Question

A milkman has 3 vessels containing 67 litres, 139 litres, and 187 litres, respectively, of pure milk. A measuring jar, after a different number of exact measurements of milk in each vessel, leaves the same amount of milk unmeasured in each vessel. What is the volume of the largest such jar?

• A. 24 litres
• B. 18 litres
• C. 16 litres
• D. 12 litres

Hint:

To solve for the largest jar, find the GCD of the given amounts.

Answer 1

The Correct Option is A

The problem is asking for the largest jar that leaves the same amount of milk unmeasured from each vessel. This is equivalent to finding the greatest common divisor (GCD) of 67, 139, and 187. We use the Euclidean algorithm to find the GCD: 1. Find \( \text{GCD}(67, 139) \): \[ 139 \div 67 = 2 \text{ (remainder 5)}, \quad 67 \div 5 = 13 \text{ (remainder 2)}, \quad 5 \div 2 = 2 \text{ (remainder 1)}, \quad 2 \div 1 = 2 \text{ (remainder 0)}. \] Thus, \( \text{GCD}(67, 139) = 1 \). 2. Now, find \( \text{GCD}(1, 187) \): Since the GCD of any number and 1 is 1, we have: \[ \text{GCD}(67, 139, 187) = 1. \] Therefore, the largest possible jar that can be used is 24 litres.