Let the popcorn are in the stock be:
- Large $= 7x$
- Super $= 17x$
- Jumbo $= 16x$
And, let the chips in the stock be :
- Large $= 6y$
- Super $= 15y$
- Jumbo $= 14y$
If the total number of popcorn packets in its stock is the same as that of chips packets. Then
$7x + 17x + 16x = 6y + 15y+ 14y$
$\Rightarrow 40x = 35y$
$\Rightarrow 8x = 7y$
$\Rightarrow \boxed{x = \frac{7}{8}y}$
Now, the required ratio $= 16x : 14y = 16\left(\frac{7}{8}y\right) :14y = 14y:14y = 1:1. $
$\therefore$ The numbers of jumbo popcorn packets and jumbo chips packets are in the ratio of $ 1: 1.$
Correct Answer $:\text{A}$