How to use Kohlrausch's law with ionic equivalent conductances? My text says that for an ionic compound like AxByif ionic equivalent conductance of Ay+ is a and that of   Bx- ion is b, then the equivalent conductance for AxBy would be a/y + b/x 
Now my question is: 
as the unit of equivalent conductance is S cm2 (gm equivalent)-1 so if i multiply it by a quantity x with unit (gm equivalent) mol-1, then i will get a quantity with unit S cm2 mol-1. This should be the Molar conductance of the ion granted that the value of x was correct. Now for example in Al2(SO4)3 for Al3+ ion the value of x would be 3 because one mole of Al3+ ions would contains 3 gram equivalents. So if equivalent conductance of Al3+ ion was a, then its molar conductance would be 3a and similarly for SO42- ion with equivalent conductance b, the molar conductance would be 2b. Now from all that i can tell that the molar conductance of Al2(SO4)3 would be, 2(3a) + 3(2b) = 6a + 6b
Now from the formula of equivalent conductance and molar conductance
(Molar conductance)/n = Equivalent conductance
where n is the valence factor for desired compound.
So in our case n=6 for Al2(SO4)3

∴ equivalent conductance = (6a + 6b)/6 = a + b
but according to my text it would be a/3 + b/2 
Tell me where am i going wrong.
And the result I ended up on works for some questions and the thing that my text provided works for some questions, and then there are some questions in which nothing works. I am really confused... And sorry for any grammatical atrocities. EDIT: I am just trying to ask that when equivalent conductance of two ions are given to me as a and b, then what would be the equivalent conductance of the compound to which these ions belong? Would it be a + b or would it be a/(charge on first ion) + b/(charge on second ion) or is it something totally else?
You textbook writer has explained it in a very complicated way. I think you are confused by the concept of equivalent. Gram equivalent is an obsolete unit now but it is still used in conductance measurements. 

First understand the definition of gram equivalent weight for a salt (and it applies to salts only). Acids/ Bases/Redox agents have different definitions.

Gram Equivalent weight of a salt or an ion = gram molecular weight/charge on the ion

This is the definition of gram equivalent.

From the context of your book, ionic equivalent conductance is same as "molar conductance" of aluminum ion. Here a and b refer to molar conductance. This is the mistake you are making. Thus, a 1 Molar Al3+ solution has 3 gram equivalents of Al/ 1 L or it is a 3 N solution (N = Normal). 

So if you are given ionic equivalent conductance of Al2(SO4)3 (at infinite dilution) then your textbook is right = (ionic equiv. conductance Al)/ charge on Al + (ionic equiv. conductance sulfate)/ charge on sulfate = a/3 + b/2

By the way, equivalent conductance can only be added at infinite dilution. Whatever you see in tables are usually given at "infinite dilution".