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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (I)

  • question_answer
    If \[a+\frac{1}{b}=1\]and \[b+\frac{1}{c}=1,\]then the value of \[c+\frac{1}{a}\]is [SSC CGL Tier II, 2017]

    A) 0

    B) 2

    C) 1

    D) 3

    Correct Answer: C

    Solution :

    [c] Given,\[a+\frac{1}{b}=1\] \[\Rightarrow \]\[ab+b\]\[\Rightarrow \]\[a=\frac{b-1}{b}\] \[\Rightarrow \]\[\frac{1}{a}=\frac{b}{b-1}\]and \[b+\frac{1}{c}=1\] \[\Rightarrow \]\[bc+1=c\] \[\Rightarrow \]\[1=c\,(1-b)\]\[\Rightarrow \]\[c=\frac{1}{1-b}\] \[\therefore \]      \[\left( c+\frac{1}{c} \right)=\frac{1}{1-b}+\frac{b}{b-1}\] \[=\frac{b}{(b-1)}-\frac{1}{(b-1)}=\frac{b-1}{b-1}=1\]


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