When India and Pakistan were partitioned, Muslims were in a majority in east Bengal whereas Hindus were in a majority in west Bengal. What is the historical reason behind this demographic statistic?
In Western Part of Bengal Shri Chaitanaya Mahaprabhu started a religious movement in the beginning of starting of Muslim age, which did not much affect the Eastern parts. As a result less number of Hindus in Western part converted to Islam or again converted back to Hinduism. It did not happen in Eastern Bengal where majority of Hindu population had converted to Islam. So in West Bengal most of the people were Hindu and In East Bengal most of them were Muslim.
Division of Bengal did not properly depend on religion. Before division a large portion of East Bengal was of Hindu majority. So one shall do a mistake if he thinks that there were a few Hindus in Eastern and a few Muslims were living in Western regions.
The assumption may not be correct mathematically.
This is discussed in vivid detail in the book "The Spoils of Partition: Bengal and India".
It was not that the West was predominantly Hindu by a large margin or the east conversely Muslim. But the politicians who wanted to have a more homogenous and therefore more controllable state did their calculation to determine which districts had more than 51% Hindus. These they proposed as a part of India. The gross error was that it did not account for the 49% other religious group.
Post partition this remaining minority group on both sides of the border had to face the brunt of communal violence, and therefore mass migrations took place. This increased the polarization.
However, West Bengal still has a huge Muslim population.
There does not have to be an identifiable reason for these things at all. But it is possible that east Bengal was more Muslim than west Bengal because the Mamluk sultanate and the Khilji dynasty both ruled over more easterly parts of Bengal. The Khilji dynasty was also effective in converting people to Islam.
Although these dynasties probably didn't create a majority of Muslims in the area, a slightly higher percentage together with other events, or just chance, can have been one reason that eastern Bengal ended up with a clear Muslim majorty.