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`        A man has a physical balance and a stone of mass 40 kg . He divides the stone into four  parts A,B,C,D of mass a kg , b kg , c kg , d kg respectively , such that using A,B,C,D he can measure any specific integral  mass from 1 kg to 40 kg . Find the mass of all four parts .i.e., a kg , b kg , c kg , d kg ? {The answer to this question is 1 kg , 3 kg , 9 kg , 27 kg .Explanation: if that man is asked to measure 2kg he will keep 3kg on one of the palm of physical balance and 1 kg on the other . So the net weight being (3-1) kg = 2 kg. For measuring 4 kg he will keep he will use 3kg and 1kg . For measuring 5 kg he will keep 9 kg on one side and 4 kg ( 3kg+1kg ) on the other side . In the same way , he can measure any of the following weights : 1 kg , 2kg , 3kg , ............ 39 kg , 40 kg using those four parts .  }.   I found this question in a magazine .Though I was able to solve this question using heat and trial method , I did not understand how to solve this question mathematically using algebra or some other convenient mathematical method. Can anyone please solve his question mathematically`
6 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear student,
I also tried this problem and devoted significant time on this and found out that hit and trial is the best way to solve questions like this..

All the best.
Win exciting gifts by                                                                                                  answering     the           questions    on                     Discussion                Forum.      So           help                          discuss            any                        query      on                    askiitians          forum     and               become     an             Elite                      Expert           League                           askiitian.

Sagar Singh
B.Tech, IIT Delhi

```
6 years ago
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