Question

For the traverse given below, the benchmark is at ground point L. The Reduced Level (RL) of L is 150.000 m. The direction of the traverse is from L to N. The readings on levelling staff using the same levelling instrument kept at Stations S1 and S2 during the traversing are shown in the figure.

Column 1	Column 2
	(P) 3.300 m
(I) Sum of Back Sights	(Q) 2.500 m
(II) Sum of Fore Sights	(R) 150.300 m
(III) RL of Point N	(S) 3.000 m
	(T) 150.500 m

Matching the information given under Column 1 and Column 2, which one of the following options is CORRECT?

• A. (I) - (P) ; (II) - (S) ; (III) - (R)
• B. (I) - (P) ; (II) - (Q) ; (III) - (R)
• C. (I) - (S) ; (II) - (P) ; (III) - (T)
• D. (I) - (S) ; (II) - (Q) ; (III) - (T)

Hint:

Use HI = RL + BS at each setup, then RL(next point) = HI - FS; M is the change point linking setup S1 to setup S2.

Answer 1

The Correct Option is A

Step 1: Build a simple rise-and-fall style table instead of height-of-instrument.
Rather than computing the height of the instrument line at each setup, let's track how the ground level rises or falls between consecutive points directly, using the rule: at a single setup, the CHANGE in level from the point read as backsight to the point read as foresight equals (backsight reading) minus (foresight reading), because a bigger staff reading means the ground is lower at that spot for the same sight line.

Step 2: Apply this from L to M (setup S1).
$BS_L = 1.5$ m, $FS_M = 2.0$ m. Change in level from L to M $= BS_L - FS_M = 1.5 - 2.0 = -0.5$ m (a fall of 0.5 m, since the foresight reading is bigger, meaning M is lower than L).
\[ RL_M = RL_L + (-0.5) = 150.000 - 0.5 = 149.500\text{ m} \]

Step 3: Apply the same rule from M to N (setup S2).
$BS_M = 1.8$ m, $FS_N = 1.0$ m. Change in level from M to N $= BS_M - FS_N = 1.8 - 1.0 = +0.8$ m (a rise of 0.8 m, since the foresight reading is smaller here, meaning N is higher than M).
\[ RL_N = RL_M + 0.8 = 149.500 + 0.8 = 150.300\text{ m} \]
This matches the RL of N found by the height-of-instrument method, confirming it by a different route.

Step 4: Add up the sights directly from the given readings.
The two readings taken while the staff was held up for a BACKSIGHT are at L (1.5 m) and at M (1.8 m), so the sum of back sights is $1.5+1.8=3.300$ m.
The two readings taken as a FORESIGHT are at M (2.0 m) and at N (1.0 m), so the sum of fore sights is $2.0+1.0=3.000$ m.

Step 5: Cross-check using the overall rule for a levelling run.
For any levelling run, the total rise minus total fall equals sum of back sights minus sum of fore sights, and both must equal the total change in level from the first point to the last:
$3.300 - 3.000 = 0.300$ m, and $RL_N - RL_L = 150.300-150.000=0.300$ m. These agree, which confirms every number above is consistent.

Final Answer:
Sum of Back Sights $=3.300$ m, matching (P); Sum of Fore Sights $=3.000$ m, matching (S); RL of N $=150.300$ m, matching (R).
\[ \boxed{(I)-(P)\ ;\ (II)-(S)\ ;\ (III)-(R)} \]