---
title: "Level book, RL of B 1380.500"
subject: "Surveying I"
chapter: 5
key: "semester_3/surveying_i:level-book-4m-staff-b-1380-500"
source: https://www.bctengineer.com/q/semester_3/surveying_i/level-book-4m-staff-b-1380-500
site: BCT Engineering
---

# Level book, RL of B 1380.500

Surveying I · Chapter 5: Leveling

- Asked in: 2061 Baisakh, 10 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/level-book-4m-staff-b-1380-500
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5

## Question

The following consecutive readings were taken with a level and a 4 m levelling staff on a continuously sloping ground at a common interval of 30 metres.

0.855 (on A), 1.545, 2.335, 3.115, 3.825, 0.455, 1.380, 2.055, 2.855, 3.455, 0.585, 1.015, 1.850, 2.755, 3.845 (on B).

The R.L. of B was 1380.500. Make a level book and apply usual checks. Determine the gradient of line AB.

## Short answer

Working backward from B (RL 1380.500 m) using the HI method gives RL of A = 1389.730 m. Over the 360 m length AB, a fall of 9.230 m results in a gradient of 1 in 39 (approximately 2.56%).

## Answer

**Assumptions:** the staff positions are 30 m apart; the readings 3.825 and 3.455 are foresights on change points, and the next readings (0.455 and 0.585) are backsights on the same points after the instrument is shifted. This gives 13 points, with A to B = 12 x 30 = 360 m. RL of B is known, so the levels are worked back from B.


| Point | Chainage | BS | IS | FS | HI | Rise | Fall | RL (m) |
|---|---|---|---|---|---|---|---|---|
| A | 0 | 0.855 |  |  | 1390.585 |  |  | 1389.730 |
| 2 | 30 |  | 1.545 |  |  |  | 0.690 | 1389.040 |
| 3 | 60 |  | 2.335 |  |  |  | 0.790 | 1388.250 |
| 4 | 90 |  | 3.115 |  |  |  | 0.780 | 1387.470 |
| 5 | 120 | 0.455 |  | 3.825 | 1387.215 |  | 0.710 | 1386.760 |
| 6 | 150 |  | 1.380 |  |  |  | 0.925 | 1385.835 |
| 7 | 180 |  | 2.055 |  |  |  | 0.675 | 1385.160 |
| 8 | 210 |  | 2.855 |  |  |  | 0.800 | 1384.360 |
| 9 | 240 | 0.585 |  | 3.455 | 1384.345 |  | 0.600 | 1383.760 |
| 10 | 270 |  | 1.015 |  |  |  | 0.430 | 1383.330 |
| 11 | 300 |  | 1.850 |  |  |  | 0.835 | 1382.495 |
| 12 | 330 |  | 2.755 |  |  |  | 0.905 | 1381.590 |
| B | 360 |  |  | 3.845 |  |  | 1.090 | 1380.500 |

HI is shown on the row where a new set-up starts. RL = previous RL + rise - fall.

#### Arithmetic checks
$$
\begin{aligned}
\Sigma BS - \Sigma FS &= 1.895 - 11.125 = -9.230 \text{ m}\\
\Sigma \text{Rise} - \Sigma \text{Fall} &= 0.000 - 9.230 = -9.230 \text{ m}\\
\text{Last RL} - \text{First RL} &= 1380.500 - 1389.730 = -9.230 \text{ m}
\end{aligned}
$$

All three are equal, so the arithmetic is correct.

#### Gradient of the line AB
RL of A = 1389.730 m, RL of B = 1380.500 m, difference = 9.230 m (A is higher).

$$
\text{Gradient} = \frac{9.230}{360} = \frac{1}{39.00}
$$

**Answer:** RL of A = 1389.730 m; the line AB falls from A to B at **1 in 39.0** (2.56 %).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. RL of B is known, not RL of A. How is the book worked?
   A. Compute falls from the readings and work back from B to get A
   B. Average the readings
   C. Assume A = 0
   D. Use only the HI method forward from A
   Answer: A. Rise/fall are computed, then the known RL of B is used to back-calculate A: 1380.500 + 9.230 = 1389.730 m. (Key point: Working from B)

2. Readings 0.855 at A and 1.545 at point 2. What is the fall?
   A. 1.545 m
   B. 0.855 m
   C. 0.690 m
   D. 2.400 m
   Answer: C. 1.545 - 0.855 = 0.690 m. (Key point: Fall at point 2)

3. What equal value comes out of the checks?
   A. -9.230 m
   B. +9.230 m
   C. 0.000 m
   D. -11.125 m
   Answer: A. 1.895 - 11.125 = -9.230 = last RL - first RL = 1380.500 - 1389.730. (Key point: Arithmetic check)

4. Fall 9.230 m over 12 x 30 = 360 m. What is the gradient?
   A. 1 in 28
   B. 1 in 39
   C. 1 in 9.23
   D. 1 in 360
   Answer: B. 9.230/360 = 1/39, falling from A to B. (Key point: Gradient of AB)

## Close variants set in other exams

- [Level book, RL of A 380.500, 3.845 on B](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-4m-staff-a-380-500-3-845) — Surveying I, chapter 5, asked 3×
- [Level book, RL of A 380.500, 3.945 on B](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-4m-staff-30m-380-500-minus) — Surveying I, chapter 5, asked 3×

## Related in Surveying I

- [Level book, staff readings at B and C (1251.250)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-15m-b-c-rl-1250-800-1251-250) — Surveying I, chapter 5, asked 3×
- [Level book, staff readings at B and C (1251.000)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-15m-b-c-rl-1250-800-1251-000) — Surveying I, chapter 5, asked 3×
- [Level book, RL of B 1180.750 m](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-dumpy-4m-staff-b-1180-750) — Surveying I, chapter 5, asked 2×
- [Level book, 5 m staff, B at 1200.800](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-5m-staff-20m-points-a-b-c-d) — Surveying I, chapter 5, asked 2×
- [Level book: profile levelling readings](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprofile-leveling-readings-3rd-7th-9th) — Surveying I, chapter 5
- [Level book, B and C, RL 50.250 base](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-15m-b-c-rl-50-800-51-000) — Surveying I, chapter 5, asked 3×