---
title: "Level book, RL of A 380.500, 3.845 on B"
subject: "Surveying I"
chapter: 5
key: "semester_3/surveying_i:level-book-4m-staff-a-380-500-3-845"
source: https://www.bctengineer.com/q/semester_3/surveying_i/level-book-4m-staff-a-380-500-3-845
site: BCT Engineering
---

# Level book, RL of A 380.500, 3.845 on B

Surveying I · Chapter 5: Leveling

- Asked in: 2057 Chaitra, 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-a-380-500-3-845
- 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 metre levelling staff on a continuously sloping ground at a common interval of 30 metres.

0.855 (on A), 1.545, 2.353, 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 A was 380.500. Make a level book and apply usual checks. Determine the gradient of the line AB.

## Short answer

From A (RL 380.500 m) applying the HI method forward yields RL of B = 371.270 m. The difference of 9.230 m over 360 m gives a falling gradient of 1 in 39 (about 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 A = 380.500 m is known. The third reading is printed as 2.353 and has been used as printed (in a similar paper it is 2.335).


| Point | Chainage | BS | IS | FS | HI | Rise | Fall | RL (m) |
|---|---|---|---|---|---|---|---|---|
| A | 0 | 0.855 |  |  | 381.355 |  |  | 380.500 |
| 2 | 30 |  | 1.545 |  |  |  | 0.690 | 379.810 |
| 3 | 60 |  | 2.353 |  |  |  | 0.808 | 379.002 |
| 4 | 90 |  | 3.115 |  |  |  | 0.762 | 378.240 |
| 5 | 120 | 0.455 |  | 3.825 | 377.985 |  | 0.710 | 377.530 |
| 6 | 150 |  | 1.380 |  |  |  | 0.925 | 376.605 |
| 7 | 180 |  | 2.055 |  |  |  | 0.675 | 375.930 |
| 8 | 210 |  | 2.855 |  |  |  | 0.800 | 375.130 |
| 9 | 240 | 0.585 |  | 3.455 | 375.115 |  | 0.600 | 374.530 |
| 10 | 270 |  | 1.015 |  |  |  | 0.430 | 374.100 |
| 11 | 300 |  | 1.850 |  |  |  | 0.835 | 373.265 |
| 12 | 330 |  | 2.755 |  |  |  | 0.905 | 372.360 |
| B | 360 |  |  | 3.845 |  |  | 1.090 | 371.270 |

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

#### Arithmetic checks
$$
\begin{aligned}
\Sigma BS - \Sigma FS &= 1.895 - 11.125 = -9.230 \text{ m}\\
\Sigma \text{Rise} - \Sigma \text{Fall} &= 0.000 - 9.230 = -9.230 \text{ m}\\
\text{Last RL} - \text{First RL} &= 371.270 - 380.500 = -9.230 \text{ m}
\end{aligned}
$$

All three are equal, so the arithmetic is correct.

#### Gradient of the line AB
RL of A = 380.500 m, RL of B = 371.270 m, difference = 9.230 m (falling from A to B).

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

**Answer:** RL of B = 371.270 m; the line AB falls 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 A is 380.500 and total fall is 9.230 m. RL of B?
   A. 389.730 m
   B. 380.500 m
   C. 371.270 m
   D. 390.585 m
   Answer: C. 380.500 - 9.230 = 371.270 m. (Key point: RL of B)

2. Third reading is 2.353 (as printed) after 1.545. The fall is:
   A. 0.808 m
   B. 3.898 m
   C. 0.790 m
   D. 0.690 m
   Answer: A. 2.353 - 1.545 = 0.808 m. (Key point: Fall 2 to 3)

3. What equal value comes out?
   A. +9.230 m
   B. -9.230 m
   C. 0.000 m
   D. -11.125 m
   Answer: B. Sum BS - sum FS = 1.895 - 11.125 = -9.230 = last RL - first RL. (Key point: Arithmetic check)

4. Gradient of AB (fall 9.230 m over 360 m):
   A. 1 in 39 falling
   B. 1 in 360
   C. 1 in 39 rising
   D. 1 in 9.23
   Answer: A. 9.230/360 = 1/39, falling from A to B. (Key point: Gradient)

## Close variants set in other exams

- [Level book, RL of B 1380.500](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-4m-staff-b-1380-500) — 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×