If a + 1/b = 1 and b + 1/c = 1 then c + 1/a is equal to?

Answer: Option C

$$\begin{array}{rl}& a+\frac{1}{b}=1\text{, }b+\frac{1}{c}=1\text{, }c+\frac{1}{a}=?\\ & \text{Put values, }\\ & a=\frac{1}{2},b=2,c=-1\\ & c+\frac{1}{a}\\ & =-1+\frac{1}{\left(\frac{1}{2}\right)}\\ & =-1+2\\ & =1\\ & \\ & \mathbf{Alternate}:\\ & \Rightarrow a+\frac{1}{b}=1\\ & \Rightarrow a=1-\frac{1}{b}=\boxed{\frac{b-1}{b}}\\ & \frac{1}{a}=\frac{b}{b-1}\\ & \Rightarrow b+\frac{1}{c}=1\\ & \Rightarrow \frac{1}{c}=1-b,\boxed{c=\frac{1}{1-b}}\\ & \therefore c+\frac{1}{a}\\ & =\frac{1}{1-b}+\frac{b}{b-1}\\ & =\frac{1}{1-b}-\frac{b}{1-b}\\ & =\frac{1-b}{1-b}\\ & =1\end{array}$$