Let G = the number of girls in the class and C = the number of chocolates received by each girl.

Then

(G+20)*(C-1) = GC    (1)    ("Had there been 20 girls more each would have received one chocolate less")
(G-20)*(C+3) = GC    (2)    ("had there been 20 girls less each would have received 3 chocolates more")

We have to equations in two unknowns, but the equations are non-linear.
Simplify each of the equations. Equation (1) becomes 

GC + 20C - G - 20 = GC,  or,  canceling GC in both sides,
20C - G - 20 = 0,  or
20C - G = 20.         (3)


Equation (2) becomes 

GC - 20C +3G - 60 = GC,  or,  canceling GC in both sides,
-20C + 3G - 60 = 0,  or
-20C + 3G = 60.       (4)


Now we have an equivalent system of two equations (3) and (4) in two unknowns, but this time the equations are linear.

Add the equation (3) and the equation (4) (both sides). You will get

2G = 20 + 60 = 80  --->  G =  = 40. 
Thus the number of girls in the class is 40.

Then from (3) 20C = G + 20 = 40 + 20 = 60.
The number of chocolates each girl received in the basic scenario is  = 3.

Please check this answer on your own.

Answer. 40 girls in the class received 3 chocolates each.