Question

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

• A. 1: 1
• B. 8: 7
• C. 4: 3
• D. 6: 5

Answer 1

The Correct Option is A

Let the numbers of large, super, and jumbo packets of popcorn be \( 7x, 17x, \) and \( 16x \) respectively. For chips, let them be \( 6y, 15y, \) and \( 14y \).

It is given that the total number of popcorn packets is equal to the total number of chips packets. Thus,

\[ 7x + 17x + 16x = 6y + 15y + 14y \]

\[ 40x = 35y \]

Simplifying, we get:

\[ 8x = 7y \]

Thus,

\[ \frac{y}{x} = \frac{8}{7} \]

The ratio of the number of jumbo popcorn packets to jumbo chips packets is:

\[ \frac{16x}{14y} = \frac{16x}{14 \cdot \frac{8}{7}x} = \frac{16 \cdot 7}{14 \cdot 8} \]

Simplifying this gives:

\[ \frac{16 \cdot 7}{14 \cdot 8} = \frac{112}{112} = \frac{1}{1} \]

Thus, the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio 1:1.