A jug can hold 9 liters and a mug can hold 4 liters. A bottle contains 48 liters. What is the minimum total number of containers (jugs and mugs) that can be used to fill the bottle exactly?

medium MCQ 2 marks Class 3 · Mathematics · Jugs and Mugs

Answer

4 jugs and 3 mugs

The correct answer is 4 jugs and 3 mugs — Thus the least number of containers is 7, obtained with $4$ jugs and $3$ mugs.

Step-by-step solution

Set up $9 j + 4 m = 48$ with $j, m \geq 0$ integers.
Test successive values of $j$ .
$j = 0 \Rightarrow m = 12$ (12 containers).
$j = 1 \Rightarrow 9 + 4 m = 48 \Rightarrow 4 m = 39$ (no integer).
$j = 2 \Rightarrow 18 + 4 m = 48 \Rightarrow 4 m = 30$ (no integer).
$j = 3 \Rightarrow 27 + 4 m = 48 \Rightarrow 4 m = 21$ (no integer).
$j = 4 \Rightarrow 36 + 4 m = 48 \Rightarrow 4 m = 12 \Rightarrow m = 3$ (7 containers).
$j = 5$ would give $45 + 4 m > 48$ .
Thus the least number of containers is 7, obtained with $4$ jugs and $3$ mugs.

Common mistake: ignoring that

m

must be an integer

Concept tested: minimum total containers using two capacities