Quantitative Aptitude Ques 1486

Question: If $ \frac{4x+y}{x+4y}=\frac{2}{3}, $ then find the value of $ \frac{x+4y}{4x+y}. $

Options:

A) $ \frac{3}{8} $

B) $ \frac{3}{4} $

C) $ \frac{3}{2} $

D) $ \frac{3}{6} $

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ \frac{4x+y}{x+4y}=\frac{2}{3} $

$ \Rightarrow $ $ 3(4x+y)=2(x+4y) $

$ \Rightarrow $ $ 12x+3y=2x+8y $

$ \Rightarrow $ $ 12x-2x=8y-3y $

$ \Rightarrow $ $ 10x=5y $

$ \Rightarrow $ $ x=\frac{5}{10}y $
$ \Rightarrow $ $ x=\frac{1}{2}y $ Now, $ \frac{x+4y}{4x+y}=\frac{\frac{1}{2}y+4y}{4\times \frac{1}{2}y+y}=\frac{\frac{y+8y}{2}}{2y+y}=\frac{\frac{9y}{2}}{3y} $

$ \Rightarrow $ $ \frac{9y}{2}\times \frac{1}{3y}=\frac{3}{2} $

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