Here’s how I solved it using equations:

B + G = 42 … (1)

(1/2)B + (2/5)G = 19 … (2)

(1) x 1/2:
(1/2)B + (1/2)G = 21 … (3) 

(3) – (2):
(1/2)G – (2/5)G = 2
((5-4)/10)G = 2
(1/10)G = 2
=> G = 20

So plug G=20 into (1):
B = 42 – 20 = 22

So there are B-G=22 -20 = 2 more boys than girls in the class #