Question

A 20 m chain was found to be 10 cm too long after chaining a distance of 1000 m. It was found to be 18 cm too long at the end of the day's work after chaining a total distance of 2000 m. What is the true distance if the chain was correct before the commencement of the day's work?

• A. 1994.5 m
• B. 2005.5 m
• C. 1998.5 m
• D. 2009.5 m

Answer 1

The correct option is D 2009.5 m

For the first 1000 m, average error is

$e=\frac{0+10}{2}=5cm=0.05m$

$\therefore \text{Incorrect length of chain},$

L' = 20 + 0.05 = 20.05 m

Measured length l' = 1000 m

True length,

$l_1=\left(\frac{L^{\prime }}{L}\right)\times l^{\prime }$

$=\left(\frac{20.05}{20}\right)\times 1000=1002.5m$

For the next 1000 m, average error is,

$e=\frac{10+18}{2}=14cm=0.14m$

$\therefore \text{Incorrect length of chain,}$

L' = 20 + 0.14 = 20.14 m

Measured length l' = 1000 m

$\therefore Truelength{l}_2=\left(\frac{L^{\prime }}{L}\right)\times l^{\prime }=\left(\frac{20.14}{20}\right)\times 1000=1007m$

$Hencetruedistancel=l_1+l_2$
= 1002.5 + 1007
= 2009.5 m