If $a, b, c$ are in $G . P$ and $x, y$ , respectively be arithmetic means between $a, b$ and $b, c$ then the value of $\frac{a}{x} + \frac{c}{y}$ is

1

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2

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1 / 2

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Solution

The correct option is A $2$
$= \frac{a}{x} + \frac{b}{y}$

$= \frac{a}{\frac{a + b}{2}} + \frac{b}{\frac{b + c}{2}}$

$= \frac{2 a}{a + b} + \frac{2 c}{b + c}$

$= 2 [\frac{a}{a + b} + \frac{c}{b + c}]$

$= 2 [\frac{a (b + c) + c (a + b)}{(a + b) (b + c)}]$

$= 2 [\frac{a b + 2 a c + b c}{a b + 2 a c + b c}]$

$= 2 \times 1 = 2$

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