The correct answer to the analogy "Sikkim : Gangtok :: Manipur : ?" is option B) Imphal.

To understand this analogy, let's break it down into its components:

Sikkim is a state in northeastern India, known for its natural beauty and rich cultural heritage. Gangtok, on the other hand, is the capital city of Sikkim. It is a popular tourist destination and serves as the administrative, cultural, and commercial center of the state.

Now, let's look at Manipur. Manipur is another state in northeastern India, situated near Sikkim. It is also known for its scenic landscapes, diverse culture, and historical significance. So, the analogy is asking for the capital city of Manipur, just like Gangtok is the capital city of Sikkim.

Hence, the correct answer is option B) Imphal. Imphal is the capital city of Manipur and plays a significant role in the state's administration, economy, and culture. It is a bustling city with historical sites, museums, and markets, attracting both tourists and locals alike.

In conclusion, the analogy "Sikkim : Gangtok :: Manipur : ?" is based on the relationship between a state and its capital city. Sikkim is the state, and Gangtok is its capital. Similarly, Manipur is the state, and Imphal is its capital.