The length of a survey line, when measured with a chain of 20 m nominal length, was found to be 841.5 m. If the chain used is 0.1 m too long, the correct length of the measured line is

This question was previously asked in
ESE Civil 2014 Paper 2: Official Paper
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  1. 845.7m
  2. 837.39 m
  3. 843.6 m
  4. 839.4 m

Answer (Detailed Solution Below)

Option 1 : 845.7m
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ST 1: UPSC ESE (IES) Civil - Building Materials
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20 Questions 40 Marks 24 Mins

Detailed Solution

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Concept:

\(l={l}'\times \left[ \frac{{{L}'}}{L} \right]\)

Where,

l = true length of the line

l= measured length of a line

L = true length of chain/tape

L’ = Incorrect length of chain/tape

Calculation:

l’= 841.5m

L  = 20m

as a chain is 0.1m too long,

L’  = 20.1m

\(\therefore l=841.5\times \left[ \frac{20.1}{20} \right]~\)

l = 845.7m

Mistake point:

● If the chain is 0.1m too long, L’ = 20.1m

● If the chain is 0.1m too short, L’ = 19.9m

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