The length of a road measured with a 30-metre chain was found to be 300 metres. What is the true length of the road if the chain was 10 cm too long?

📏 Core Concept: Correction for a "Long" Chain

When a survey chain is longer than its standard designated length, it introduces a systematic error. Since each "chain length" measured is actually longer than it's supposed to be, the final recorded distance is shorter than the true distance.

• If a chain is too long, it will 'under-measure' the distance. The recorded measurement will be less than the true distance.
• Therefore, the correction to be applied will be positive.

🔬 Calculation and Formula

The relationship for correcting this error is based on a simple proportion. The standard formula is:

$$ \text{Correct Length} \times \text{True Distance} = \text{Incorrect Length} \times \text{Measured Distance} $$

Given Information:

• Correct Chain Length: 30 m
• Incorrect Chain Length: 30 m + 10 cm = 30 m + 0.1 m = 30.1 m
• Measured Distance: 300 m
• True Distance: ?

Applying the formula:

$$ 30 \times \text{True Distance} = 30.1 \times 300 $$

$$ \text{True Distance} = \frac{30.1 \times 300}{30} $$

$$ \text{True Distance} = 30.1 \times 10 $$

$$ \text{True Distance} = 301 \, \text{m} $$

💡 Study Tip

A quick mental check can prevent simple mistakes. Since the chain was too long, you are effectively using a longer ruler. This means you will count fewer "chain lengths" to cover the same distance. Therefore, the true length must be greater than the measured 300 m. This immediately helps you eliminate options B and C.