Whatever the speciation of chromium (Cr+III or +VI), both are coloured and prone to be adsorbed at the surface of activated carbon (AC). So your absorbance should logically decrease, at least at the suitable wavelengths, hence the need to have the absorbance spectrum of the solution before adsorption by AC. Indeed, interferences with other chemicals can never be excluded, so it is required to have the initial spectrum and compare with others obtained after given adsorption times. Usually, working at the wavelength of maximum absorption (Lambda max) is enough.
Obviously, I may add that refence spectra obtained with different concentrations of Cr can be used for building a calibration curve, so that you can deduce the remaining amount of Cr in the solution only based on the decrease of absorbance at Lambda max.
Yes, activated carbon will adsorb chromium, and the absorbance will fall. As Alain suggested though, you need to use the right wavelength. For Cr(VI), I guess it is 540 nm.
Yes iits obvious that its absorbance will change after adding activated carbon. But i want to know that whatever will be the absorbance after adding activated carbon , it will remain same after four days?
This depends on the adsorption kinetics, on the amount of Cr, on the amount of activated carbon (high enough of not), an on temperature. All these parameters may strongly influence the result, leading to a complete adsorption after a few hours, or after a few days only. You can never guess that, it is all about experimental conditions. Four days are not that long, better doing the experiment in your own experimental conditions.