WAEC 2023 Mathematics · Question 24

A student measured the height of a pole as 5.98 m which is less than the actual height. If the percentage…

Question

A student measured the height of a pole as 5.98 m which is less than the actual height. If the percentage error is 5%, find correct to two d.p the actual height of the pole.

A.6.29m
B.7.67m
C.7.18m
D.6.65m

Answer: A. 6.29m

Explanation written with AI and checked against the answer key

Analyze the question: The measured height (5.98 m) is less than the actual height. The percentage error is 5%. We need the actual height. Concept: Percentage error = (error ÷ actual value) × 100% Error = actual − measured Solution: Let the actual height = H. (H − 5.98)/H × 100 = 5 H − 5.98 = 0.05H 0.95H = 5.98 H = 5.98 ÷ 0.95 = 6.2947... H ≈ 6.29 m Check: 5% of 6.29 = 0.3145, and 6.29 − 0.3145 = 5.9755 ≈ 5.98 ✓. (Note: if you wrongly took the error as 5% of the measured value, you would get 5.98 × 1.05 = 6.28, which isn't an option. The correct approach uses the actual value as the base, giving 6.29.) Answer: Option A, 6.29 m. Tip: Percentage error is always based on the actual (true) value, not the measured one. Set up the equation as (error/actual) × 100 and solve for the actual value.

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