Question

In levelling between two points A and B on the opposite banks of a river, the readings are taken by setting the instrument both at A and B, as shown in the table. If the RL of A is 150.000 m, the RL of B (in m) is ....... (rounded off to 3 decimal places). 

Hint:

When calculating the reduced level (RL) in levelling, always use the average height difference between the readings to find the RL of the second point.

Answer 1

Calculation of Reduced Level (RL) Using Height of Instrument Method

Step 1: Define Given Data

The height difference between two points (A and B) in levelling is calculated using the formula:

\[ H_{{avg}} = \frac{(H_1 - H_2) + (H_3 - H_4)}{2} \]

where:

• \( H_1 \) and \( H_2 \) are the staff readings at A and B in the first instrument setup.
• \( H_3 \) and \( H_4 \) are the readings for the reverse instrument setup.

Step 2: Substitute Given Values

From the problem statement:

• \( H_1 = 1.800 \) m at point A
• \( H_2 = 1.350 \) m at point B
• \( H_3 = 1.450 \) m at point A
• \( H_4 = 0.950 \) m at point B

Now, calculating the average height difference:

\[ H_{{avg}} = \frac{(1.8 - 1.35) + (1.45 - 0.95)}{2} \]

\[ H_{{avg}} = \frac{0.45 + 0.5}{2} = \frac{0.95}{2} = 0.475 \, \text{m} \]

Step 3: Compute the RL of Point B

Given that the RL of point A is 150.000 m, we calculate:

\[ \text{RL of B} = \text{RL of A} + H_{{avg}} \]

\[ = 150.000 + 0.475 = 150.475 \, \text{m} \]

Final Answer:

Correct Answer: \( \mathbf{150.475} \) m (rounded to three decimal places).