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

$1:1$

$8:7$

$4:3$

$6:5$

✅ Correct Option: 1

We have a stall selling popcorn and chips in three sizes. The key information:

Popcorn ratio (large : super : jumbo) = 7 : 17 : 16

Chips ratio (large : super : jumbo) = 6 : 15 : 14

Total popcorn packets = Total chips packets

We need to find: jumbo popcorn : jumbo chips

When we say popcorn packets are in ratio 7:17:16, this means:

Out of every (7+17+16) = 40 popcorn packets, 16 are jumbo

So jumbo popcorn = $\tfrac{16}{40}$ of total popcorn packets

Similarly for chips:

Out of every (6+15+14) = 35 chips packets, 14 are jumbo

So jumbo chips = $\tfrac{14}{35}$ of total chips packets

Since total popcorn packets = total chips packets, let's call this common total T.

Therefore:

Number of jumbo popcorn packets = $\tfrac{16}{40} \times T$

Number of jumbo chips packets = $\tfrac{14}{35} \times T$

Jumbo popcorn : Jumbo chips = $\tfrac{16}{40}T : \tfrac{14}{35}T$

Since both terms have T, we can cancel it out:

= $\tfrac{16}{40} : \tfrac{14}{35}$

Let's simplify each fraction:

$\tfrac{16}{40} = \tfrac{16 ÷ 8}{40 ÷ 8} = \tfrac{2}{5}$

$\tfrac{14}{35} = \tfrac{14 ÷ 7}{35 ÷ 7} = \tfrac{2}{5}$

Jumbo popcorn : Jumbo chips = $\tfrac{2}{5} : \tfrac{2}{5} = 1:1$

Even though the individual ratios for popcorn (7:17:16) and chips (6:15:14) look different, the fraction of jumbo packets in each case works out to be the same! This is why we get a 1:1 ratio.

Answer: 1:1

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