State true or false.
If $5 m - n = m + 2 n$ then the value of $(4 m + n) : (4 m - n)$ is $2 : 1$

True

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False

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Solution

The correct option is A True
$5 m - n = m + 2 n$
$=> 4 m = 3 n$
$=> \frac{m}{n} = \frac{3}{4}$
$=> m : n = 3 : 4$
Let $m = 3 a; n = 4 a$

So, $(4 m + n) : (4 m - n) = 4 (3 a) + 4 a : 4 (3 a) - 4 a$
$=> (4 m + n) : (4 m - n) = 16 a : 8 a = 2 : 1$

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