The levelling is carried out between two stations P and Q separated by 1000 m. The Back Sight (BS) reading is noted as 0.70 m on station P, whose BM is 240.00 m. Next, the Fore Sight (FS) reading is taken on an intermediate point and the value is 1.25 m. Then the instrument is shifted to a new location and BS is taken on intermediate point as 0.85 m. Finally, the FS reading is taken on station Q as 1.10 m. What is the Reduced Level of Q?
- A239.20 mCorrect
- B240.80 m
- C241.25 m
- D241.80 m
Solution
Concept
RL of a point = Height of Instrument - Fore Sight; HI = RL + Back Sight
Formula
HI = RL + BS; RL = HI - FS; RLQ = RLP + ΣBS - ΣFS
Step-by-step solution
1. HI at first setup = 240.00 + 0.70 = 240.70 m 2. RL of change point = 240.70 - 1.25 = 239.45 m 3. HI at second setup = 239.45 + 0.85 = 240.30 m 4. RL of Q = 240.30 - 1.10 = 239.20 m 5. Check: ΣBS - ΣFS = 1.55 - 2.35 = -0.80 m, so 240.00 - 0.80 = 239.20 m
Explanation
The point where the instrument is shifted is a change point. Add each BS to get the HI, and subtract each FS to get the RL. Q is 0.80 m lower than P, so RL of Q is 239.20 m.
Why the other options are wrong
B: adds 0.80 m instead of subtracting it. C and D: wrong combination of BS and FS readings.
Shortcut
RLQ = 240.00 + (0.70 + 0.85) - (1.25 + 1.10) = 239.20 m
Common mistake
Adding FS or subtracting BS, which gives 240.80 m.
Correct answer: A) 239.20 m