What will be the sum of two numbers?
I. Among the two numbers, the bigger number is greater than the smaller number by 6.
II. 40 % of the smaller number is equal to 30 % of the bigger number.
III. The ratio of half of the bigger number to one third of the smaller number is 2 : 1.

Case 1 : I and II

Let smaller number be  x => bigger number = x+6

$$\frac{40}{100}\cdot x=\frac{30}{100}\left(x+6\right)$$

=> x=18 , Sum of bigger and smaller number = 42

Case 2 : I and III

Let smaller number be x => bigger number = x+6

$$\frac{\left(x+6\right)}{2}\cdot\frac{3}{x}=\frac{2}{1}$$

On solving , x=18 . So sum = 42

Case 3 : II and III

Only the ratio between bigger and smaller number can be found out