How does paint of two color mix to form one of new color? Suppose I take bit from two paints of different color and I smudge both on the same spot on a piece of paper, I will get a new color. What exactly is the physics behind this?
 A: when you shine white light (containing all colors) at a splotch of paint, the splotch absorbs almost all the colors except one, which it instead reflects back to your eye- which tells you that the splotch is, for example, green because very little red or blue light is reflected back to your eye.
This absorption trick is performed by chemicals called pigments that are mixed into the paint.
Now if you mix two colors of paint, then both sets of pigments are trying to absorb all but their own special reflective colors at the same time and almost all of the incident white light gets absorbed, because what wasn't absorbed by one pigment will be absorbed by the other. What does manage to get reflected is some wavelength which is not too strongly absorbed by either of the pigments- and so you get a new color.
That new color is going to appear less bright to your eye because less light is being reflected off the paint mixture, and if you mix all the colors in your paint set together you'll get a dull, muddy blackish-brown color as a result.
A: The perception of colors is influenced by 3 factors:

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*The spectrum of the light that illuminates the objects

*The spectrum absorbed by the object

*The detector (example: eye+brain)

Subtractive color combination
The second point helps to understand the case of two inks mixed on a paper. With ink you have subtractive color combination: each ink has a set of pigments and the color you see is made of only those wavelengths reflected by all pigments.
Let's see two experiments as examples of what happen:
IDEAL EXPERIMENT
If you have ideal yellow and blue pigments, those will absorb all the light except one specific wavelegth: 580nm for yellow and 470nm for blue. If you mix them, you will have no wavelength reflected by both the pigments (so you see black): indeed the yellow will absorb the 470nm and the blue will absorb 580nm light.
(more) REAL EXPERIMENT
Consider a more real yellow and cyan pigment: they do not have a single wavelength but a little spectrum made of:

*

*Yellow: will reflect yellow light with a little bit of green

*Cyan: will reflect blue with a little bit of green
If you mix them, the result is that you see a smooth green light not very saturated.
This explains why blue ink + yellow ink makes green.

Further considerations
Alway consider that in real experiments you have contribution of the other two factors:

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*Illumination: the experiments above use a white light. In a real case usually is not perfectly white, so if the light that illuminates the paper do not have the green in its spectrum, you will see black in both experiments.

*Light mix: the mixing of light from different sources (i.e. light with different colors) brings to the additive colo mixing that is different from subtractive mixing.

*Detector: colors do not exists in nature. They are the way that our brain pictures to us the ensamble of wavelength perceived by the eyes (the detectors). Each person has a little bit different perception of colors: the same mix can be perceived with different saturation, intensity and sometimes prevalent colors. Example: Cyan do not have its own wavelength but what you see how your brain pictures a specific spectrum.

