Work done by ladder on the boy and work done by boy on ladder I was stuck in a question:

In a children's park there is a slide which has a total length of $10 \,\mathrm m$ and a height of $8 \,\mathrm m$. Vertical ladder is provided to reach the top. A boy weighing $200 \,\mathrm N$ climbs up the ladder to the top of the slide.

The questions further asks for the work done by the boy on the ladder as he goes up and the work done by the ladder on the boy as he goes up.
The answer to the former part is $0  \,\mathrm J$ and for the later one is $1600 \,\mathrm J$. I am really confused about on what basis they are giving this answer. Because from the frame of reference of the boy the ladder is moving downwards. Also there is a force exerted on the ladder so the boy must do some work on the ladder. In the frame of reference of the ground the point of application of the force on the ladder is continuously changing so how should we handle this case?
 A: Remember that work is only done if the object is displaced. Thus, no work is done on the ladder. The work formula is
$$W=\mathbf F\cdot \mathbf d,$$
so the fact that a force is exerted on the ladder is not enough - there also must be displacement of the ladder, and since there isn't, then no work is done on it.
On the boy on the other hand work is being done. Because the ladder exerts an upwards force on him and he is displaced upwards! Using the formula for two vertical vectors:
$$W=\mathbf F\cdot \mathbf d=Fd=200\,\mathrm N\cdot 8 \;\mathrm m=1600\,\mathrm{J},$$
where the Joule unit $[\mathrm{J}]$ is a symbol for $[\mathrm{N\cdot m}]$.
You could look at this in the frame of the boy, sure. Then the ladder would appear as moving, and thus work would be done on the ladder. But then the boy would be stationary within this frame and no work would be done on him. A change of inertial frame does not change the fact that work is only done by one of these two bodies.

When trying to make intuitive sense of work, then think of some extreme cases:

*

*Push a balloon and it moves far, so large displacement $\mathbf d$. But basically no force was required. Noone would agree that you did any demanding work.

*Push on a wall. You can push with a large force $\mathbf F$ and still not move it, so no displacement. Again, despite your effort, noone would agree that you did any useful work because nothing happened.

Work is in this sense the technical term for the intuitive idea of "effort and result". With only effort or only result, then we do not consider any work to have been done.
A: The ladder doesn't move in Earth gravitational field, while a boy - does.
Hence former is $0$, and latter - $200~\text{N} \times 8~ \text{m} = 1.6~\text{kJ}$
