A line AB between the stations A and B was measured as 348.28 m using a 20 m tape, too short by 0.05 m. What is the correct length of line AB? 

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UPSC ESE (Prelims) Civil Engineering 19 Feb 2023 Official Paper
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  1. 349.15 m 
  2. 348.41 m
  3. 347.41 m
  4. 346.15 m

Answer (Detailed Solution Below)

Option 3 : 347.41 m
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ST 1: UPSC ESE (IES) Civil - Building Materials
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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’= 348.28 m

L  = 20 m

as a chain is 0.05 m too short,

L’  = 19.95 m

\(\therefore l=348.28\times \left[ \frac{19.95}{20} \right]~\)

l = 347.409 m

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