​

Step 3: Simplify the numerical expression

Since $\frac{15.5}{155} = 0.1$ , multiplying by $0.155$ gives $K = 0.1 \times 0.155 = 0.0155$

K=0.0155K = 0.0155K=0.0155

✅

C is correct because simplifying the given equation yields $K = 0.0155$ .

Core Concepts Used

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Decimal Proportions Cross Multiplication Simplification of Fractions

💡 EXAM TIP

Mastering decimal shifts helps quickly solve similar proportion and percentage problems in quantitative aptitude exams.

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