How to define equivalents here $3g$ of activated charcial was added to $50 ml$ of acetic acid solution ($0.06N$) and filtred after an hour and it was found to be $0.042 N$ .The amount of acetic acid adsorbed (per gram of charcoal) is


The solution for this question is exactly given as I have written below

No of equivalents before adsorption $=50\times0.06 =3$

No of equivalents after adsorption $=50 \times 0.042=2.1$

No of equivalents left $=0.9/1000 \times 60=54mg$
Acetic acid per gm $= 54mg/3=18mg$

Now I have some doubts regarding the question and it's answer


  
  Why is normality being decreased here?
  Why are they taking volume to be same when it generally increases when we add solutes?
  What does equivalent mean here? According to Wikipedia, it is said to be "the mass of one equivalent, that is the mass of a given substance which will 1)  combine or displace directly or indirectly with 1.008 parts by mass of hydrogen or 8 parts by mass of oxygen or 35.5 parts by mass of chlorine – these values correspond to the atomic weight divided by the usual valence; or  2) supply or react with one mole of hydrogen cations (H+) in an acid–base reaction or 3) supply or react with one mole of electrons (e−) in a redox reaction." The equivalent talked in the question doesn't meet any of this criteria so what is its role here. Can somebody please explain me this?
Number of equivalents and normality are out-of-date concepts in chemistry. For acids, they are just like number of mols and molar concentration (or molarity), with an extra factor indicating how many hydrogens can be effectively ionized in solution. Because acetic acid ($\ce{CH3COOH}$) is monoprotic, you can just exchange the terms by number of mols and molarity and you are good.


  Why is normality being decreased here?


Some of the acetic acid adsorbs - meaning it bonds - in the charcoal. So the concentration in solution is decreased. Pay attention to the fact that the charcoal remains solid and does not dissolve.


  Why are they taking volume to be same when it generally increases when we add solutes?


As I wrote above, the charcoal stays solid, so it has no effect on the solution volume. The loss of acetid acid in solution might have a slight effect on volume, but that is mostly negligible.