The investment of A is twice as that of B and thrice as that of C B invested for twice the months th...........

Explanation:

If A invested Rs x, then B Rs (x/2) and C invests Rs (x/3).
Let B invested for y months, then A for (y/2)months, and C for (y/3) months
So ratio of profit shares-
A : B : C
x*(y/2) : (x/2)*(y) : (x/3)*(y/3)
1/2 : 1/2 : 1/9 = 9 : 9 : 2
Both A and B gets equal and highest profits.