The mean proportional between 12x2 and 27y2

Option a: 18xy. Solution: By definition, the mean proportional between two quantities a and b is given by: Mean Proportional = sqrt(a × b) Here, the two quantities are a = 12x2 and b = 27y2 . Substituting these values into the formula: Mean Proportional = sqrt(12x2 × 27y2) Multiply the numerical coefficients and the variables: Mean Proportional = sqrt((12 × 27) × x2 y2) Mean Proportional = sqrt(324 x2 y2) Since 182 = 324 , the square root of 324x2y2 is: Mean Proportional = 18xy This matches Option A. Hence, Option A is the correct answer.

Ratio, Proportion, Indices, LogarithmMCQMTP Jun 23 - Series IIQuestion 857 of 305

All Questions

The mean proportional between $\displaystyle 12x^2$ and $\displaystyle 27y^2$

Options

\displaystyle 18xy

\displaystyle 81xy

\displaystyle 8xy

\displaystyle 9xy

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Correct Answer

✅ Option a — $\displaystyle 18xy$

All Options:

A $\displaystyle 18xy$
B $\displaystyle 81xy$
C $\displaystyle 8xy$
D $\displaystyle 9xy$

Detailed Solution & Explanation

By definition, the mean proportional between two quantities

\displaystyle a

and

\displaystyle b

is given by:

\text{Mean Proportional} = \sqrt{a \cdot b}

Here, the two quantities are

\displaystyle a = 12x^2

and

\displaystyle b = 27y^2

.
Substituting these values into the formula:

\text{Mean Proportional} = \sqrt{12x^2 \cdot 27y^2}

Multiply the numerical coefficients and the variables:

\text{Mean Proportional} = \sqrt{(12 \times 27) \cdot x^2 y^2}

\text{Mean Proportional} = \sqrt{324 x^2 y^2}

Since

\displaystyle 18^2 = 324

, the square root of

\displaystyle 324x^2y^2

is:

\text{Mean Proportional} = 18xy

This matches **Option A**.
Hence, **Option A** is the correct answer.

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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The mean proportional between 12x2\displaystyle 12x^212x2 and 27y2\displaystyle 27y^227y2