Question

ten years ago a age was half of b if the
ratio of their present age is 3 ratio 4 what
will be the sum of their age

Answer 1

given a:b=3:4, then present age of a and b be 3x and 4x 
given ten years ago, a was half of b 
=> 2(3x X 10) = (4x X 10)
=> 6x X 20 = 4x X 10
=> 2x = 10
=> x = 5

Answer 2

Ten years ago let the age of 'a' be 'p'  and the age of 'b' be 'q'   
p=q/2
Now present (p+10)/(q+10) = 3/4
          4(p+10) = 3(q+10)
           4p+40  = 3q  + 30
           4p - 3q = 30 - 40
   but we know that p = q/2 ⇒2p = q
           2(2p) - 3q = -10
            2q - 3q = -10
               -q = -10
                q = 10
   the age of 'b' ten years ago was 'q' = 10
now present  age of 'b' = q+10 
                                 = 10+10
                                 = 20 
ten years ago the age of 'a' is p=q/2 = 10/2 = 5
now present age of 'a' is p+10 = 5+10 = 15
therefore the sum of the ages of 'a' and 'b' is 20+15 = 35