Question

The length of a survey line was measured with a 20 m chain and was found to be equal to 1200 m. As a check, the length was again measured with a 25 m chain and was found to be 1212 m. On comparing the 20 m chain with test gauge length, It was found to be 1 decimeter too long. The 25 m chain was _______ cm too short.

• A. 12.4

Answer 1

The correct option is A 12.4
For $20m$ chain

True length of 20 m chain $L^{\prime }=20+0.1=20.1m$

$\therefore$ Actual length of survey line,

$l=1200\times \frac{20.1}{20}=1206m$

For 25 m chain,

Actual length of survey line,

$l=\text{Measured length}\times \frac{\text{Wrong length of chain}}{\text{True length of chain}}$

$1206=1212\times \frac{L^{\prime }}{25}$

$L^{\prime }=24.876m$

$\therefore (25-24.876)\times 100=12.4cm$

$\therefore \text{The 25 m chain was 12.4 cm too short.}$