NECO 2005 Mathematics · Question 15

A surveyor measured the length of a obtained 42.55 metres. If his measurement was more than the actual length…

Question

A surveyor measured the length of a obtained 42.55 metres. If his measurement was more than the actual length and the percentage error of his measurement was 8%, calculate the actual length of the land

A.39.40 metres
B.46.20 metres
C.46.25 metres
D.46.50 metres
E.48.25 metres

Answer: A. 39.40 metres

Explanation written with AI and checked against the answer key

Analyze the question: The surveyor's measurement (42.55 m) was more than the actual length, and the percentage error was 8%. We need the actual length. Concept: Percentage error = (error ÷ actual value) × 100% Here, error = measured − actual (because the measurement was too big). Solution: Let the actual length = L. Error = 42.55 − L (42.55 − L) / L × 100 = 8 42.55 − L = 0.08L 42.55 = 1.08L L = 42.55 ÷ 1.08 ≈ 39.40 m Check: 8% of 39.40 = 3.152, and 39.40 + 3.152 = 42.552 ≈ 42.55 ✓ Options B to E are all greater than 42.55, which cannot be the actual length, since the measurement was more than the actual length. Only option A fits. Answer: The actual length is 39. Tip: Read the direction of the error carefully. If the measured value is more than the actual, then measured = actual × (1 + error%). If it is less, use (1 − error%). Percentage error is always based on the actual value, not the measured one.

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