Why is necessary to increase back elevator pressure to maintain altitude during a medium to steep turn?
A the rudder's function has been transferred to the elevator as the bank approaches 45 degrees
B To keep the aero plane's nose moving in the direction of the turn.
C To compensate for the loss of vertical lift and the increased centrifugal force.
D To compensate for the effect of drag caused by the deflection of the ailerons.

Can anyone help me with this question?
C and D look both correct to me.

The discussion presumes that the elevator trim setting remains constant.

As bank increases, the aircraft's lift vector inclines into the turn and the vertical component (ie what is balancing weight) reduces. If the pilot does naught, then the aircraft must descend. To maintain height, wing incidence (angle of attack) must increase to generate an increase in CL to increase overall lift and the vertical component of lift. So the pilot must apply a pull force to the controls. (We could increase speed to generate some increased lift but that probably isn't a usable option).

So let's have a think about the answer options ...

(a) the rudder's function has been transferred to the elevator as the bank approaches 45 degrees

Rudder has to do with yawing moments, elevator with pitching moments. We need more lift which we get by an increased pitch attitude. The option doesn't make much sense. (a) ? I don't think so.

(b) to keep the aeroplane's nose moving in the direction of the turn.

The existing lift force has a horizontal component towards the centre of the turn which provides the centripetal acceleration needed to make the turn happen. While we can increase that accelerating force by increasing pitch attitude, the turn will keep going without any change in pitch attitude ... so (b) doesn't hold much water.

(c) to compensate for the loss of vertical lift and the increased centrifugal force.

This is more promising. As suggested earlier, we need an increase in pitch to provide an increase in lift to increase the vertical component of lift which balances weight .. that compensates for the loss of (the) vertical (component of) lift due to the bank. The increased wing normal force (vertical component lift, horizontal component centripetal force) provides for a better turning solution whether we like or not.

Strictly, we should be talking about centripetal force (the force inwards towards the centre of the turn) rather than centrifugal reaction (the outwards load which is opposite to the inwards accelerating force). However, I think that battle is well and truly lost as just about everyone talks about centrifugal force. The reason for this is we sense the outwards reaction during a turn rather than the inwards accelerating force.

Option (c) certainly could be an acceptable answer alternative.

(d) to compensate for the effect of drag caused by the deflection of the ailerons.

If we are talking about the drag overall, the pitch control isn't going to do much for us .. what we need is thrust if we don't want to accept a small loss in speed. If we are talking about differential drag (which results in adverse yaw) we would use a bit of rudder to address that .. not pitch. I think we can give (d) a miss.

Looking through the options, (c) is the only one which should float your boat, so let's run with that one, shall we ?