Problem Of Weight.

A baker made two big cakes , which were identical , that is both of them had the same dimensions , same colour and same weight .
He wanted to know the weight of each of them . But he had only a 200 gm. and a 50 gm weights with him .
He had the facility to cut the cakes exactly into half , quarter , 1/8 ,1/16 ..etc.
Hence he placed one of the cakes ,in full , on one pan , say, the first pan , of the balance and on the other pan , say , the second pan , he placed half of the other cake and the weights of 250 gms.
The first pan , the pan with the full cake , went down.
Then he added a quarter of the cake, from the remaining half cake , to the second pan , ( with half of the cake and 250 gms weight ).
Even then the first pan went down.
He then added 1/8 of the cake to the second pan .
Now the balance showed neutral.
What was the weight of one full cake ?

 

1).Pan no. 1 has one full cake.
The second cake is on the table. Cut it into two halves.
Place one half along with 250 gms weight on the second pan.
What remains on the table ?
Half of the second cake .
Is it OK ?
First pan goes down.
2). Cut the half-cake on the table into two .
Now you will have two quarter cakes
= 1/4 + 1/4 cakes on the table.
Take one of them and add it to Pan no.2 .
What remains on the table is 1/4 of a full cake.
Is it clear ?
Even now Pan no. 1 goes down.
3). Cut the 1/4 cake on the table into two halves = 1/8 + 1/8 of a full cake.
Take of them and add it to the second pan.
What remains on the table is 1/8 of a full cake.
Understood ?
Now the two pans balance each other.
It means the 250 gms weight is replacing the weight of the 1/8 cake on the table.
Up to this is it clear ?
That is 1/8 cake weighs 250 gms.
Hence one full cake will weigh 250 × 8 =
2000 gms = 2 kg.
Am I understood ?
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Thank you for your response and encouragement .