Levelling Computation – RL by Height of Instrument Method with Given BS and FS A back sight of 2.685 m is taken on a benchmark of RL 500.000 m. A fore sight of 1.345 m is then taken on a point. Compute the reduced level (RL) of the point.

Introduction / Context:
The Height of Instrument (HI) method in levelling computes RLs by first establishing the instrument height above a known benchmark and then subtracting staff readings at other points. It is fast and reliable when BS and FS are correctly identified and the level is properly adjusted.

Given Data / Assumptions:

• Benchmark RL = 500.000 m.
• Back sight (BS) on BM = 2.685 m.
• Fore sight (FS) on point = 1.345 m.
• Instrument is correctly levelled; no collimation error.

Concept / Approach:

Using HI method: HI = RL_BM + BS. Then RL_point = HI − FS. Careful sign discipline (add BS, subtract FS) avoids frequent mistakes. Units remain in metres throughout.

Step-by-Step Solution:

Verification / Alternative check:

Perform the standard arithmetic check after a full run: ΣBS − ΣFS should equal RL_last − RL_first. With one setup, 2.685 − 1.345 = 1.340 which matches 501.340 − 500.000 = 1.340.

Why Other Options Are Wrong:

502.685 m is HI, not the point RL; 501.345 m is a rounding/typo; 504.030 m is impossible; 502.585 m incorrectly subtracts 0.100 m.

Common Pitfalls:

Subtracting BS instead of adding; mixing IS with FS; transposing digits when copying field-book entries.

Final Answer:

501.340 m