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

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.

Step 1: Calculate the scale ratio (RF) for the incorrect and correct scales:
The incorrect scale (used in the survey) gives: \[ \text{RF of incorrect scale} = \frac{1}{40} \] The correct scale should have been: \[ \text{RF of correct scale} = \frac{1}{20} \]
Step 2: Use the formula for corrected length:
To find the corrected length, we use the ratio of the two scale factors: \[ \text{Corrected length} = \left( \frac{\text{RF of correct scale}}{\text{RF of incorrect scale}} \right) \times \text{Measured length} \] Substituting the values: \[ \text{Corrected length} = \left( \frac{\frac{1}{20}}{\frac{1}{40}} \right) \times 468 = 2 \times 468 = 936 \text{ m} \]
Final Answer:
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 twice the real distance per cm compared to the incorrect scale, the actual distance must be doubled. Thus, the final corrected value of 936 m is obtained by multiplying the measured value by 2.