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 468 m. Later, it was discovered that the scale used was 1 cm = 20 m.
The true distance between the points (in m) is __________ (round off to the nearest integer).

Hint:

Always check the scale carefully. When scaling errors are discovered, use the ratio of the scale factors to adjust the measured values.

Answer 1

Correct Answer: 936

In this problem, we are asked to find the true distance between the points after a scaling error was detected. The surveyor initially used a scale where 1 cm on the plan represented 40 m in reality. However, the correct scale should have been 1 cm = 20 m. 1. Step 1: Calculate the scale ratio (RF) for the wrong and correct scales: The wrong scale gives: \[ {RF of wrong scale} = \frac{1}{20} \] The correct scale gives: \[ {RF of corrected scale} = \frac{1}{40} \] 2. Step 2: Use the formula for corrected length: To find the corrected length, we use the ratio of the two scale factors: \[ {Corrected length} = \left( \frac{{RF of wrong scale}}{{RF of corrected scale}} \right) \times {Measured length} \] Substituting the values: \[ {Corrected length} = \left( \frac{\frac{1}{20}}{\frac{1}{40}} \right) \times 468 = 2 \times 468 = 936 \ {m} \] Thus, the true distance between the points is \( \boxed{936} \, {m} \).
Explanation:
The correction is made by adjusting the scale factor from the incorrect value to the correct value. Since the correct scale represents half the length of the wrong scale, the actual distance is double the measured length. Hence, the final corrected value of 936 m is obtained by multiplying the measured value by 2.