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

Correct Answer: 150.47

In levelling, the height difference between two points is calculated by using the readings taken at different positions. The readings of both A and B are given, and we need to calculate the difference in height (called the height of the instrument, \( H_{{avg}} \)). The formula for calculating the height of the instrument is: \[ H_{{avg}} = \frac{(H_1 - H_2) + (H_3 - H_4)}{2} \] where \( H_1 \) and \( H_2 \) are the staff readings at A and B, and \( H_3 \) and \( H_4 \) are the corresponding readings for the reverse instrument setup. This formula takes the average of the readings to account for any discrepancies in the instrument setup. From the given staff readings: - For the first setup, \( H_1 = 1.800 \) m at point A and \( H_2 = 1.350 \) m at point B. - For the second setup, \( H_3 = 1.450 \) m at point A and \( H_4 = 0.950 \) m at point B. Now, we calculate the average height difference: \[ H_{{avg}} = \frac{(1.8 - 1.35) + (1.45 - 0.95)}{2} = \frac{0.45 + 0.5}{2} = 0.475 \, {m} \] The RL (Reduced Level) of point B can be found by adding this height difference to the RL of point A. Given that the RL of point A is 150.000 m, we add the height difference \( H_{{avg}} \) to it: \[ {RL of B} = {RL of A} + H_{{avg}} = 150.000 + 0.475 = 150.475 \, {m}. \] Thus, the RL of B is \( \boxed{150.475} \) m (rounded to 3 decimal places).