Here's how to solve this problem:

• Understanding the Concepts

  • Backsight (BS): A reading taken on a point of known elevation (in this case, the benchmark).
  • Reduced Level (RL): The elevation of a point above a datum (reference point).
  • Inverse Staff Reading: When measuring upwards from an instrument, the staff is held upside down. This is common in tunnels or under bridges.

• Calculations

  1. Height of Instrument (HI): This is the elevation of the line of sight of the leveling instrument.

     HI = RL of Benchmark + BS

     HI = 100.00 m + 3.25 m = 103.25 m

  2. RL of Roof Station: Since the staff is held upside down, the reading needs to be added to the HI.

     RL of Roof Station = HI + Inverse Staff Reading

     RL of Roof Station = 103.25 m + 1.25 m = 104.50 m

• Answer

  The RL of the roof station is 104.50 m.

This value fits between 104 and 105, as requested.