Pakistan Defence

Hey guys. The other day I was watching a program, may be it was of Najam Sethi. The guy pointed out something very interesting.

How is it that both India and Pakistan achieved freedom at the same time but Pakistan celebrates it's independence day on 14th August while India celebrates its independence on 15th August.

Shouldn't, logically, the independence day have been same? Either 14th or 15th August but it should have been same. Whatsay you?