How to Find Faulty Machine

How to Find Faulty Machine ?

We have 10 Machines that produce Chocolate, each weighing 100 grams.  

One of the machines, however, produces chocolate weighing 90 grams only. 

We are allowed only one weighing and need to determine which machine is faulty.

you have to find faulty machine in only once try.

Machine :  [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

Bucket    :  [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

 

 

 

Solutions:

Pick 1   Chocolate From Bucket - 1

Pick 2   Chocolate From Bucket - 2

Pick 3   Chocolate From Bucket - 3

Pick 4   Chocolate From Bucket - 4

Pick 5   Chocolate From Bucket - 5

Pick 6   Chocolate From Bucket - 6

Pick 7   Chocolate From Bucket  -7

Pick 8   Chocolate From Bucket  - 8

Pick 9   Chocolate From Bucket  - 9

Pick 10 Chocolate From Bucket  - 10      
 

If All Machine are Perfect then Weight should be

Total Weight : (1 * 100) + (2 * 100) + (3 * 100) + (4 * 100) + (5 * 100) +

(6 * 100) + (7 * 100) + (8 * 100) + (9 * 100) + (10 * 100)

= 5500

 But Here 1 Machine is Faulty so Weight will be Less then 5500.

Suppose Weight is X;

you will find faulty machine No by below equation :

 

(5500 - X) / 10

will gives you faulty machine No.

lets take an example.

If 6th Machine is Faulty then 

Weight will be:

(1 * 100) + (2 * 100) + (3 * 100) + (4 * 100) + (5 * 100) +

(6 * 90) + (7 * 100) + (8 * 100) + (9 * 100) + (10 * 100)

= 5440

then 

 

= (5500 - 5440) /10 

= 60 / 10 

= 6th Machine is faulty.

as Per this you will get faulty Machine No by Only Once Weighing in One Try.