Answer:

(A+B) ×10/100=(A-B)×50/100

(A+B) /10=(A-B) /2

A/B=3/2

P+Q=3+2=5

Verified answer

Answer: 5x.

minimum value is 5.   x is an integer

Step-by-step explanation:
  10% of (a+b) = 50%of (a-b)
=>(a+b)*10/100  =  (a-b)*50/100

=>(a+b)/10 = (a-b)/2
=> (a+b)/5 = (a-b)
=> (a+b) = 5a - 5b
=> 4a = 6b
=> a/b = 6/4 = 3/2 = p/q

let x be an integer:
a:b = 3:2 = p: q
so, p=3x and q=2x
then, p+q will be    3x + 2x = 5x,  where x can range from (1,2,3,4,........)

minimum value of a+q will be 5