If $x : y = 6 : 11$ , find $(8 x - 3 y) : (3 x + 2 y)$ .

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Solution

Given:
$x : y = 6 : 11$
$\Rightarrow x = 6 k, y = 11 k$ , where $k$ is a constant.

Therefore,
$(8 x - 3 y) : (3 x + 2 y) = (8 \times 6 k - 3 \times 11 k) : (3 \times 6 k + 2 \times 11 k)$
$= 15 k : 40 k$
$= 3 : 8$

Hence, this is the required ratio.

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