Question

$if \frac{x}{y} = \frac{4}{5} then \: find \: the \: value \: of \: the \: ratio \: \frac{4x - y}{4x + y} .$
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Answer 1

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

$\dfrac{4x}{y} = 4 \times \dfrac{4}{5} = \dfrac{16}{5}$

Using Componendo-Dividendo

$\dfrac{4x - y}{4x + y} = \dfrac{16 - 5}{16 + 5}$

$\dfrac{4x - y}{4x + y} = \dfrac{11}{21}$

Answer 2

FINAL ANSWER:-

$11:21$

GIVEN:-

$x:y=4:5$

or

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

TO FIND:-

the value of ratio of $\frac{4x-y}{4x+y}$

SOLUTION:-

here $\frac{x}{y} =\frac{4}{5}$ can b written as $x=\frac{4y}{5}$

as we got the value of x so , let's put it in equation

we get,

$=\frac{4(\frac{4y}{5})-y}{4(\frac{4y}{5})+y}$ ⇒ $\frac{\frac{16y}{5}-y }{\frac{16y}{5}+y}$

$=\frac{\frac{16y-5y}{5} }{\frac{16y+5y}5}$ ⇒$\frac{\frac{11y}{5} }{\frac{21y}5}$

$=\frac{5(11y)}{5(21y)}$ ⇒ $\frac{55y}{105y}$

$=\frac{11}{21}$

or

$11:21$

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