Question

A surveyor measured the distance between two points on the plan drawn to a scale of 1 cm = 40 m and the result was 450 m. Later, he discovered that he used a scale of 1 cm = 20 m. Find the true distance between the two points
1. 225
2. 900
3. 2250
4. 1125
5. 450

Answer 1

Correct Answer - Option 2 : 900

Concept:

Representative factor

• It is a map scale in which figures representing units (as cm, inches, or feet) are expressed in the form of the fraction 1 / x (as 1/250,000) or of the ratio 1: x to indicate that one unit on the map represents x units (as 250,000 cm) on the earth's surface.
• Representative factor = Map distance / Ground distance

​Calculation:

Given,

Wrong scale, 1 cm = 20 m

Correct scale, 1 cm = 40 m

Measured distance = 450 m

R.F of wrong scale = 1 / 2000

R.F of correct scale = 1 / 4000

Corrected length, \(L = \frac{{\frac{1}{{2000}}}}{{\frac{1}{{4000}}}} \times 450 = 900\)

The true distance between the two points is 900 m.