Explanation:

- "While travelling to Bangalore I ran _____ a very old friend of mine." The sentence requires a phrase or word that indicates encountering someone by chance.

- Option 1, "across": "Ran across" is a correct phrase often used to mean meeting or finding someone or something by chance. It fits perfectly here.

- Option 2, "up": "Ran up" usually indicates moving quickly towards someone or something, not suitable for conveying a chance encounter.

- Option 3, "against": "Ran against" might imply encountering opposition or conflict, not typically used for meeting people.

- Option 4, "into": "Ran into" is a common expression used to describe meeting someone unexpectedly. It's particularly well-suited for this context.