Instructions:
This answer to this question can be broken down into two parts.
Who won the battle and what was mentioned in the treaty that was signed.
What powers did the East India Company get after the Battle of Buxar.
Solution:
The Britishers won the battle and signed a treaty with Siraj - ud - Daulah and Shah Alam II in 1765 AD. According to the treaty, Awadh will be given back to Siraj - ud - Daulah for Rs. 50 lakhs. In return, the East India Company got the right to trade without paying taxes.
Mughal emperor Shah Alam II was allowed to stay on the throne and was given the areas of Kara and Allahabad to rule. In return, he gave the Diwani of Bengal to the East India Company. This means they got special powers to administer land and organize revenue.