Why is the maximum efficiency of a push-pull amplifier 78.5%?
Push-Pull is used for analog , digital, Class B, D,E, half-bridge switches and all sorts of applications.

In theory with sine wave and ideal saturation =0V say with MOSFETs, it is η=π/4 or 78.5% but 78% may be closer to what is possible but given no assumptions choose (c) (d) for sine as this is the typical signal not a square wave which in theory is 100% but a practical design goal might be 99% for Class D or E. 

The problem is lack of assumptions or specs so the question is vague but assume by push-pull they imply Class B not Class D or E.  Unless one states signal shape, and distortion allowed, efficiency must be based on some standard test method.  like 1KHz sine 1% THD, so the question is very typical of an academic one.

The archaic nature of this academic question leads me to suggest they only want you to compute the integral of a sine current (I-peak) squared times a fixed resistance, which I leave for you to figure out.