SSC Sample Paper Mock Test-11 SSC CGL Tear-II Paper-1

If \[a+\frac{1}{b}=1\] and \[b+\frac{1}{c}=1,\] then \[c+\frac{1}{a}\] is equal to

A) 0

B) \[\frac{1}{2}\]

C) 1

D) 2

Correct Answer: C

Solution :

\[a+\frac{1}{b}=1\]\[\Rightarrow \]\[a=1-\frac{1}{b}=\frac{b-1}{b}\]

\[\Rightarrow \]\[\frac{1}{a}=\frac{b}{b-1}\]and\[b+\frac{1}{c}=1\]\[\Rightarrow \]\[\frac{1}{c}=1-b\]

\[\Rightarrow \]\[c=\frac{1}{1-b}\]

\[\therefore \]\[c+\frac{1}{a}=\frac{1}{1-b}+\frac{b}{b-1}=\frac{1}{1-b}-\frac{b}{1-b}=\frac{1-b}{1-b}=1\]