Question

how can a 40kg. of stone be divided into 4 parts so that it can be used to weigh 1kg to 40 kg.

Answer 1

Up to 40 kg:

Weights are: 1 kg, 3 kg, 9 kg, 27 kg

Like this:

You can put the weights on the other side of the balance, therefore subtracting some of the weight from the other side. Using this system the objects can be weighed thus:

1kg = 1kg
2kg = 3kg - 1kg
3kg = 3kg
...
39kg = 27kg + 9kg + 3kg
40kg = 27kg + 9kg + 3kg + 1kg

Answer 2

First of all you can measure wt. in the balance in two ways.

By putting the weight on one side and the object on the other side.By putting a higher weight or two or more weight altogether on one side and a lower weight or two or more weight s.t. the sum of those is lower than the higher weight along with the object to be measured on the other side. ( I.e. measuring by the difference between the two weights )

From my observations I have seen a similarity in these kind of problems.

Whatever the total weight. If you have to break it in pieces and then measure from that, in that case you have to find a term X s.t. 3X+1 equals the total weight of the object (in this case 40).

So here X is 13. Now write 40 in the form

13+(14+13)=40 ~ 13+27=40

Now interestingly if you can find a way to measure any weight from 1 to 13 you can measure any weight in the range 40.

If you can measure upto 13, you can measure 14 from 27 kg wt (27-13).Then you can measure any weight from 14 to 27 by putting 27 kg in one side and putting the weights in other side from 13 kg to 1 kg.

Now even you can measure 27 kg to 40 kg by putting the object on one side and putting the 27 kg combining with the other weights from 1 kg to 13 kg.

In similar way you can find how to divide the 13 kg weight in the same pattern.

Find x from 3x+1=13 I.e. x=4.

Now write 13 in the form

4+(5+4)=13 ~ 4+9=13

Similarly if you find a way to get the range of 1 to 4 kg you can measure 5 kg (9-4).

And then can measure upto 9 kg similarly by substacting and upto 13 kg in same way by addition.

To divide 4 kg in same way find x and write 4 like

1+(2+1)=4 ~ 1+3=4

Now you can see that you can find upto 4 kg by 1 and 3 kg weight.

So then we need a 9 kg wt. to measure upto 13 kg and then a 27 kg wt. to measure upto 40 kg.

hope it may help you :-)