This document contains 20 problems related to leveling surveying. The problems involve taking staff readings at intervals, reducing the readings to calculate reduced levels (RLs) using the rise and fall method or collimation plane method, and applying arithmetic checks. Some problems also involve calculating gradients between points. The document provides leveling data, blank leveling tables, and instructions to complete the tables and solve the problems.

1. Page 1
QUESTION BANK
PROBLEMS ON LEVELLING
1. The following consecutive readings were taken with dumpy level on 5 m leveling staff at 20 m
intervals. 0.385, 1.030, 1.925, 2.825, 3.730, 4.685, 0.625, 2.005, 3.110, 4.485. The very first
reading on a point whose RL was 208.125 m. The level was shifted after sixth reading.
Calculate the gradient of the line joining first and last point. Use rise and fall method.
(10 Mks)
Point B.S. I.S. F.S. Rise Fall R.L. Remark
Arithmetical
Checks
Sample Calculation:

2. Page 2
2. Following staff reading were recorded in a leveling work along a hill slope. 3.075, 2.270,
1.900, 3.785, 3.015, 2.490, 2.065, 0.880, 3.310, 2.195, 1.175, 0.540, 2.785, 1.790, 0.895,
3.300, 2.665 and 1.685. Levelling staff used was 4 m length. The first reading was taken on
B.M. having RL = 500.00 m. calculate RL’s of other staff positions by Rise and Fall
Method. Apply arithmetical checks.
Point B.S. I.S. F.S. Rise Fall R.L. Remark
Arithmetical
Checks
Sample Calculation:

3. Page 3
3. Fill up the missing entries and complete the page of the level book: (10 Mks)
Point B.S. I.S. F.S. Rise Fall R.L. Remark
A 3.00 A B.M. I
B C B 1.00 101.00 C.P.1
C 2.00 0.5 D
D E F 101.500
E I 2.5 G H C.P.2
F 1.5 3.0 2.00 J C.P.3
G 3.5 K L
H M N 97.500 B.M. II
Arithmetical
Checks
Ans:
Point B.S. I.S. F.S. Rise Fall R.L. Remark
A 3.00 B.M. I
B 1.00 101.00 C.P.1
C 2.00 0.5
D 101.500
E 2.5 C.P.2
F 1.5 3.0 2.00 C.P.3
G 3.5
H 97.500 B.M. II
Arithmetical
Checks
Sample Calculation:

4. Page 4
4. The following consecutive readings were taken with a leveling instrument at interval of 20
m. 2.375, 1.730, 0.615, 3.450, 2.835, 2.070, 1.835, 0.985, 0.435, 1.630, 2.255 and 3.630 m.
T he instrument was shifted after fourth and eighth readings. The last reading was taken on
a B.M. of R.L. 110.200 m. Find the RLs of all the points.
(10 Mks)
By Rise and Fall Method:
Point B.S. I.S. F.S. Rise Fall R.L. Remark
Arithmetical
Checks
Sample Calculation:

5. Page 5
By Collimation Plane Method:
Point B.S. I.S. F.S. Height of
Instrument
Or
Collimation
R.L. Remark
Arithmetical
Checks
Sample Calculation:

6. Page 6
5. Following staff readings were observed with level. The instrument was shifted after fourth
and seventh reading. Enter readings in a tabular form and calculate reduced levels of all
stations by Rise and Fall method assuming R. L. of first station as 500.000 m station.
1, 2, 3, 4, 1.5, 2.5, 3.5, 0.5, 1 10
By Rise and Fall Method:
Point B.S. I.S. F.S. Rise Fall R.L. Remark
Arithmetical
Checks
Sample Calculation:

7. Page 7
6. The following staff readings were taken on a hill slope in a leveling work.
3.075, 2.270, 1.900, 3.785, 2.490, 2.065, 0.880, 3.310, 2.195, 1.175, 0.540, 2.785, 1.790,
0.895, 3.300, 2.665and 1.685.
Levelling staff used was 4 m length. The first reading was taken on B.M., having RL =
500.00 m. Calculate RL’s of ofther staff positions by Rise and fall methid. Apply
arithmetical checks.
By Rise and Fall Method:
Point B.S. I.S. F.S. Rise Fall R.L. Remark
Arithmetical
Checks
Sample Calculation:

8. Page 8
7. The following staff readings were taken with a dumpy level. The instrument was shifted
after 4th, 7th and 10th readings. The RLs of the starting BM is 100.00 m. Enter the readings
in tabular form and reduce the level by Rise and Fall method. Apply arithmetical checks.
1.00, 2.00, 3.00, 1.00, 2.00, 3.00, 4.00, 0.50, 1.50, 2.50, 3.50, 1.00
By Rise and Fall Method:
Point B.S. I.S. F.S. Rise Fall R.L. Remark
Arithmetical
Checks
Sample Calculation:

9. Page 9
By Collimation Plane Method:
Point B.S. I.S. F.S. Height of
Instrument
Or
Collimation
R.L. Remark
Arithmetical
Checks
Sample Calculation:

10. Page 10
8. During fly leveling the following observation were made:
B.S. = 0.650, 2.155, 1.405, 2.655, 2.435 m
F.S. = 2.455, 1.305, 0.555, 2.405 m
The first reading was taken on a BM of RL 90.500 m from the last BS. It is required to set
four pegs each at a distance of 30 m on a following gradient of 1 in 100. Calculate the RLs
of these four pegs.
By Rise and Fall Method:
Point B.S. I.S. F.S. Rise Fall R.L. Remark
Arithmetical
Checks
Sample Calculation:

11. Page 11
9. Calculate the RL of last station, if the RL of first station is 500 m. The staff readings
observed is as below: 5.00 (staff inverted), 2.00, 3.00, 4.00 (staff inverted), 1.00, 2.00, 3.00,
4.00. Enter the data in standard leveling table. Apply Arithmetical checks. (Rise and Fall
method).
By Rise and Fall Method:
Point B.S. I.S. F.S. Rise Fall R.L. Remark
Arithmetical
Checks
Sample Calculation:

12. Page 12
18. Calculate the reduced level of last station, If the reduced level of first station is 500 m. The
staff readings observed are as shown; below: (in meter). 1.000 (Staff inverted), 2.000,
3.000,4.000 (Instrument shifted), 1.000,2.000, 3.000, 4.000. Enter the data in a standard
levelling table. Apply Arithmetic checks (Use Rise and Fall method).
Station B.S. I.S. F.S. Rise Fall R.L. Remark
1 2.285 232.46 BM1
2 1.65 2.265 X X X
3 2.105 X X
4 X 1.96 X X X
5 2.05 1.925 0.3 X X
6 X X 232.255 BM2
7 1.69 X 0.34 X X
8 2.865 2.1 X X X
-
9 X X 233.425 BM3
Ans:
Station B.S. I.S. F.S. Rise Fall R.L. Remark
1 2.285 232.46 BM1
2 1.65 2.265
3 2.105
4 1.96
5 2.05 1.925 0.3
6 232.255 BM2
7 1.69 0.34
8 2.865 2.1
-
9 233.425 BM3

13. Page 13
10. The following consecutive readings were taken with a leveling instrument at interval of 20
m. 2.375, 1.730, 0.615, 3.450, 2.835, 2.070, 1.835, 0.985, 0.435, 1.630, 2.255 and 3.630 m.
The instrument was shifted after fourth and eighth readings. The last reading was taken on
a B.M. of R.L. 110.200 m. Find the RLs of all the points. (10)
11. The following consecutive readings were taken with a leveling instrument on 5 m leveling
staff at 20 m interval. 0.385, 1.030, 1.925, 2.825, 3.730, 4.685, 0.625, 2.005, 3.110, 4.485.
The very first reading on a point whose RL was 208.125 m. The level was shifted after
sixth reading. Calculate the gradient of the line joining first and last point. Use Rise and
Fall method. (10)
12. The following consecutive readings were taken with a leveling instrument at interval of 20
m. 2.375, 1.730, 0.615, 3.450, 2.835, 2.070, 1.835, 0.985, 0.435, 1.630, 2.255 and 3.630 m.
The instrument was shifted after fourth and eighth readings. The last reading was taken on a
B.M. of R.L. 110.200 m. Find the RLs of all the points.
13. Following staff readings were observed with level. The instrument was shifted after
fourth and seventh reading. Enter readings in a tabular form and calculate reduced levels
of all stations by Plane collimation method, assuming R.L of first station as 500 m. Find
gradient of a line joining first station and last station.
1, 2,3, 4,1.5,2.5,3.5,0.5,1 (08)
14. The following consecutive readings were taken with a leveling instrument at interval of 20
m. 2.375, 1.730, 0.615, 3.450, 2.835, 2.070, 1.835, 0.985, 0.435, 1.630, 2.255 and 3.630 m.
The instrument was shifted after fourth and eighth readings. The last reading was taken on a
B.M. of R.L. 110.200 m. Find the RLs of all the points. (10 Mks)
15. The following consecutive readings were taken with a leveling instrument on 5 m leveling
staff at 20 m interval. 0.385, 1.030, 1.925, 2.825, 3.730, 4.685, 0.625, 2.005, 3.110, 4.485.
The very first reading on a point whose RL was 208.125 m. The level was shifted after
sixth reading. Calculate the gradient of the line joining first and last point. Use Rise and
Fall method. (10 Mks)
16. Following staff readings were recorded in a levelling work along a hill slope. 3.075, 2.270,
1.900, 3.785, 3.015, 2.490, 2.065, 0.880, 3.310, 2.195, 1.175, 0.540, 2.785, 1.790, 0.895,
3.300, 2.665, and 1.685. Levelling staff used was 4 m length. The first reading was taken

14. Page 14
on B.M., having R.L. = 500.00 m. Calculate RL's of other staff positions by Rise and Fall
Method. Apply arithmetical check. (10)
17. During Fly levelling operation; the following observations were made:
BS 0.650; 2.155; 1.405; 2.655; 2.435 m
FS 2.455; 1.305; 0.555; 2.405 m
The first backsight reading was taken on a B .M. of R.L. 90.500 m from the last backsight;
it is required to set four pegs each at a distance of 30 m on a falling gradient of 1 in 100.
Calculate the RL's of these four pegs.
19. Following staff readings were observed with level. The instrument was
shifted after fourth and seventh reading. Enter readings in a tabular form
and calculate reduced levels of all stations, assuming R.L. of first station as
500m. 1, 2, 3, 4, 1.5, 2.5, 3.5, 0.5, 1. (7)
20. The following reading was taken on a continuously sloping ground at 30 m interval 4.000,
2.000, 1.000, 4.000, 3.000, and 2.000. The R.L. of starting point was 500.000 m Rule out
page of levelling field book and enters the above readings. Carry out reduction of levels by
rise and fall method. Apply usual arithmetic checks. Determine the gradient of the line
joining the first and last point.