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CAT 2017 Set-1 | Question: 76

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A stall sells popcorn and chips in packets of three sizes: large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio $7: 17: 16$ for popcorn and $6: 15: 14$ for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio

  1. $1:1$
  2. $8:7$
  3. $4:3$
  4. $6:5$
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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 $:\text{A}$

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