If 1-5 - 1-x - 1-x - 1-1-25- then the value of x is

The correct option is C 2.5 1/5 : 1/x = 1/x : 100/125 ⇒ (1/x × 1/x ) = (1/5 × 100/125 ) = 4/25 ⇒ 1/x^2 = 4/25 ⇒ x^2 = 25/4 ⇒ ...

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Standard VI

Mathematics

Proportions

If 1/5 : 1/...

Question

If $\frac{1}{5} : \frac{1}{x} = \frac{1}{x} : \frac{1}{1.25}$ , then the value of $x$ is

1.5

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2

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2.5

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3.5

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Solution

The correct option is C $2.5$
$\frac{1}{5} : \frac{1}{x} = \frac{1}{x} : \frac{100}{125}$
$\Rightarrow (\frac{1}{x} \times \frac{1}{x}) = (\frac{1}{5} \times \frac{100}{125}) = \frac{4}{25}$
$\Rightarrow \frac{1}{x^{2}} = \frac{4}{25} \Rightarrow x^{2} = \frac{25}{4}$
$\Rightarrow x = \frac{5}{2} = 2.5$

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