To solve this problem, we can use the concept of relative speed.
Let's assume the speed of the train from Calcutta to Mumbai is (x) km/h, and the speed of the train from Mumbai to Calcutta is (y) km/h.
The distance between Calcutta and Nagpur is 700 km, and the distance between Nagpur and Mumbai is 900 km (1600 km - 700 km).
We can calculate the time taken by each train to reach Nagpur using the formula: time = distance / speed.
For the train from Calcutta to Mumbai:
Time taken = 700 km / (x) km/h
For the train from Mumbai to Calcutta:
Time taken = 900 km / (y) km/h
Since both trains start at the same time, they will meet at Nagpur when they have traveled for the same amount of time.
Setting the two equations equal to each other:
700 / (x) = 900 / (y)
Cross-multiplying, we get:
700y = 900x
Simplifying, we get:
(\frac{x}{y} = \frac{700}{900})
To find the ratio of the speeds, we need to simplify the equation further. We can divide both sides by 100:
(\frac{x}{y} = \frac{7}{9})
So, the ratio of the speeds of the trains is 7:9.
The correct answer is option D) 9:7.