If a, b, c are non - zero $$a + \frac{1}{b} = 1$$   and $$b + \frac{1}{c} = 1,$$   then the value of abc is?

Solution (By Examveda Team)

$$\eqalign{ & a + \frac{1}{b} = 1,{\text{ }}b + \frac{1}{c} = 1 \cr & {\text{Values of }}a,{\text{ }}b,{\text{ }}c{\text{ assume}} \cr & a = \frac{1}{2} \cr & b = 2 \cr & c = - 1 \cr & \therefore abc \cr & = \frac{1}{2} \times 2 \times - 1 \cr & = - 1 \cr} $$