Question

The distance AB on the ground as measured on a plan drawn to a scale of 1 cm = 50 m was found to be 500 m. Later, it was detected that the surveyor wrongly used a scale of 1 cm = 40 m in the calculations. What will be the true length of the line AB?

• A. 400 m
• B. 512.5 m
• C. 625 m
• D. 412.5 m

Hint:

For scale correction:
\[\text{True Length} = \text{Measured Length} \times \frac{\text{Correct Scale}}{\text{Wrong Scale}}.\]  
Always verify the scale before calculations.

Answer 1

The Correct Option is C

The relationship between the measured length and the true length is based on the scale ratio. If the wrong scale was used, the true length can be recalculated using:
\[\text{True Length} = \frac{\text{Measured Length} \times \text{True Scale}}{\text{Wrong Scale}}\]
Given:
 Measured Length = 500 m,
   True Scale = 1 cm = 50 m,
   Wrong Scale = 1 cm = 40 m.
Substitute these values into the formula:
\[\text{True Length} = \frac{500 \times 50}{40}\]
Simplify:
\[\text{True Length} = \frac{25000}{40}\]
Calculate:
\[\text{True Length} = 625 \, \text{m}\]