Civil Engineering > GATE 2026 SET-1 > Levelling
Locations P and Q are separated by a wide valley. The difference in levels of locations P and Q measured by a levelling instrument stationed near P is 3.0 m. The same instrument stationed near Q measures the difference in levels of locations P and Q as −1.0 m. Assume that the atmospheric refraction is same during the measurements. The true difference in levels (in m) of locations P and Q is
A
1.0
B
1.5
C
2.0
D
4.0

Correct : a

In reciprocal levelling across a wide valley, both observations are affected by the combined error due to earth''s curvature and atmospheric refraction. Let h be the true difference in level (Q − P) and e be the combined error. Since refraction is the same for both observations and the distance PQ is the same, e is identical for both.
When the instrument is stationed near P, the error e makes Q appear higher than its true level:
Observed (Q − P) = h + e = 3.0 m ... (i)
When the instrument is stationed near Q, the same error e makes P appear higher, so Q appears lower:
Observed (Q − P) = h − e = −1.0 m ... (ii)
Adding both equations:
2h = 3.0 + (−1.0) = 2.0
h = 1.0 m (Q is 1.0 m above P)
This is the standard reciprocal levelling formula: true difference = average of the two observed differences = (3.0 + (−1.0))/2 = 1.0 m ✓
Correct answer: A — 1.0 m ✓

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Related Topics

reciprocal levelling true difference level GATE 2026 GATE Civil 2026 Set-1 Q43 reciprocal levelling wide valley curvature refraction GATE true difference level average observations GATE civil curvature refraction error reciprocal levelling GATE

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