Levelling data: Q BS=−3.45 RL=150 (BM, inverted); R IS=2.60; S BS=1.60 FS=2.25 (CP); T IS=1.85; U BS=2.15 FS=1.70 (CP); V FS=−2.35. Which option is INCORRECT?
📚 Detailed Explanation: INCORRECT Option — RL of Station U is 144.20 m, Not 142.35 m
Setup 1 (covers Q, R, S):
HI1 = RL(Q) + BS(Q) = 150 + (-3.45) = 146.55 m ← matches option D ✓
RL(R) = HI1 – IS(R) = 146.55 – 2.60 = 143.95 m
RL(S) = HI1 – FS(S) = 146.55 – 2.25 = 144.30 m ← matches option B ✓
[S is Change Point]
Setup 2 (covers S, T, U):
HI2 = RL(S) + BS(S) = 144.30 + 1.60 = 145.90 m ← HI for readings at T: matches option A ✓
RL(T) = HI2 – IS(T) = 145.90 – 1.85 = 144.05 m
RL(U) = HI2 – FS(U) = 145.90 – 1.70 = 144.20 m ← NOT 142.35 m → option C is INCORRECT ✓
Setup 3 (covers U, V):
HI3 = RL(U) + BS(U) = 144.20 + 2.15 = 146.35 m
RL(V) = HI3 – FS(V) = 146.35 – (-2.35) = 148.70 m (V has inverted FS)
Verification of All Options
| Option | Claim | Calculated Value | Verdict |
|---|---|---|---|
| A | HI at Station T = 145.90 m | HI2 = 145.90 m ✓ | ✓ Correct |
| B | RL of S = 144.30 m | RL(S) = 144.30 m ✓ | ✓ Correct |
| C | RL of U = 142.35 m | RL(U) = 144.20 m ✗ | ✗ INCORRECT — Answer |
| D | HI at Station R = 146.55 m | HI1 = 146.55 m ✓ | ✓ Correct |
- Inverted BS at BM: RL + (−BS) gives a lower HI than the BM elevation.
- RL(U) = 145.90 − 1.70 = 144.20 m, not 142.35 m — option C is INCORRECT.
- The error in option C is 144.20 − 142.35 = 1.85 m, which equals IS at T — likely a computational mix-up.