Q.9 There are eight bags of rice looking alike, seven of which have equal weight and one is slightly
heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number
of weighings required to identify the heavier bag is
(A) 2 (B) 3 (C) 4 (D) 8
Minimum Number of Weighings to Identify a Heavier Bag
Weighing balance problems are classic logical reasoning questions that frequently
appear in competitive exams. This problem focuses on finding the
minimum number of weighings required to identify a
slightly heavier bag among identical-looking bags.
Key Logical Idea
Each weighing should divide the remaining possibilities into
as equal groups as possible to eliminate the maximum number of cases.
Step-by-Step Solution
Step 1: First Weighing
Divide the 8 bags into two groups of 4 bags each and weigh them.
The heavier side contains the heavier bag.
Remaining possibilities = 4 bags
Step 2: Second Weighing
From the heavier group of 4 bags, divide them into two groups of 2 bags each.
Weigh the two groups against each other.
The heavier side contains the heavier bag.
Remaining possibilities = 2 bags
Step 3: Third Weighing
Weigh the remaining 2 bags against each other.
The heavier one is immediately identified.
Logical Calculation
Each weighing gives 2 possible outcomes.
Maximum distinguishable cases with n weighings = 2n
To identify 1 bag out of 8:
2n ≥ 8 → n = 3
Final Answer
The minimum number of weighings required is 3.
