Assertion (A): In the Center Line Method of estimation, the total length of the center line is reduced by half the breadth of the main wall at every T-junction. Reason (R): T-junctions cause a double counting of the corner area if the full center line length is used without correction. Choose the correct answer: (A) Both (A) and (R) are correct and (R) is the correct explanation of
- ABoth (A) and (R) are correct and (R) is the correct explanation of (A)Correct
- BBoth (A) and (R) are correct, but (R) is not the correct explanation of (A)
- C(A) is correct but (R) is incorrect
- D(A) is incorrect but (R) is correct
Solution
Concept
Center Line Method Deductions at T-Junctions
Formula
Deduction = (1/2) × Width of Wall × Number of T-Junctions
Step-by-step solution
1. Read Assertion (A) and Reason (R) regarding center line length deduction at T-junctions. 2. Recall that overlapping joint areas at T-junctions cause double counting of the wall area. 3. Apply the deduction formula: Deduction = (1/2) × Width of Wall × Number of T-Junctions to correct the total length. 4. Conclude that both (A) and (R) are correct and (R) is the correct explanation of (A).
Explanation
In the Center Line Method, when two walls meet to form a T-junction, calculating the full center line length causes the overlapping joint area to be counted twice. To fix this double counting, half the width (breadth) of the main wall is subtracted at every T-junction, making both the assertion and reason correct and directly related.
Shortcut
To remember Center Line Method deductions, use these simple rules: - L-Junctions (Corners): No deduction (0 × width) - T-Junctions: Deduct half the wall width (1/2 × width) - Cross (+)-Junctions: Deduct full wall width (1 × width)
Common mistake
A common mistake is selecting Option B by assuming that Reason (R) is an independent correct statement rather than the direct explanation of Assertion (A), failing to realize that the overlapping area at T-junctions is the exact cause for deducting half the wall breadth. Another frequent mistake is confusing T-junctions with corner (L-junctions), where no deduction is necessary.
Correct answer: A) Both (A) and (R) are correct and (R) is the correct explanation of (A)