Correct Answer

📐 MA • Math Direct FormulaMathematicsRatio & Proportion

Option B

Quick Summary:

Given: Three numbers are given: 4, 8, and 10. We need to find the fourth proportional y.

📐MAMath SolutionDirect Formula

📋 Given

Three numbers are given: 4, 8, and 10. We need to find the fourth proportional y.

🔢 Formula Used

ab=cy  ⟹  y=b×ca\frac{a}{b} = \frac{c}{y} \implies y = \frac{b \times c}{a}ba​=yc​⟹y=ab×c​

⚡ Exam Hall Shortcut / Speed Trick

Notice the ratio of the first two numbers: $8/4 = 2$ . Therefore, the fourth proportional is simply $10 \times 2 = 20$ .

⚠️ Common Student Trap / Pitfall

Many students mistake the order and calculate $y = (a \times b) / c$ instead of $(b \times c) / a$ , or try to find the third proportional instead of the fourth.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define the relationship

By definition of the fourth proportional, if $a, b, c, y$ are in proportion, then $a:b:: c:y$ .

4:8=10:y4: 8 = 10: y4:8=10:y

Set up the equation

Convert the ratio into a fraction: $\frac{4}{8} = \frac{10}{y}$ .

y=8×104y = \frac{8 \times 10}{4}y=48×10​

Calculate the final value

Simplify the expression to find $y$ : $y = 80 / 4 = 20$ .

y=20y = 20y=20

✅

B is correct because the calculation $y = (8 \times 10) / 4$ results in 20.

Core Concepts Used

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Ratio and Proportion Fourth Proportional Cross Multiplication

💡 EXAM TIP

This concept is a precursor to understanding 'Direct Variation' in physics, where $y = kx$ and constant $k$ is determined by proportionality.

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