The true length of a line measured from a plan as per scale was 1276.54 m. When the line was measured with a 30-m-long chain, the length was measured as 1274.84 m. Find the true length of the chain.

Concept:

True length of the line:

\(L=({l'\over l})\times L'\)

Where, L = Actual true length of line, L' = Wrong measured length of the line, \(l\) = Designated length of tape or chain, \(l'\) = Actual length of tape or chain

Calculation:

Given

Actual length of line (L) = 1276.54 m, Designated length of chain (\(l\)) = 30 m, Wrong measured length of the line (L') = 1274.84 m, True length of chain (\(l'\)) =?

\(L=({l'\over l})\times L'\)

\(1276.54={l'\over 30}\times 1274.84\)

\(l'={1276.54\over 1274.84}\times 30=30.040\, m\)

True length of chain (\(l'\)) = 30.040 m

Hence option (2) is correct.