India and Bangladesh had a dispute over water rights to the ____ after the Farakka Dam was constructed.

The correct answer to this question is the Ganges River. 
The Farakka Dam, which is also known as the Farakka Barrage, was built across the Ganges
River and was completed in 1975.  The building of this dam has caused issues that have
led to major disputes between India and Bangladesh.

The
point of the Farakka Dam was to divert water from the Ganges into another river during
the dry season.  By diverting the water, India has been accused of contributing to a
number of problems in Bangladesh, one of which desertification.