Answer:
present Age of " A " will be (x) = 45 years 
present Age of " B " will be (y) = 24 years 
Explanation:
Age of " A " = x years 
Age of " B " = y years 
 
 
 
 
(Three years ago A's age was double of B's age.) 
 
==> (x-3) = 2 * (y-3) 
 
==> x - 2y = -6 + 3 
 
==> x - 2y = -3 -------------(1) 
 
 
 
(Seven years hence, the sum of their ages will be 83 years ) 
 
==> (x+7)+(y+7) = 83 
 
==> x + y = 83 - 14 
 
==> x + y = 69 ------------(2) 
 
Subtract equ.(1) & equ(2) 
 
==> -2y - y = -3 - 69 
 
==> -3y = -72 
 
==> y = -72/(-3) 
 
==> y = 24 
 
Keep value of y in equ(2) 
 
==> x + 24 = 69 
 
==> x = 69 - 24 
 
==> x = 45