Ratio, Proportion, Indices, LogarithmMCQMTP Jun 23 - Series IIQuestion 857 of 302
All Questions

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

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — $18xy$

All Options:

  • A$18xy$
  • B$81xy$
  • C$8xy$
  • D$9xy$

Detailed Solution & Explanation

By definition, the mean proportional between two quantities a\displaystyle a and b\displaystyle b is given by:
Mean Proportional=a⋅b\displaystyle \text{Mean Proportional} = \sqrt{a ⋅\displaystyle \cdot b}
Here, the two quantities are a=12x2\displaystyle a = 12x^2 and b=27y2\displaystyle b = 27y^2.
Substituting these values into the formula:
Mean Proportional=12x2⋅27y2\displaystyle \text{Mean Proportional} = \sqrt{12x^2 ⋅\displaystyle \cdot 27y^2}
Multiply the numerical coefficients and the variables:
Mean Proportional=(12×27)⋅x2y2\displaystyle \text{Mean Proportional} = \sqrt{(12 ×\displaystyle \times 27) ⋅\displaystyle \cdot x^2 y^2}
Mean Proportional=324x2y2\displaystyle \text{Mean Proportional} = \sqrt{324 x^2 y^2}
Since $18^2 = 324\displaystyle , the square root of $324x^2y^2 is:
Mean Proportional=18xyMean Proportional=18xy\displaystyle \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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