Why colors on CMYK looks much different than RGB on screens ?

simply for CMYK colors are pigment means ink, and for RGB are light colors.

when you mix3 of pigment colors C+M+K = Black

when you mix3 light colors R+G+B = white

so mixing and matching colors are totally different. usually when you design in RGB and print it gives a dark and dull colors. but there are some of printers can calibrate your system to the right output.

Ahmed has given a good response to your question.

Your display monitors have pixels each pixel is based on3 colors. That is the reason why they look different on screens, and the science behind it.

it's so simple because the RGB mode has a great range of colors and some of it can't be created by the printers for that some of the colors at RGB documents disappears when it comes out from the printer because the printers can generate a limited number of colors using four colors (Cyan, Magenta, Yellow, Black)

When a user generates graphics on a computer for printing, or wishes to print images from a digital camera, it is a common mistake to assume that the colors seen on the screen will look the same in print. As a result of this mistake, files for printing are often erroneously sent in the Red-Green-Blue (RGB) format for printing. The issue lies in the fact that the computer screen and many photo editing programs show colors in RGB mode, while images are printed on paper in Cyan-Magenta-Yellow-Black (CMYK) format. Sometimes the conversion from RGB to CMYK works without any problems arising, and a printout will look identical to what shows up on the computer. In other cases, there will be noticeable differences between the shades of color. The key to avoiding this potential problem is to convert all graphics to CMYK format during the layout design phase.

RGB Color Mode

RGB is the color scheme that is associated with electronic displays, such as CRT, LCD monitors, digital cameras and scanners. It is an additive type of color mode, that combines the primary colors, red, green and blue, in various degrees to create a variety of different colors. When all three of the colors are combined and displayed to their full extent, the result is a pure white. When all three colors are combined to the lowest degree, or value, the result is black. Software such as photo editing programs use the RGB color mode because it offers the widest range of colors.

CMYK Color Mode

Printers print color onto paper using the CMYK color mode only. This is a four color mode that utilizes the colors cyan, magenta, yellow and black in various amounts to create all of the necessary colors when printing images. It is a subtractive process, which means that each additional unique color means more light is removed, or absorbed, to create colors. When the first three colors are added together, the result is not pure black, but rather a very dark brown. The K color, or black, is used to completely remove light from the printed picture, which is why the eye perceives the color as black.

What you see on your HDTV, computer monitor, smart phone or tablet is an RGB display. The letters RGB stand for the colors that are used to display the image on your screen: Red, Green and Blue. The pixels in your screen blend those three colors of light together to achieve the resulting myriad of tones, shades and hues you enjoy. Because the colors are made from combined light, all three together make white. On the other hand, the absence of each color means no light, and, you guessed it—black! Since RGB color is made by adding light together, it is known as an additive color model.

The output of most inkjet printers and digital copiers is referred to as CMYK, which represents the color pallet they use to render images: Cyan, Magenta, Yellow and blacK. With these printers, white is derived by the paper itself, while black is either black ink, or the combination of all of the colors. CMYK color is known as a subtractive color model because it uses ink to subtract from the light that is being reflected off the paper.

CMY(K) colors work by "subtracting" or absorbing light reflected from a white piece of paper. With no ink or toner on the page,100% of the light is reflected back to the eye and the paper appears white. By adding100% density of each C, M, Y, (ink, toner) to a sheet, they absorb all the (white) light and we perceive the color as black (the absence of all color). By varying the amounts of Cyan, Magenta and Yellow, we can produce a immense number of colors, however, not as extensive as the gamut of color produced in the RGB method. While100% CMY will produce black by themselves, black toner/ink is often added to them to provide more density and smoother transitions.