Did British Empire and Bangladesh exist in the same era?

Yes, the two civilizations both existed around 1971 CE.

Which lasted longer, British Empire or Bangladesh?

British Empire lasted longer (414 years).

British Empire: Avrupa; Bangladesh: Asya

British Empire (1583 CE – 1997 CE) and Bangladesh (1971 CE – present) lived in the same era.

The empire with the most extensive territory in history. It was referred to as "the empire on which the sun never sets."

People's Republic of Bangladesh · Asia

Did British Empire and Bangladesh exist in the same era?: Yes, the two civilizations both existed around 1971 CE.
Which lasted longer, British Empire or Bangladesh?: British Empire lasted longer (414 years).
Which regions did British Empire and Bangladesh rule?: British Empire: Avrupa; Bangladesh: Asya