If a + 1/b = b + 1/c = c + 1/a (where a ≠ b ≠ c), then abc is equal to?

Answer: Option C

$$\begin{array}{rl}& a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}\\ & \text{Put , }a=\frac{1}{2},b=2,c=-1\\ & \Rightarrow \frac{1}{2}+\frac{1}{2}=2-1=-1+2\\ & \Rightarrow 1=1=1\\ & abc=\frac{1}{2}\times 2\times -1\\ & \boxed{abc=-1}\\ & \text{Again put}\\ & a=-\frac{1}{2},b=-2,c=1\\ & \Rightarrow a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}\\ & \Rightarrow -\frac{1}{2}-\frac{1}{2}=-2+1=1-2\\ & \Rightarrow -1=-1=-1\\ & \text{Equation satisfied}\\ & \Rightarrow abc=-\frac{1}{2}\times -2\times 1\\ & \boxed{abc=+1}\\ & \text{So, }abc\text{ can be }-1\text{ and }+1\end{array}$$