Question

A merchant had a 40 kg measuring weight that broke into four pieces as the result of a fall. When the pieces were subsequently weighed, it was found that the weight of each piece was a whole number of kilograms and that the four pieces could be used to weigh every integral weight between 1 and 40 kg. What were the weight of the pieces.


30 points!!!

Answer 1

1 kg weight for aal 1to 40 broken piece

Answer 2

Dear student,

Please find below the solution to the asked query:

We have to find weights of the 4 different pieces that can eb broken from a total wieght of 40 kg so that we can measure weight between 1 to 40.These four weights can be 1, 3, 9 and 27 kg.Then the weights from 1 to 40 can be measured as follows:   1 (given)   2=3−1   3 (given)   4=3+1   5=9−3−1   6=9−3   7=9−3−1   8=9−1   9  (given)  10=9+1  11=9+3−1  12=9+3  13=9+3+1    ⋮    ⋮    ⋮  38=27+9+3−1  39=27+9+3  40=27+9+3+1Thus the required weights are,  1, 3, 9 and 27 kg  

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