If $x : y = 5 : 4$ and $2 : x = 3 : 8$ , find the value of $y$ .

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Solution

$\frac{2}{x} = \frac{3}{8}$

$\Rightarrow x = \frac{16}{3}$ ;

$\frac{x}{y} = \frac{5}{4}$

$\Rightarrow y = \frac{4 x}{5}$

$\Rightarrow y = \frac{4}{5} \times \frac{16}{3} = \frac{64}{15}$

$\Rightarrow y = \frac{64}{15}$ .

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