How can static friction do work? 
By definition, the work done by a force is $W = F\cdot d$, so how can static friction do work? 
Can this force move the body a distance of $75~\text{m}$?
 A: I think you are confused about what $d$ is supposed to mean in the equation $W=F\cdot d.$ You seem to be under the impression that $d$ is the distance that the object being acted on moves relative to the object providing the force. But this is not the correct meaning of $d$ in the equation and you know it. 
Imagine if the car crate were in front of the truck, and the truck were pushing the crate. Then I think you would have no problem saying that the truck is doing work on the crate even though there is no change in the relative distance between the truck and the crate.
Now the situation in your question is basically the same as this one except the force acts on the bottom of the crate instead of the side, and the force is due to friction instead of a normal force. But neither of these differences ought to change the amount of work being done.
That being said, you would have a valid point if the problem were asking for the work done in the frame of the car. In that frame, the box does not move (assuming the coefficient of static friction is sufficiently large), so that $d$ really is zero. Thus no work is done in this frame.
A: Without friction between the crate and the truck bed, the crate would remain at rest in the frame of reference of the road, as the truck accelerates away down the road.
The crate moves in the frame of reference of the road, because of the force of friction acting on it.
So the work done on the crate, in the frame of reference of the road, is the friction force times the distance the crate has traveled in the frame of reference of the road (which could be less than the distance the truck has traveled).
A: 
By definition, the work done by a force is $W = F\cdot d$, so how can static
  friction do work ?
Can this force move the body a distance of $75~\text{m}$ ?

Friction does negative work on the truck, slowing it down and does not move it forward.
What does positive work on the truck, accelerates it and makes it translate $75~\text{m}$ is the engine of the truck.
The 80-Kg crate does negative work on it, because it is opposing the truck which is trying to push it forward, and acts over a distance of 75m. 

Knowing that in $75~\text{m}$ of space, it reaches the velocity of $72~\text{Km/h}$, you can find the acceleration of the crate/truck. Using the weight of the crate and the coefficients of friction, you can find out the negative work done by the crate on the truck, subtracting energy and slowing it down.
Static friction locks the crate to the truck and prevents it from slipping back and off the truck's bed.

yes, this is the work done by the friction force on the truck not on
  the crate. I need to understand the work done by the friction force on
  the crate . –  mech.eng

As I said, friction just locks the crate, it is an interface, like the clutch on a motor-car. The amount of positive work on the crate equals the amount of negative work $-W = +W$ on the truck. But the work on the crate is actually done by the engine of the truck. 
The black arrow to the right shows the truck pulling the crate (thanks to friction) speeding it up to $v=20m/s$ and therefore giving it $W = E =16,000J$. I hope it is clear now.
A: It doesn't. 
The work is done by the active force(ex. A human trying to pull a bull.). This work is converted into frictional energy(ex. Heat generated b/w surfaces)
A: Static friction does not produce or consume work in most of the times. For example for a solid body that rolls without sliding the velocity of the base point $A$ is $\vec v_a = \vec v_{cm} + \vec v_{tangential} \Rightarrow v_a = v_{cm} - \omega R = \omega R - \omega R =0$ which implies that $x_a = 0$. The static friction is a force that acts on $A$ so $W_T = T x_a = 0$ 
But when the object slides then the friction force is constant and equal to $T = \mu N$ and is is always opposite to the velocity of the body. So then $W_T = - Ts$ where $s$ is the total space traveled by the body.
