Is the tension amplified by the number of turns made by the string? In the following question:

When I first attempted it, I considered only 1 force/Tension, which is produced directly by man on the string, because I thought that its the same force which goes around and acts on the whole system. But when I saw the solution, the Free Body Diagram was this:

And the equation formed was: 3T - (M+m)g = 0
Now my question is,

*

*It seems very counterintuitive, doesn't that 3T in the equation and the FBD of the situation implies that the force applied by the man is amplified by 3 times i.e. tripled?

*What's the correct way to understand this situation intuitively?

 A: There are three parts of the rope pulling up on the man plus plank system. These three parts each have a tension of $T$ for net tension of $3T$. The total mass of the system is $(M+m)$ and since the system is not accelerating we get $$\tag 1 3T-(M+m)g=0$$

doesn't that 3T in the equation and the FBD of the situation implies that the force applied by the man is amplified by 3 times i.e. tripled?

The man pulls on his rope with a tension $T$ and this means the other two parts of the rope will have the same tension. It's not that the tension the man pulls with is tripled as such, but because of what's termed, mechanical advantage of a pulley system, meaning that $\frac{W}{3}$ of the load is shared with each one of the rope segments. That is,

Free body diagrams: 

The mechanical advantage of a pulley system can be analyzed using free body diagrams which balance the tension force in the rope with the force of gravity on the load. In an ideal system, the massless and frictionless pulleys do not dissipate energy and allow for a change of direction of a rope that does not stretch or wear. A force balance on a free body that includes the load, $W$, and $n$ supporting sections of a rope with tension $T$ yields $$nT-W=0$$

meaning that each segment of rope will handle $$T=\frac{W}{n}=\frac{W}{3}$$ of the load.
This is consistent with the result above where the load is given by the wieght of the plank and worker $$W=(M+m)g$$
Note that the horizontal part of the rope will also have the same tension, but because it is in the horizontal direction, it does not contribute to the equation of motion (1).
A: Yes, the force applied by the man is amplified by 3 times.
However energy is conserved, if the man pulls 3m of rope, the work done = force x distance is
$$W= T \times 3$$
The platform will then be lifted by 1m (each vertical part of the rope is shortened by 1m), so the work done on the platform is
$$W= 3T \times 1$$
