The correct answer is option 1, Patna. In this question, we are looking for the city or town that lies at the northern-most latitude. Latitude measures the distance north or south of the equator, with the north pole being at 90 degrees north latitude. Patna, being located in the state of Bihar in northern India, has a higher latitude compared to the other options.

Option 2, Allahabad, is also located in northern India but at a lower latitude compared to Patna. Option 3, Pachmarhi, is located in the central part of India, and option 4, Ahmedabad, is located in western India. Therefore, neither of these options is the northern-most city or town.

In conclusion, Patna is the correct answer as it lies at the northern-most latitude among the given options.