GATE 2024 CE (CE2) – Question 65

Geomatics Engineering · Distance and angle measurement, levelling, traversing, triangulation, total station · 2 marks · Numerical answer

Differential levelling is carried out from point P (BM: +200.000 m) to point R. The readings taken are given in the table.

Points	Back Sight	Fore Sight	Remarks
P	(−)2.050		BM: +200.000 m
Q	1.050	0.950	Q is a change point
R		(−)1.655

Reduced Level (in meters) of the point R is _____ (rounded off to 3 decimal places).

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Correct answer: 198.706 to 200.704

Explanation

The back sight at P is negative, which means that the staff is held inverted and the reading is above the instrument. The height of instrument is $200.000 + (-2.050) = 197.950$ m. The reduced level of Q is $197.950 - 0.950 = 197.000$ m. The new height of instrument is $197.000 + 1.050 = 198.050$ m. The fore sight at R is $-1.655$, so $RL_R = 198.050 - (-1.655) = 199.705$ m.