A 20m chain was found to be 6cm too long after chaining a distance of 1059m. It was found to be 9cm too short after chaining at the end 1985m. If the chain was correct before commencement of work find the true distance.

A 20m chain was found to be 6cm too long after chaining a distance of 1059m. It was found to be 9cm too short after chaining at the end 1985m. If the chain was correct before commencement of work find the true distance.
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1 Answer

Answer :

Given : Line ABC, AB=1059m, AC=1985m

 L= 20m, No error at start, 0.06m too long at B,

 0.09m too short

 Find : True distance of AC = ?

Solution :

For part AB

L = Length of chain= 20 m

e = Average error in Chain = 0+0.06 /2 = 0.03m

L’ = Incorrect length of chain = L + e = 20 + 0.03 = 20.03 m

 ( since chain is too Long)

Measured Distance AB = 1059 m

True Distance = (L’/L) X Measured distance

True Distance AB = (20.03/20) X 1059 = 1060.59 m

Similarly,

For part BC

L = Length of chain= 20 m

e = Average error in Chain = 0.06+0.09 /2 = 0.075m

L’ = Incorrect length of chain = L + e = 20 - 0.075 = 19.925 m

 ( since chain is too Long)

Measured Distance BC = 1985 – 1059 = 926m

True Distance = (L’/L) X Measured distance

True Distance AB = (19.925/20) X 926 = 922.52 m

Total true distance of AC = True distance of (AB + BC)

 = 1060.59 m + 922.52 m

 = 1983.11 m
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