Question

A king asks a learned man to visit his palace. The man says I will come any day next month. But give me gold in gms equal to the date on which I come. The king asks the jeweler to make rings of 1 to 31 gms. The jeweler was smart and makes only 5 rings. What are the weights of those rings?

Answer 1

You must have heard about binary digits. Just by using powers of 2, any number can be represented. This is a problem of binary digit calculation. The jeweler knew binary digits could represent anything. So he made rings of weight of 1 g, 2 g, 4 g, 8 g and 16 g. And every number below 32 can be represented as the sum of the weights of these rings.

Answer 2

Seems like the jeweller was more intelligent than king and that's why he made 5 rings and helped king save on some budget! :D 

The Jeweller was knew Binary Counting  and with 5 digits it seems like all the 31 days can be counted
as $2^{5}$ =32

so jeweller will make rings of 1 gram ,2 gram , 4 gram , 8 gram ,and 16 gram
all the day can be achieved using this 
For if the learned man comes on 30th
king can give 16 gram, 8 gram ,4 gram and 2 gram ring
I hope it helps!