Why biplanes are not used in modern high speed aircrafts? Explain why the high speed and commercial air crafts are monoplanes why not biplanes?
 A: The advantage of the biplane wings are:
(1) 2x times bigger surface, thus roughly 2x times bigger elevating force
The disadvantages are numerous:
(2) (Roughly) double drag (double required fuel)
(3) (Roughly) double service, etc. costs
Now the drag, and also the elevating force, depends (roughly) quadratically on the speed. In the ancient times, the speed of the planes were at most some hundreds of km/h. Now they near the speed of the sound.
Contrary the misconception, most of the fuel of the planes isn't used for to hold the plane in the air. It is used against the drag.
Biplanes were useful as holding the plane in the air was a big engineering challenge, because their speed was slow. Now the problem is the drag.
Thus, also a monoplane is enough to hold the plane in the air, and it is even needed, because the drag have to be minimized.

Extension:

Why does a biplane have to have double the wing surface and double the
  drag? Why couldn't the size of each of the two sets of wings be scaled
  down so that both the total wing surface and the total drag of a
  biplane are similar to a comparably sized mono-wing airplane?

The drag is a very complex, nonlinear thing, but (very) roughly it depends linearly on the cross-section. Most important non-linear effect that we need to have a drop-like streamlined form, as the form of the plane deviates from it, we will have higher drag. In extreme case we can call it parachute. Thus, biplanes have higher drag even with the same cross-section as a monoplane. And majority of the costs of the planes is coming from the fuel, and the majority of the fuel is going to handle the drag.
Included from @SamuelWeir 's comment:
Consider also that not the wings are doubled, but we also have additional drag from the wires and trusses between the wings.
Notable link about supersonic biplanes.
