--- title: "Level book, 5 m staff, B at 1200.800" subject: "Surveying I" chapter: 5 key: "semester_3/surveying_i:level-book-5m-staff-20m-points-a-b-c-d" source: https://www.bctengineer.com/q/semester_3/surveying_i/level-book-5m-staff-20m-points-a-b-c-d site: BCT Engineering --- # Level book, 5 m staff, B at 1200.800 Surveying I · Chapter 5: Leveling - Asked in: 2068 Baisakh, 8 marks - Video: [Problem on Levelling No 4 - Rise & Fall Method and Height of Instrument Method ( Sloping Ground )](https://www.youtube.com/watch?v=SS9qQyp2LuY) — Stan Academy - 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-5m-staff-20m-points-a-b-c-d - 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 5 meter levelling staff on a continuously sloping ground at a common interval of 20 meters: 0.385 (Point A), 1.030, 1.925, 2.825, 3.730, 4.685 (Point B), 0.625, 2.005, 3.110, 4.485 (Point C), 0.975, 1.382, 1.836, 2.702, 3.59 (Point D). The reduced level of the point B was 1200.800 m. Rule out a page of a level field book and enter the above readings. Calculate the reduced levels of the points by rise and fall method and the gradient of the line joining the first and the last point. ## Short answer By rise and fall method, reduced levels: A=1205.100 m, B=1200.800 m, C=1196.940 m, D=1194.325 m. The line falls 10.775 m over 240 m, giving a gradient of 1 in 22.3 (4.49% downward). ## Answer **Assumptions:** the readings 4.685 (B) and 4.485 (C) are foresights on change points, and the next readings 0.625 and 0.975 are backsights on the same points after the instrument is shifted. Chainage is taken from A at 20 m per staff position, so A to B = 100 m, B to C = 60 m, C to D = 80 m (total 240 m). B is the 6th reading, so its RL is fixed first (1200.800 m) and the others are found upwards and downwards from it. | Point | Chainage | BS | IS | FS | HI | Rise | Fall | RL (m) | |---|---|---|---|---|---|---|---|---| | A | 0 | 0.385 | | | 1205.485 | | | 1205.100 | | 2 | 20 | | 1.030 | | | | 0.645 | 1204.455 | | 3 | 40 | | 1.925 | | | | 0.895 | 1203.560 | | 4 | 60 | | 2.825 | | | | 0.900 | 1202.660 | | 5 | 80 | | 3.730 | | | | 0.905 | 1201.755 | | B | 100 | 0.625 | | 4.685 | 1201.425 | | 0.955 | 1200.800 | | 7 | 120 | | 2.005 | | | | 1.380 | 1199.420 | | 8 | 140 | | 3.110 | | | | 1.105 | 1198.315 | | C | 160 | 0.975 | | 4.485 | 1197.915 | | 1.375 | 1196.940 | | 10 | 180 | | 1.382 | | | | 0.407 | 1196.533 | | 11 | 200 | | 1.836 | | | | 0.454 | 1196.079 | | 12 | 220 | | 2.702 | | | | 0.866 | 1195.213 | | D | 240 | | | 3.590 | | | 0.888 | 1194.325 | HI is shown on the row where a new set-up starts. RL = previous RL + rise - fall. #### Arithmetic checks $$ \begin{aligned} \Sigma BS - \Sigma FS &= 1.985 - 12.760 = -10.775 \text{ m}\\ \Sigma \text{Rise} - \Sigma \text{Fall} &= 0.000 - 10.775 = -10.775 \text{ m}\\ \text{Last RL} - \text{First RL} &= 1194.325 - 1205.100 = -10.775 \text{ m} \end{aligned} $$ All three are equal, so the arithmetic is correct. #### Gradient of the line AD (first to last point) RL of A = 1205.100 m, RL of D = 1194.325 m. Difference in level = 10.775 m (falling). Horizontal distance = 240 m. $$ \text{Gradient} = \frac{10.775}{240} = \frac{1}{22.27} $$ **Answer:** RLs: A 1205.100, B 1200.800, C 1196.940, D 1194.325 m. The line AD falls at about **1 in 22.3** from A to D (4.49 %). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why are 4.685 and 0.625 both entered at point B? A. B is a change point: 4.685 is the FS before shifting and 0.625 the BS after shifting the instrument B. B is a benchmark read twice C. 0.625 is a check reading by a second observer D. They are two IS readings on B Answer: A. After the instrument is shifted, the old FS and the new BS are read on the same point. (Key point: Change points) 2. RL of B is 1200.800 m and the total fall from A to B is 4.685 - 0.385 = 4.300 m. What is RL of A? A. 1205.485 m B. 1200.800 m C. 1196.500 m D. 1205.100 m Answer: D. A is higher than B by 4.300 m, so RL A = 1205.100 m. (Key point: RL of A) 3. Which gives the correct check for this book? A. Sum BS = sum FS B. Sum rise = sum fall C. Last RL = first RL D. Sum BS - sum FS = Sum rise - sum fall = last RL - first RL = -10.775 m Answer: D. The three differences must be equal; here all are -10.775 m. (Key point: Arithmetic check) 4. Difference in level between A and D is 10.775 m over 240 m. What is the gradient? A. 1 in 22.3 rising B. 1 in 240 C. 1 in 10.8 falling D. 1 in 22.3 falling Answer: D. 10.775/240 = 1/22.27, and RL falls from A to D. (Key point: Gradient of AD) ## Close variants set in other exams - [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× ## 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: 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, 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× - [Level book, 20 m interval, RL 1280 to 1279.924](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-20m-interval-1280-1279-924) — Surveying I, chapter 5 - [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×