Find the mean proportional of 49 and 25. | Stage I (CBT I) MCQ | Examoogle

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

Find the mean proportional of 49 and 25.

Correct Answer

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

Option D

Quick Summary:

Given: Two numbers are 49 and 25.

📐MAMath SolutionDirect Formula

📋 Given

Two numbers are 49 and 25.

🔢 Formula Used

Mean  Proportional=a×bMean \; Proportional = \sqrt{a \times b}MeanProportional=a×b​

⚡ Exam Hall Shortcut / Speed Trick

Calculate the square root of the product: $\sqrt{49} = 7$ and $\sqrt{25} = 5$ . Then simply multiply: $7 \times 5 = 35$ .

⚠️ Common Student Trap / Pitfall

Students often try to calculate the arithmetic mean ( $49+25$ )/2 = 37$ instead of the geometric mean (mean proportional).

🔢 Step-by-Step Solution

Identify the formula

The mean proportional between two numbers $a$ and $b$ is given by the square root of their product.

Mean  Proportional=a×bMean \; Proportional = \sqrt{a \times b}MeanProportional=a×b​

Substitute the values

Substitute $a = 49$ and $b = 25$ into the formula.

Mean  Proportional=49×25Mean \; Proportional = \sqrt{49 \times 25}MeanProportional=49×25​

Calculate the product

Using properties of square roots, $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ .

49×25=7×5\sqrt{49} \times \sqrt{25} = 7 \times 549​×25​=7×5

Final Result

Multiplying the results gives the mean proportional.

7×5=357 \times 5 = 357×5=35

✅

D is correct because the mean proportional is the square root of $49 \times 25$ , which equals $35$ .

Core Concepts Used

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💡 EXAM TIP

This concept is a specific case of a geometric progression where $a, x, b$ are in GP, meaning $x/a = b/x$ , leading to $x^2 = ab$ .

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