Ok this is a really weird question and whoever came up with it should be fired on the spot, but I will try to answer it.

So weirdly enough we are omitting the initial phase of acceleration of the object, which might actually be the point of confusion here. Anyway, as the velocity is constant, this means that there is *no net force acting upon the object*, because of F=ma we know that any net force would accelerate the object and therefore change its velocity. This means that, no matter the velocity, the force applied to the object (upwards) is exactly equal to the gravitational force on the object, mg.

​

Now this is where the answer becomes a bit fuzzy. Because if we say that the object has constant velocity in the time interval we're considering, no net force is acting on the object, thus no work (W = F*h) is done and all the answers (A) through (E) would be correct (as F=0 and P=0 in both cases). What they are probably referring to is the work done by "lifting the object up". So just looking at the upwards pointing force, we would get W = F*h in both cases, but P=W/t in the first case and P = 2W/t in the second case. But this is physically nonsensical really because the real work is done during the acceleration phase of the object, which we are supposed to ignore. It's just like when you lift up a suitcase. During the acceleration phase, work is done. But simply countering the gravitational force (by simply holding the suitcase, for example), would not do work.

​

I don't know if I was able to make it clear. And if anyone spots an error in my argument, I am happy to be corrected!