Given levelling data: P BS=1.265 (BM); Q IS=1.415; R IS=1.715; S BS=2.330 FS=2.165 (CP); T FS=2.930. RL of P = 550.50 m. Which statement is INCORRECT?
Correct Answer: A. Station R is at a higher elevation than Station P
📚 Detailed Explanation: INCORRECT Statement — Station R is NOT Higher than Station P
This question asks for the INCORRECT option. All four options are claims about relative elevations. After calculating all RLs, option A is false: R (550.05 m) is actually LOWER than P (550.50 m).
Step-by-Step RL Calculation
Given: RL of P = 550.50 m
Setup 1 (instrument covers P, Q, R, S):
HI1 = RL(P) + BS(P) = 550.50 + 1.265 = 551.765 m
RL(Q) = HI1 – IS(Q) = 551.765 – 1.415 = 550.350 m
RL(R) = HI1 – IS(R) = 551.765 – 1.715 = 550.050 m
RL(S) = HI1 – FS(S) = 551.765 – 2.165 = 549.600 m [S is Change Point]
Setup 2 (instrument covers S onwards):
HI2 = RL(S) + BS(S) = 549.600 + 2.330 = 551.930 m
RL(T) = HI2 – FS(T) = 551.930 – 2.930 = 549.000 m
Summary of Calculated RLs
| Station | RL (m) |
|---|---|
| P (BM) | 550.500 |
| Q | 550.350 |
| R | 550.050 |
| S (CP) | 549.600 |
| T | 549.000 |
Checking Each Option
| Option | Claim | Actual Comparison | Verdict |
|---|---|---|---|
| A | R > P | 550.05 < 550.50 → R is LOWER than P | ✗ INCORRECT — Answer |
| B | S < P | 549.60 < 550.50 ✓ | ✓ Correct |
| C | S < Q | 549.60 < 550.35 ✓ | ✓ Correct |
| D | R > T | 550.05 > 549.00 ✓ | ✓ Correct |
- RL(R) = 550.05 m < RL(P) = 550.50 m → R is lower than P, not higher.
- Option A is the INCORRECT statement.
- Arithmetic check: ΣBS − ΣFS = (1.265 + 2.330) − (2.165 + 2.930) = 3.595 − 5.095 = −1.500; Last RL − First RL = 549.000 − 550.500 = −1.500 ✓