CONCEPT: The question is based on the concept of equations.

SOLUTION:

 
The two equations can be written as

x^2 (6k+2) + rx + (3k-1) = 0 …… (i)

& x^2(12k + 4) + px + (6k - 2) = 0 ….. (ii)

Divide (ii) by 2

Thus, we get x^2 (6k+2)+ p/2*x + (3k-1)=0 …. (iii)

Comparing (i) and (iii), we get r = p/2
Thus 2r-p = 2(p/2)-p= 0. (OPTION A)