Question

An Engineer measured the distance between two locations on a plan having a scale of 1 cm = 50 m as 600 m. Later, however, he found that he used a wrong scale of 1 cm = 30 m to measure the distance. The true distance between the locations is:
1. 200 m
2. 250 m
3. 500 m
4. 1000 m

Answer 1

Correct Answer - Option 4 : 1000 m

 Explanation

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 = 30 m

Correct scale, 1 cm = 50 m

Measured distance = 600 m

R.F of wrong scale = 1 / 3000

R.F of correct scale = 1 / 5000

Corrected length, \(L = \frac{{\frac{1}{{3000}}}}{{\frac{1}{{5000}}}} \times 600 = 1000\)

The true distance between the two points is 1000 m.