The elevation of a benchmark is +100.00. The backsight is taken on a staff held vertically is 2.30 m. If the foresight taken as a point of ‘A’ is + 2.45 m. then R.L. of ‘A’ is
- A100.15
- B99.85Correct
- C102.45
- D102.3
Solution
Concept
Computation of reduced level in levelling
Formula
RL = RLBM + BS - FS
Step-by-step solution
1. Height of Instrument (HI) = Reduced Level of Benchmark + Backsight (BS) = 100.00 m + 2.30 m = 102.30 m. 2. Reduced Level (R.L.) of point A = HI - Foresight (FS) = 102.30 m - 2.45 m. 3. R.L. of point A = 99.85 m. Answer: B
Explanation
The Height of Instrument is calculated by adding the backsight reading to the benchmark elevation, resulting in 100.00 m plus 2.30 m to equal 102.30 m. The Reduced Level of point A is then determined by subtracting the foresight reading from the Height of Instrument, giving 102.30 m minus 2.45 m. This yields a final Reduced Level of 99.85 m for point A.
Why the other options are wrong
A) 100.15 is the result of arithmetic errors in combining backsight and foresight values. C) 102.45 incorrectly adds the foresight value to the Height of Instrument. D) 102.30 is the Height of Instrument (100.00 + 2.30), not the final Reduced Level of point A.
Shortcut
RL of Point = Benchmark + Backsight - Foresight (100.00 + 2.30 - 2.45 = 99.85).
Common mistake
Adding foresight instead of subtracting it from the Height of Instrument when calculating Reduced Level.
Correct answer: B) 99.85