Question

A distance of 2000m was measured by 20m chain, Later on it was detected that the chain was 0.1 m too long. Another 1000m (i.e. total 3000 m) was measured and it was detected that the chain was 0.20 m too long. If the length of the chain in the initial stage was correct, then the exact length that was measured is __________.
(Report the answer in m, correct upto two decimal places)

• A. 3012.5

Answer 1

The correct option is A 3012.5
For the first 2000 m

Mean length of the tape

$l=\frac{20+20.10}{2}=20.05m$

$\text{Correct length}=\frac{\text{Actual length of tape}}{\text{Nominal length of tape}}\times \text{Measured distance}$

$=\frac{20.05}{20}\times 2000$

$=2005m$

For the last 1000 m,

$Meanlength{}^{\prime }{l}^{\prime }=\frac{20.10+20.20}{2}=20.15m$

$\therefore \text{Correct length}=\frac{20.15}{20}\times 1000=1007.5m$

Hence, correct distance = (2005+1007.5) = 3012.5 m