GATE 2026 CE (CE1) – Question 62
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*).
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Correct answer: 5
Explanation
The sixth reading is on a change point, and the seventh reading is the back sight on the same point from the new position. So there are 9 stations and 8 intervals, a distance of $8 \times 20 = 160$ m. In the first setup the level falls by $4.850 - 0.385 = 4.465$ m, because larger staff readings mean lower ground. In the second setup it falls by $4.580 - 1.045 = 3.535$ m. The total fall is $8.000$ m over 160 m, so the gradient is $\frac{8}{160} = 5\%$ (downward).