Two distances 200 m and 298 m are measured from a tacheometer instrument and corresponding staff intercepts are 2 m and 3 m respectively. The additive constant will be:

Detailed Explanation: Solving for the Additive Constant from Field Data

This is the additive-constant counterpart to Q7's multiplying-constant problem — using the same two-equation, two-unknown technique, but solving for C instead of K.

Step-by-step solution:
Using D = KS + C:

Equation 1: 200 = K(2) + C
Equation 2: 298 = K(3) + C

Subtracting Equation 1 from Equation 2:
298 − 200 = K(3 − 2)
98 = K(1)
K = 98

Substituting K = 98 back into Equation 1:
200 = 98(2) + C
200 = 196 + C
C = 200 − 196 = 4

Why the Other Options Are Wrong

B — 1: This does not match the correctly solved value of C; it likely results from an arithmetic slip in the substitution step.

C — 2: Similarly an incorrect intermediate result, possibly confusing the staff intercept value (2 m) with the computed additive constant.

D — 98: This is actually the correctly computed value of K (the multiplying constant), not C — a common mistake is stopping the calculation at the first unknown solved and reporting it as the final answer to whichever constant was asked for, without continuing to substitute back and solve for the second unknown.

Key Concepts for Students

• Subtracting equations isolates K first, then back-substitute for C: This two-step process (subtract to find K, then substitute into either original equation to find C) is the standard technique whenever two distance/intercept pairs are given and both constants are unknown.
• Always double-check you're reporting the constant actually asked for: Since this same two-equation method yields both K and C as intermediate and final results, carefully re-read the question to confirm whether it wants K, C, or both, before finalising your answer (compare with Q7, which asks for K-related values instead).
• Sanity-check your answer against typical magnitudes: A multiplying constant near 100 (here, 98) and a small additive constant (here, just 4, in whatever distance unit) are both consistent with realistic tacheometer designs — if your computed values look wildly different from these typical magnitudes, suspect an arithmetic error.