Quantitative Aptitude Ques 2289

Question: If $ x+\frac{1}{y}=1 $ and $ y+\frac{1}{z}=1, $ then find the value of $ z+\frac{1}{x}. $

Options:

A) 0

B) 1

C) 2

D) 4

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ x+\frac{1}{y}=1 $ … (i) $ y+\frac{1}{z}=1 $ … (ii)

$ \Rightarrow $ $ x=1-\frac{1}{y}=\frac{y-1}{y} $
$ \Rightarrow $ $ \frac{1}{x}=\frac{y}{y-1} $ Again, $ y+\frac{1}{z}=1 $

$ \Rightarrow $ $ \frac{1}{z}=1-y $
$ \Rightarrow $ $ z=\frac{1}{1-y} $ By putting the value, $ z+\frac{1}{x}=\frac{1}{1-y}+\frac{y}{y-1}=\frac{y-1}{y-1}=1 $

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