Civil Engineering > GATE 2026 SET-1 > Levelling
The following consecutive readings (in m) were taken with a dumpy level and a levelling staff at a common interval of 20 m:
0.385; 1.030; 1.925; 2.825; 3.730; 4.850; 1.045; 2.005; 3.330; 4.580
The dumpy level was shifted after taking the sixth reading.
The gradient (in %) of the ground between the first and the last location of the reading is ______ (in integer).
0.385; 1.030; 1.925; 2.825; 3.730; 4.850; 1.045; 2.005; 3.330; 4.580
The dumpy level was shifted after taking the sixth reading.
The gradient (in %) of the ground between the first and the last location of the reading is ______ (in integer).
Correct : -4
The 10 staff readings are taken at 10 consecutive points spaced 20 m apart. The instrument is shifted after the 6th reading, with reading 6 serving as the foresight at the change point and reading 7 as the backsight at the same change point.
Setting RL of point 1 = 0 (arbitrary datum):
HI₁ = 0 + 0.385 = 0.385 m
RL₂ = −0.645 m, RL₃ = −1.540 m, RL₄ = −2.440 m, RL₅ = −3.345 m, RL₆ = −4.465 m
After instrument shift: HI₂ = −4.465 + 1.045 = −3.420 m
RL₈ = −5.425 m, RL₉ = −6.750 m, RL₁₀ = −8.000 m
Total fall = 8.000 m over 9 intervals × 20 m = 180 m
Gradient = −8.000/180 × 100 = −4.44%
Correct answer: −4 (rounded to integer)
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