The difference between two numbers is 16. If one-third of the smaller number is greater than one-seventh of the larger number by 4, then the two numbers are :

Let the numbers be x and (x + 16)
Then,
$$\eqalign{ & \Leftrightarrow \frac{x}{3} - \frac{{\left( {x + 16} \right)}}{7} = 4 \cr & \Leftrightarrow 7x - 3\left( {x + 16} \right) = 84 \cr & \Leftrightarrow 4x = 84 + 48 \cr & \Leftrightarrow 4x = 132 \cr & \Leftrightarrow x = 33 \cr} $$
Hence, the numbers are 33 and 49