A drink vendor has 368 liters of Maaza, 80 liters of Pepsi, and 144 liters of Sprite. He wants to pack them in cans such that: • Each can contains the same volume (in liters), • No can contains a mix of two different drinks, and • All the drink is packed completely with no leftover. What is the least number of cans required?

Introduction / Context:
This problem combines the idea of HCF with an optimization goal. To minimize the number of cans, each can should have the maximum possible capacity that divides each drink quantity exactly. Once the can size is fixed, we simply divide each total volume by that size and add them up to get the least number of cans.

Given Data / Assumptions:

• Maaza = 368 liters
• Pepsi = 80 liters
• Sprite = 144 liters
• All cans must be of equal capacity
• No mixing of drinks in the same can and no leftover liquid

Concept / Approach:
If the capacity of each can is x liters, then x must be a common divisor of 368, 80, and 144. To minimize the number of cans, x should be as large as possible, which means:
x = HCF(368, 80, 144)
Once we find x, we compute the total number of cans needed for each drink separately and then add them.

Step-by-Step Solution:
Step 1: Find gcd(368, 80).368 mod 80 = 48.80 mod 48 = 32.48 mod 32 = 16.32 mod 16 = 0, so gcd(368, 80) = 16.Step 2: Find gcd(16, 144).144 mod 16 = 0, so gcd(16, 144) = 16.Therefore, can capacity x = 16 liters.Step 3: Number of cans for each drink:Maaza cans = 368 / 16 = 23.Pepsi cans = 80 / 16 = 5.Sprite cans = 144 / 16 = 9.Step 4: Total cans = 23 + 5 + 9 = 37.

Verification / Alternative check:
If we choose any smaller can size that also divides all three quantities, such as 8 liters, the total number of cans would be 368/8 + 80/8 + 144/8 = 46 + 10 + 18 = 74, which is larger than 37. Since 16 is the greatest common divisor, it guarantees the least possible number of cans.

Why Other Options Are Wrong:
35: Would correspond to a different and smaller can size that does not divide all three quantities exactly.46 and 47: These totals would occur only if the can size were smaller than 16 liters, which is not optimal.53: Too large and inconsistent with the HCF-based calculation.

Common Pitfalls:
Using the LCM instead of the HCF when choosing can capacity.Forgetting that each drink must be packed separately with no mixing.Not summing the cans across all types of drinks when computing the final count.

Final Answer:
37