Answer
(a) Decreases
(b) III
Work Step by Step
(a) Let us say that all the resistors have the same. Then, we have: $ R_1=R_2=R_3=R $
The two resistors connected in parallel have the equivalent resistance $\frac{1}{R_{12}}=\frac{1}{R}+\frac{1}{R}=$
$\implies R_{12}=\frac{R}{2}$
Now if the third resistor $ R_3$ is connected, then we have
$\frac{1}{R_{effective}}=\frac{1}{R_{12}}+\frac{1}{R_3}=\frac{R}{3}$
Thus, the equivalent resistance will decrease.
(b) We know that the best explanation is option (III) -- that is, the third resistor gives yet another path for current to flow into the circuit, which means that the equivalent resistance is less.
