Of Rama and Usha the latter is the more responsible. I think use of the is superfluous before competative degree more. But my book suggest that the given sentence is absolutely right. Please explain if there is any rule regarding this in English grammar.
The sentence would be correct either with or without the inclusion of the.
When the is included, the sense is that Usha is the more responsible person; or the more responsible of the two.
When the the is omitted, more simply acts to modify responsible.
Another example might be:
She is more capable.
She is the more capable (person is implied)
She is the more capable administrator.
Both constructions are correct. It depends on exactly what you want to say.