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Direct Proportions

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Question

The following measurements were made during testing a levelling instrument.

$P_{1} = 2.800$
$P_{2} = 2.700$
$Q_{1} = 1.700$
$Q_{2} = 1.800$

$P_{1}$ is closed to P and $Q_{1}$ is closed to Q. If the reduced level of station P is 100.000 m, the reduced level of station Q is

A

101.000 m

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B

99.000 m

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C

100.000 m

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D

102.000 m

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Solution

The correct option is A 101.000 m
Exact height difference,

$H = \frac{(h_{Q 1} - h_{P 1}) + (h_{Q 2} - h_{P 2})}{2}$
$H = \frac{(1.700 - 2.800) + (1.800 - 2.700)}{2}$
$H = - 1 m$
R.L of Q = R.L of P $-$ H

R.L of Q = $100.000 - (- 1)$

R.L of Q = $101.000 m$

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