Explanation:

- I. R reached his destination in 5 hours and P reached his destination in 3 hours: This statement can be true if the speeds and distances for R and P allow for these times. It does not conflict with any given conditions and can be independently true.

- II. R reached his destination in 3 hours and P reached his destination in 5 hours: Similar to the first statement, this can also be true if the conditions of speed and distance allow it.

- III. If the distance increased by 90 km, and the speed of P is 1/5th of the speed of Q, then R reached the new distance at 3:30 p.m.: Without specific data about R's original time or speed, it's unclear when R would arrive, making this statement more speculative without further context.

- Based on possibilities, both statements I and II can independently be true, given flexible speed and distance values.

Option: 4, Only I and II is plausible because either scenario is possible without more detailed information.