If a + 1/b = b + 1/c = c + 1/a ( a b c ) then the value of abc is?

Answer: Option A

$$a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}$$
To save your time assume values of a, b, c according to the question.
$$\begin{array}{rl}& \text{Let }a=2,b=-1\&c=\frac{1}{2}\\ & 2+\frac{1}{-1}=-1+\frac{1}{\frac{1}{2}}=\frac{1}{2}+\frac{1}{2}\\ & \therefore abc=2\times -1\times \frac{1}{2}=-1\end{array}$$