Background:
In 1686, a war broke out in Bengal between Aurangzeb, the Mughal emperor, and the English East India Company. This conflict was primarily driven by the East India Company's growing influence and control over trade in the region, which threatened the Mughal authority and revenue.

Outcome:
The outcome of the war between Aurangzeb and the English East India Company was that the company suffered heavy losses. This can be attributed to several factors:

1. Mughal Military Strength:
The Mughal Empire under Aurangzeb was a formidable military power. It had a large and well-trained army, which gave them a significant advantage over the English East India Company's smaller and less experienced military force.

2. Siege of Hugli:
During the war, Aurangzeb's forces laid siege to the English trading post of Hugli (present-day Haldia in West Bengal). The English East India Company's garrison in Hugli was outnumbered and ill-equipped to withstand the Mughal assault.

3. Capture of English Forts:
As the war progressed, the Mughal forces successfully captured several English forts, including Fort William in Calcutta. These victories further weakened the East India Company's position and limited their ability to defend their interests in Bengal.

4. Economic Impact:
The war had a significant economic impact on the English East India Company. They suffered heavy financial losses due to the disruption of their trade activities, destruction of their trading posts, and loss of valuable goods and resources.

5. Diplomatic Negotiations:
Realizing the futility of continuing the war, the English East India Company initiated diplomatic negotiations with Aurangzeb. They sought a peaceful resolution and offered to pay a large sum of money as reparations for the damages inflicted during the conflict.

6. Ceded Territories:
As a result of these negotiations, Aurangzeb agreed to a treaty known as the Treaty of Hugli in 1689. Under this treaty, the East India Company was granted permission to resume their trading activities in Bengal, albeit with certain restrictions. However, it is important to note that Hugli was not ceded to the East India Company by Aurangzeb as mentioned in option (c).

Conclusion:
In conclusion, the war between Aurangzeb and the English East India Company in Bengal resulted in heavy losses for the company. They suffered military defeats, economic setbacks, and had to negotiate a treaty to regain their trading privileges. Hence, the correct answer is option 'B' - The East India Company suffered heavy losses.