Age of A : Age of B is 3 : 2. Ten years hence, the sum of their ages will be 80. What are their present ages?

Let the age of A be "x"

Let the age of B be "y"

then,as respect to the question : Age of A/Age of B

x/y= 3/2.............(I)

10 years later, A age will be= x+10

                      B age will be = y+10

Then,  

x+10+y+10=80 (Given)   ...............(II)

x/y=3/2 

Therefore, x= (3*y)/2..........(applying this in eq.II)

((3*y)/2)+10+y+10=80

((3*y)/2)+20+y=80

(3y+40+2y)/2=80

(5y+40)=160

5y=120     -> y=24

Apply value of y in eq.1

x/24=3/2    -> x=(3*24)/2     ->x=36

Therefore, Age of A = 36

                 Age of B = 24