The roof of a room was considered as the BM. Inverted staff reading on this BM was 3.500 m. The staff reading of point P on the ground was 1.200 m. Find the RL of point P, if the RL of the bench mark is 100 m.
- A104.7 m
- B95.3 mCorrect
- C97.7 m
- D102.3 m
Solution
Concept
An inverted staff reading (staff held upside down on a roof or ceiling) is taken as negative in level calculations.
Formula
HI = RLBM + BS ; RLP = HI − FS (inverted reading taken as negative)
Step-by-step solution
1. The staff is inverted on the BM (roof), so BS = −3.500 m. 2. HI = RL of BM + BS = 100 + (−3.500) = 96.500 m. 3. FS on P = 1.200 m (normal staff). 4. RL of P = HI − FS = 96.500 − 1.200 = 95.300 m.
Explanation
The roof BM is above the line of sight, so the inverted reading is negative. The line of sight is 3.5 m below the BM, which gives 96.5 m. Point P is 1.2 m below the line of sight, so its RL is 95.3 m.
Why the other options are wrong
A (104.7) adds both readings. C (97.7) uses wrong signs. D (102.3) treats the inverted reading as positive and subtracts the FS.
Shortcut
RLP = 100 − 3.5 − 1.2 = 95.3 m
Common mistake
Taking the inverted staff reading as positive, which gives 102.3 m.
Correct answer: B) 95.3 m