The mean proportion of {a²}{b³}and {9b²}{4a³} is _________.

Correct Answer is : 32ab{3}{2{ab}}2ab3

Correct Answer is : 32ab{3}{2{ab}}2ab3

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SSC GD Constable 6 Feb 2025 Shift 1 Paper

Section: Elementary Mathematics

Question : 54 of 80

Marks: +1, -0

The mean proportion of

\frac{a^{2}}{b^{3}}

\frac{9b^{2}}{4a^{3}}

is _________.

Solution:

The mean proportion of

\frac{a^{2}}{b^{3}}

and

\frac{9b^{2}}{4a^{3}}

Formula used:

Mean proportion between two values x and

y = \sqrt{} x \times y

Calculations:

Let

x = \frac{a^{2}}{b^{3}}

and

y = \frac{9b^{2}}{4a^{3}}

\Rightarrow \text{ Mean proportion } = \sqrt{ \frac{a^{2}}{b^{3}} \times \frac{9b^{2}}{4a^{3}} }

\Rightarrow \text{ Mean proportion } = \sqrt{ \frac{a^{2} \times 9b^{2}}{b^{3} \times 4a^{3}} }

\Rightarrow \text{ Mean proportion } = \sqrt{ \frac{9 \times b^{2} \times a^{2}}{4 \times b^{3} \times a^{3}} }

\Rightarrow \text{ Mean proportion } = \sqrt{ \frac{9}{4} \times \frac{b^{2}}{b^{3}} \times \frac{a^{2}}{a^{3}} }

\Rightarrow \text{ Mean proportion } = \sqrt{ \frac{9}{4} \times \frac{1}{b} \times \frac{1}{a} }

\Rightarrow \text{ Mean proportion } = \sqrt{ \frac{9}{4 \times a \times b} }

\Rightarrow \text{ Mean proportion } = \frac{ \sqrt{9} }{ \sqrt{4} \times a \times b }

\Rightarrow \text{ Mean proportion } = \frac{3}{2 \sqrt{} a b}

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