Question

The length of the survey line was measured with a 30 m tape and was found to be 1000 m. As a check, the length was again measured with another 20 m tape, and was found to be 1010 m. On comparing the 30 m tape with a test gauge, it was found to be 0.10 m too long. Find the actual length of the 20 m chain.

• A. 19.87 m
• B. 20.87 m
• C. 21.87 m
• D. 22.87 m

Hint:

When measuring with a tape that is known to be too long, subtract the overestimation to get the correct length.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
The given measurement with the 30 m tape is 1000 m, but the tape is 0.10 m too long. This means that every measurement with the 30 m tape is 0.10 m longer than the actual length.
Step 2: Calculating the Actual Length.
The length measured with the 30 m tape is 1000 m. To get the correct length, we need to subtract the overestimation of 0.10 m. The actual length is: \[ 1000 - 0.10 = 999.90 \, \text{m}. \]
Step 3: Correcting for the 20 m Chain.
The 20 m chain was used to measure the length as 1010 m. Since it was used with a tape that overestimates, we can use the ratio of actual to measured lengths to correct it. \[ \text{Actual Length} = \left(\frac{999.90}{1000}\right) \times 1010 = 1010 \, \text{m} \times 0.9999 = 19.87 \, \text{m}. \]
Step 4: Conclusion.
The actual length of the 20 m chain is 19.87 m. Hence, the correct answer is (1).

Final Answer: \[ \boxed{19.87 \, \text{m}} \]