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If x : y = 3 : 4, then the value of (4x - y) : (2x + 3y) is = ?

14 : 9
28 : 9
34 : 3
48 : 3

Answer:- 1

Explanation:-

Solution:

\begin{aligned} x : y = 3 : 4 \\ ∴ \frac{x}{y} = \frac{3}{4} \\ \Rightarrow \frac{4 x - y}{2 x + 3 y} \\ \Rightarrow \frac{y (4 \frac{x}{y} - 1)}{y (2 \frac{x}{y} + 3)} \\ \Rightarrow \frac{4 \times \frac{3}{4} - 1}{2 \times \frac{3}{4} + 3} \\ \Rightarrow \frac{(3 - 1) \times 2}{3 + 6} \\ \Rightarrow \frac{4}{9} \\ \Rightarrow 4 : 9 \end{aligned}

$\eqalign{ & x:y = 3:4 \cr & \therefore \frac{x}{y} = \frac{3}{4} \cr & \Rightarrow \frac{{4x - y}}{{2x + 3y}} \cr & \Rightarrow \frac{{y\left( {4\frac{x}{y} - 1} \right)}}{{y\left( {2\frac{x}{y} + 3} \right)}} \cr & \Rightarrow \frac{{4 \times \frac{3}{4} - 1}}{{2 \times \frac{3}{4} + 3}} \cr & \Rightarrow \frac{{\left( {3 - 1} \right) \times 2}}{{3 + 6}} \cr & \Rightarrow \frac{4}{9} \cr & \Rightarrow 4:9 \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} x : y = 3 : 4 \\ ∴ \frac{x}{y} = \frac{3}{4} \\ \Rightarrow \frac{4 x - y}{2 x + 3 y} \\ \Rightarrow \frac{y (4 \frac{x}{y} - 1)}{y (2 \frac{x}{y} + 3)} \\ \Rightarrow \frac{4 \times \frac{3}{4} - 1}{2 \times \frac{3}{4} + 3} \\ \Rightarrow \frac{(3 - 1) \times 2}{3 + 6} \\ \Rightarrow \frac{4}{9} \\ \Rightarrow 4 : 9 \end{aligned}

$\eqalign{ & x:y = 3:4 \cr & \therefore \frac{x}{y} = \frac{3}{4} \cr & \Rightarrow \frac{{4x - y}}{{2x + 3y}} \cr & \Rightarrow \frac{{y\left( {4\frac{x}{y} - 1} \right)}}{{y\left( {2\frac{x}{y} + 3} \right)}} \cr & \Rightarrow \frac{{4 \times \frac{3}{4} - 1}}{{2 \times \frac{3}{4} + 3}} \cr & \Rightarrow \frac{{\left( {3 - 1} \right) \times 2}}{{3 + 6}} \cr & \Rightarrow \frac{4}{9} \cr & \Rightarrow 4:9 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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