350 boxes can be placed in 25 cartons.

Let x be the required number of boxes.

Less number of boxes will require less number of cartons. 

So, it is a case of direct proportion.

Now, $\frac{350}{25}=\frac{x}{16}$

$\Rightarrow x=\frac{350 \times 16}{25}$

$\Rightarrow x=224$

∴ 224 boxes can be placed in 16 cartoons.