Explanation:

according to the question we know
in the month of june number of girls were half of the number of boys present i.e
girls(g) = 1/2 boys(b)
but in the month of july, as 5 new girls took admission to the school total number of girls now are g+5
and similarly in the same month 5 boys left the school making the number of boys to be b-5
now with this the total number of boys and girls now became equal i.e
 =>   g+5 = b-5 
we know g is half of b so apply the same value in the above given equation we get
1/2 b+5=b-5
b+10 = 2b-10
b=20 
therefore similarly g = 10 
hence number of boys in the month of june = 20
           number of girls in the month of june = 10
so the total number of students in the month of june is 10+20=30

hence option 2 is the correct answer.