Question

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Whole circle bearing of a line is preferred to a quadrantal bearing.
Reason (R): Bearing is completely specified by an angle.
In the light of the above statements, choose the most appropriate answer from the options given below:

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

To convert QB to WCB in the 3rd quadrant (SW): $WCB = 180^\circ + QB$. In the 4th quadrant (NW): $WCB = 360^\circ - QB$.

Answer 1

The Correct Option is A

Concept: Bearings in surveying are expressed either as Whole Circle Bearing (WCB, 0-360$^\circ$) or Reduced/Quadrantal Bearing (QB, N/S direction E/W).

Step 1: Evaluate Assertion (A).
In WCB, the direction is measured from North in a clockwise direction. It is generally preferred in engineering calculations, theodolite surveys, and computer programming because it is a continuous numerical value that doesn't require directional prefixes (N, S, E, W). Thus, (A) is correct.

Step 2: Evaluate Reason (R).
In the WCB system, an angle alone (e.g., 210$^\circ$) completely and uniquely identifies the direction of the line. In contrast, in the QB system, the angle ($30^\circ$) is not enough; you must specify the quadrant ($S 30^\circ W$). The simplicity of needing only the angle makes the WCB more efficient. Thus, (R) is correct.

Step 3: Relationship.
The reason that WCB is uniquely specified by just one numerical angle (R) is exactly why it is preferred (A) over the multi-part QB system.