GATE ECE 2012 | Question: 63

Question

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. $8$

Answer 1

Divide the $8$ bags into $3$ parts. $3,3\space and \space 2$. Weigh the two $3,3$ Bags pair

Case $1$: if both are equal , then go to 2 remaining bag and weight them, we will get the heavier bag.

Case $2$: If one side is heavier than other side, take any 2 bags from it and weight them, if they are equal the left out bag that is the 3rd bag is the heavier bag else one of them would have been heavier.

Hence, Answer is option $\boxed{A.\space2}$

Answer 2

Option A 

Step 1 place 3 , 3 bags on balance  - Case 1 :  if the weight is equal then this 6 bags are with same weight .

                                                            Case 2: if the weight is not equal then the heavier sids bags have that heavier bag

Step 2 place reamin 2 bags from step 1 case 1: from that 2 one will be fixed  heavier cause 6 bags are with same weight .

Step 2 place reamin 2 bags from step 1 case 2: Form heavier sids bags  any 2 are placed on the balance if same the not place is heavier ... if not then the heavier side bag is heavier ..

 

the minimum number of weighings required to identify the heavier bag is 2