CAT 2017Slot 1QAQuestion & Solution
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
Options
1 : 1
8 : 7
4 : 3
6 : 5
Solution
1. Concept Used
- Topic: Ratio and Proportion
- Formula: $$\text{If total popcorn} = \text{total chips, then } 40x = 35y \Rightarrow \frac{x}{y} = \frac{7}{8}$$
2. Calculation
Let the number of large, super, and jumbo popcorn packets be in the ratio (7 : 17 : 16). Assign a multiplier (x), so the counts are (7x,\ 17x,\ 16x).
Total popcorn packets (= 7x + 17x + 16x = 40x).
Let the number of large, super, and jumbo chips packets be in the ratio (6 : 15 : 14). Assign a multiplier (y), so the counts are (6y,\ 15y,\ 14y).
Total chips packets (= 6y + 15y + 14y = 35y).
We are given that total popcorn packets equal total chips packets: $$40x = 35y$$ $$\frac{x}{y} = \frac{35}{40} = \frac{7}{8}$$
So we can write (x = 7k) and (y = 8k) for some constant (k).
Now, jumbo popcorn packets (= 16x = 16 \times 7k = 112k).
Jumbo chips packets (= 14y = 14 \times 8k = 112k).
Ratio of jumbo popcorn to jumbo chips: $$\frac{112k}{112k} = \frac{1}{1} = 1 : 1$$
3. Solution
Answer = Option A ✅
The ratio of jumbo popcorn packets to jumbo chips packets is 1 : 1.