Almost everyone in India knows this by heart — Britishers ruled India for 200 years. We got rid of them in 1947 and Robert Clive won the battle of Plassey in 1757, so that is a neat 190 years. What’s the problem?
The problem is that Robert Clive only won over Bengal in 1757, which was a (major) province/kingdom in India. Here is how British rule in India looked like in 1805
Some other dates are pertinent: Mysore state was won over in 1799, Marathas were finally defeated in 1818, and Sikh empire was finally defeated only by 1849. There might be other smaller kingdoms that fought even later but these three were major powers of the sub-continent.
It seems that we can with better accuracy say that the British took nearly 100 years to conquer India and then ruled India for 100 years. In fact, the suppression of the 1857 revolt is when the rule really consolidated and officially passed to the British Empire. It was with the East India Company before that. The Company was one of the great powers on the Indian sub-continent but surely not its ruler.
So why is this 200 years interpretation the popular one?
Historical narrative is often subjected to current political constraints. The slaves of a foreign power for 200 years narrative seeks to build modern nationalism. As Benedict Anderson has found, shame is an important foundation of nationalism. Would a narrative saying Britishers ruled India for 90 years have the same impact in coalescing Indians with their primary loyalties to local communities or kingdoms into modern nationalistic Indian? The only power that could contradict the narrative — the British — would never do it for the opposite reason — pride. Rulers of India for 200 years? Sure, we will take that on our collective resumes.
In the same vein, there is a new narrative of 1200 years of slavery that has been mentioned by the PM himself on multiple occassions. Now that we understand the underlying mechanism, this is similar to building a sense of shame that can create Hindu nationalism. Kashmiri separatists try the same with a narrative of foreign rule since 1586 (when Akbar invaded Kashmir) to instill the feelings of Kashmiri nationalism.