The true length of a line is known to be 200 m. When this is measured with a 20 m tape, the length is 200.80 m. What is the correct length of the 20 m

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The true length of a line is known to be 200 m. When this is measured with a 20 m tape, the length is 200.80 m. What is the correct length of the 20 m tape?

1. 19.98 m
2. 20.08 m
3. 20.04 m
4. 19.92 m

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Correct Answer - Option 4 : 19.92 m

Concept:

$True\;length\;line = \frac{{l'}}{l} \times measured\;length\\$

Calculation:

True length of line (L) = 200 m

Actual length of chain (l) = 20 m

Measured length of line (L') = 200.80 m

Corrected length of chain (l') = ?

So, we know

$True\;length\;line = \frac{{l'}}{l} \times measured\;length\\$

$\Rightarrow 200 = \frac{{l'}}{{20}} \times 200.80$

∴ l' = 19.92 m