Calculate the total correction (m) required, if a line measured using a 20 m chain is 2380 m. The actual length of the chain is 20.2 m.

Discussion - Chain Correction MCQ

A. 22.6

B. 23.56

C. 23.8

D. 476

Correct Answer (Calculated): C. 23.8

🔗 Understanding Chain Correction

When a surveying chain has an actual length different from its designated length, any measurement made with it will be incorrect. If the chain is too long (like in this case), it under-measures the distance, so the measured length is less than the true length. A positive correction is needed.

The fundamental principle is:

Correct Length × Correct Distance = Incorrect Length × Incorrect Distance

🔬 Detailed Calculation

We are given the following values:

Correct (designated) length of chain (L) = 20 m
Incorrect (actual) length of chain (L') = 20.2 m
Incorrect measured distance (D') = 2380 m

First, we find the correct distance (D):

Correct Distance (D) = (L' / L) × D'

D = (20.2 m / 20 m) × 2380 m

D = 2403.8 m

The correction is the difference between the correct distance and the measured distance:

Correction = Correct Distance - Measured Distance

Correction = 2403.8 m - 2380 m

Correction = 23.8 m

Important Note: The provided solution mentions that in a revised answer key, option (b) 23.56 was considered correct. This might be due to a typo in the question or options in the original exam. However, based on the data given, 23.8 m is the mathematically correct answer.

💡 Study Tips

Logical Check: If the chain is too long (20.2 m > 20 m), the measured distance will be too short. Therefore, the correction must be positive (added to the measured value). This helps you confirm the direction of your calculation.
Remember the Formula: The relationship L × D = L' × D' is fundamental for solving these problems.
Correction vs. Corrected Length: Be careful whether the question asks for the "correction" (the difference) or the "corrected length" (the final true distance).