If so, then why does efficiency effect current and not voltage? Shouldn't it affect power overall, (P=IV).
i.e. 0.8P = 0.8(IV).
Hey! Really good question - The efficiency of transformers is actually a fairly complicated topic, the HSC glosses over it just a little bit. Essentially, the exact effect of efficiency on output voltage and current depends a bit on where the power loss occurs. Is it due to resistance in the windings? Eddy currents in the core? There are different models for transformer efficiency and different ways of accounting for this. The HSC tends to not worry about this and give you extra values to help you hone in on the answer.
Problem here is that you aren't given that additional direction - Like your induction question, I don't think this is worded in the best way. So you've got to make some assumptions to answer this. I think your assumption is fair - It says, "Okay, my output voltage is locked, so all of my power loss occurs due to some of the current being used elsewhere in the transformer." Incidentally, this would occur due to the current needed to magnetise the core, and you can also account for eddy current loss in this way. You've assumed there is no resistance in either primary or secondary coil, and that there is no leakage flux.
Are you expected to know all of that in your assumption? Of course not. You just assumed the output current was what was affected by efficiency, which given the lack of information suggesting otherwise, is a fair assumption to make