How can normalities be interchangeably used? So I was doing the following question on stoichiometry . The part $\pu{1.80N}\ \ce{HCl}$ can also be written as $\pu{0.9 N}\ \ce{   H_2SO_4}$  but I don't understand why . 

$\pu{10 g}$ sample of 'gas liquor' ($\ce{NH}^+_4$ salt) is boiled with $\ce{NaOH}$ and the resulting $\ce{NH3}$ is passed into $\pu{60 ml}$        of $\pu{1.8 N}\ \ce{HCl}$ . Excess $\ce{H_2SO4}$ required $\pu{10cm^3}$ of $\pu{0.40 N}\ \ce{NaOH}$. What is the % of $\ce{NH3}$ in gas liquor?

I got the answer but just can't understand why the two can be used interchangeably.
The fundamental idea behind gram equivalents and normality is that one gram equivalent of an acid reacts with one gram equivalent of a base. This idea eliminates the need of using molarity and thinking about mole ratios for any acid base titration.

Equal volume 1 N HCl will react with 1 N NaOH. Similarly, 1 liter of 1 N $\ce{H2SO4}$  or 1 N $\ce{H3PO4}$ will consume 1 L of 1 N NaOH.

The key calculations is that you should know how to calculate normality from a given molecular weight and a balanced equation:

For example: 
$\ce{HCl}$ -> $\ce{H+}$ + $\ce{Cl-}$
gram equivalent weight= formula weight/ (No. of acidic protons) = 36/1 =36

$\ce{H2SO4}$ -> $\ce{2H+}$ + $\ce{SO4^2-}$
gram equivalent weight= formula weight/ (No. of acidic protons) = 98/2 = 49

Can you now make the connection that why "The part 1.80 N HCl can also be written as 0.9 N H2SO4" is quite wrong? because

1 N HCl = 1 N $\ce{H2SO4}$

and both solutions contain 1 gram equivalents of protons.

Yes if your teacher were comparing normality and molarity, then it is different.

Molarity calculations are different and far more easier. By definition, M of X= moles of A/ Total volume in which X is present.

A 1 M HCl just means there is one mole HCl (gas) dissolved in 1 L of solution
Similarly, 
1 M $\ce{H2SO4}$ is 1 mole $\ce{H2SO4}$ dissolved in 1 L of solution.

If you were to titrate  1 L of 1 M NaOH with 1 M HCl you would require 1 L of HCl. However, since  sulfuric acid furnishes two moles of proton $\ce{H+}$ for each mole of sulfuric acid, only 500 mL would be required.

In short, 1 M HCl is equivalent to 0.5 M $\ce{H2SO4}$ in terms of titer for $\ce{OH-}$ ion.

Contrast this molarity unit with normality which is almost obsolete except in some South Asian colleges.