The distance between two points measured during a hot summer by using a 30 m long chain was 2.4 km. At the end of the day’s work, it was found that the chain was 2 decimetre longer. Which of the following is the correct option?

Concept:

If a chain is too short, the measured distance will be more, the error will be positive, and the correction will be negative.

\(True\;length\;of\;line\;\left( l \right)\)

\(= Measured\;length\;of\;line\;\left( {l'} \right) \times \frac{{Incorrect\;length\;of\;the\;chain\;\left( {L'} \right)}}{{True\;length\;of\;the\;chain\;\left( L \right)}}\)

Calculations:

With 30 m chain:

Measured length of line = 2.4 km = 2400 m

True length of chain = 30 m

Incorrect length of chain = 30 + 0.2 = 30.2 m

Therefore, True length of line =

\(= \;Measured\;length\;of\;line\;\left( {l'} \right) \times \frac{{Incorrect\;length\;of\;the\;chain\;\left( {L'} \right)}}{{True\;length\;of\;the\;chain\;\left( L \right)}}\)

\(= 2400 \times \frac{{30.2}}{{30}}\)

= 2416 m

Difference in measured distance and actual distance = 2416 - 2400 = 16 m = 1600 cm