Question

how did the partition of India lead to several problems

Answer 1

http://wiki.answers.com/Q/Why_did_the_partitioning_of_India_cause_violence

Answer 2

A family has been living in the same town for generations. Then one day a person decides that all of the family should migrate / walk to another town/city in another country. in addition the family cannot come back or visit the place where they have been living for generations. They are asked to leave all that they possess,which they cannot carry with them to new country like ancestral houses and other possessions. This family does not even know the exact place they are supposed to go to, what will become of them once they reach there, let alone how will they get there or will they ever be able to get to the new city or not.
That is what was faced by the people of India when the partition happened. One side blamed the other for the partition - the reason because of which they had to leave their hometowns, friends and even families. There was so much chaos and emotions ran high at this time of great stress and uncertainty. As the partition was based on religion. The religion which was the cause of partition, the people belonging to this religion were thought to be self-centered villains who were short-sighted and wished to break - away. Both sides blamed the other and took their frustration out on the other religion for the hardships they had to put up with. This was the cause of violence .