Latest Others Aptitude Question SOLUTION: Every day in his business, a merchant had to weigh amounts from one pound to one hundred and twenty-one pounds, to the nearest pound. To do this, what is the minimum number of weig

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Every day in his business, a merchant had to weigh amounts from one pound to one hundred and twenty-one pounds, to the nearest pound. To do this, what is the minimum number of weights he needs and how heavy should each weight be?

Asked In Others phani (11 years ago)

Solved chaitanya Read Solution (2)

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chaitanya  (11 years ago)

The minimum number of weights required is five and these should weigh 1, 3, 9, 27 and 81 pounds.

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chaitanya  (11 years ago)

The solution wud be in powers of 3 ..ie 3^0 , 3^! , 3^2 ,3^3 , 3^4 ..we dont require the 6th weight nor we can have less than 5 weights .

we can obtain..
1 itself
3-1=2
3 itself
3+1=4
9-3-1=5
9-3=6
9-3+1=7
9-1=8
9+1=10
9+3-1=11
9+3=12
9+3+1=13
27-9-3-1=14
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27+9+3+1=40
81-27-9-3-1=41
81-27-9-3 =42
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81+27+9+3=120
So this way we effectively used only 5 weightz viz, 1,3,9,27,81

Now suppose if we had to weigh in such a weigh that we can only add weight and never reduce weight ,
then ,
the weights required wud be in the powers of 2
like
1,2,4,8,16,32 .....and so on.....

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