What will happen if both AC & DC pass through a common conductor simultaneously ?

Actually, the promise of the question isn't quite correct. Current is actually a result of (induced by) voltage. Ideal DC comes from constant voltage, while ideal AC comes from voltage which reverses direction in a sinusoidal manner. So you can apply a constant voltage on top of an alternating voltage, but you would just result in a pulsating current (which may or may not be direct) with the value equal to the sum of both components.