Question

An area of \(100\,\text{m}^2\) is measured on a plan having an R.F. of \(\dfrac{1}{800}\). If the R.F. were changed to \(\dfrac{1}{2000}\), the area on the new plan in \(\text{m}^2\) would be

• A. \(16\)
• B. \(40\)
• C. \(250\)
• D. \(625\)

Hint:

For the same ground area, \[ \boxed{ \text{Plan area} \propto (\text{R.F.})^2. } \]

Answer 1

The Correct Option is A

Step 1: Use the relation between plan area and scale. Plan area is proportional to the square of the representative fraction (R.F.). Thus, \[ \frac{A_2}{A_1} = \left( \frac{R.F._2}{R.F._1} \right)^2. \]

Step 2: Substitute the given values. Given, \[ A_1=100, \qquad R.F._1=\frac1{800}, \qquad R.F._2=\frac1{2000}. \] Therefore, \[ A_2 = 100 \left( \frac{800}{2000} \right)^2 = 100 \left(\frac25\right)^2 = 100\times\frac4{25} = 16. \] Hence, \[ \boxed{16} \] is the required area. Therefore, \[ \boxed{(A)} \] is the correct answer.