Solution:

Given,

Actual length of the road = 1330 m

Measured length of the road using a defective chain = 1316 m

Length of the defective chain = 30 m

To find:

Correction required for the defective chain

Calculation:

Let us assume that the defective chain is shorter than the standard length chain.

Let the actual length of the chain be L.

Then, the measured length of the road using the defective chain can be given by the formula

Actual length of the road = Measured length of the road x (Actual length of the chain / Measured length of the chain)

1330 = 1316 x (L/30)

L = (30 x 1330) / 1316

L = 30.22 m

Therefore, the actual length of the chain is 30.22 m.

Now, the correction required for the defective chain can be calculated as

Correction = Actual length of the chain - Measured length of the chain

Correction = 30.22 - 30

Correction = 0.22 m

Therefore, the defective chain needs a correction of 0.22 m.

Explanation:

- The given problem is related to errors in measurement in civil engineering.
- In this problem, we are given the actual length of a road and the measured length of the road using a defective chain.
- We are also given the length of the defective chain.
- The problem asks us to find the correction required for the defective chain.
- To solve this problem, we need to use the concept of proportionality.
- We assume that the defective chain is shorter than the standard length chain.
- Using the formula for proportionality, we can find the actual length of the chain.
- Once we have the actual length of the chain, we can calculate the correction required for the defective chain.
- In this way, we can solve the given problem.