In the month of June, the number of girls in a class was half of the number of boys. In July, five more girls took admission, whereas five boys left the school. Now, the number of boys and girls is equal in the class. How many students in total were there in the class in June?

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) = $$\frac{1}{2}$$ 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

$$\frac{1}{2}$$ 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