This is from a map found on the net:
Ypu can download it from https://www.flickriver.com/photos/124446949@N06/49078963546/
Otherwise you can refer to the cropped portions below.
The blue color indicates the IMR and the orange indicates the GIPR.
More basic history can be seen here:
The IMR was short-lived and existed only from 1885 to 1900 when it was absorbed by the GIPR. This particular map seems to be from the 1890s.
The station presently known as Bina was then known as Etawah or Itawa. Note the other old spellings such as Cawnpoor.
We can also see that the Agra-Mathura-Delhi line was not built yet. But one could go from Agra to Tundla and then to Delhi. Indeed, during the 1890s the GIP trains from Bombay to Delhi did follow this route.
And the BBCIR had not advanced much from Baroda towards Delhi. But it was also a regular practice for travelers from Bombay to Delhi to travel to Ahmedabad and then by MG to Delhi.
This box item from the IMR map has some points of interest:
It lists out the lines which existed then, including “Etawah” to Saugor, i.e. Bina to Saugor, though the extension to Katni was completed later.
The “Comparison of Distances” provides insight into the rivalry of different companies connecting the same pairs of cities. In later years the BBCI and GIP kept trying to show that their services between Bombay and Delhi/Punjab were better. This ended only when the railways were regrouped to form the WR, CR etc in the early 1950s.
Here we see that the IMR route from Bombay to Kanpur was shortest, :
1. Via Jhansi-Kanpur 830 miles (1336 km) which is the standard route today
2. Via Itarsi-Jabalpur-Allahabad-Kanpur 964 miles (1552 km)
3. Via Baroda, Ahmedabad-Delhi by MG, Delhi-Kanpur 1006 miles (1620 km)
And similarly for Bombay to Agra:
1. Via Jhansi-Agra 830* miles (1336 km) which is the standard route today
* So Jhansi-Agra and Jhansi-Kanpur are the same distance?
2. Via Itarsi-Jabalpur-Allahabad-Tundla-Agra 1123 miles (1808 km)
3. Via Baroda, Ahmedabad-Bandikui-Agra by MG 849 miles (1367 km)
Once the BBCIR got going and completed the Baroda-Mathura section by around 1910, they clearly had a shorter route between Bombay and Delhi.
The GIPR and EIR met at Jabalpur (Jubbulpore in those days). By the 1920s the Allahabad-Jabalpur section was transferred to the GIPR.
Some jokes from those days:
GIP stood for “Great Improvement Possible”
BBCI stood for “Beastly, Bad and Cannot Improve”
Then there were “Bribes Never Refused”, “Mails Slowly Moving” and “Sambar Idli Railway” which you should be able to guess.
However, the EIR escaped these nicknames.