Question

if x+y/2x+y = 4/5 then 2x+y/3x+y = ?​

Answer 1

Answer:

5 / 6

Step-by-step explanation:

       $\Rightarrow\mathrm{\dfrac{x+y}{2x+y}=\dfrac{4}{5}}\\\\\\\Rightarrow\mathrm{\dfrac{\dfrac{x+y}{y}}{\dfrac{2x+y}{y}}=\dfrac{4}{5} }\\\\\\\Rightarrow\mathrm{\dfrac{\dfrac{x}{y}+1}{\dfrac{2x}{y}+1} =\dfrac{4}{5}}$

Let x/y = a

       $\Rightarrow\mathrm{\dfrac{a+1}{2a+1}=\dfrac{4}{5} }\\\\\\\Rightarrow\mathrm{5(a+1)=4(2a+1) }\\\\\Rightarrow\mathrm{5a+5=8a+4 }\\\\\Rightarrow\mathrm{5-4=8a-5a }\\\\\Rightarrow\mathrm{a=\dfrac{1}{3} }$

  Hence,

         $\Rightarrow\mathrm{\dfrac{2x+y}{3x+y} }\\\\\\\Rightarrow\mathrm{\dfrac{\dfrac{2x}{y}+1}{\dfrac{3x}{y}+1} }\\\\\\\Rightarrow\mathrm{\dfrac{\dfrac{2}{3}+1}{\dfrac{3}{3}+1} }\\\\\\\Rightarrow\mathrm{\dfrac{\dfrac{2+3}{3}}{\dfrac{3+3}{3}} }\\\\\\\Rightarrow\mathrm{\dfrac{5}{6}}$