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    Question

    A rectangular park is 120 m long and 80 m wide. A path

    of uniform width is made inside the park along the boundary such that the area of the path is 6400 sq m. Find the width of the path.
    A 50 Correct Answer Incorrect Answer
    B 20 Correct Answer Incorrect Answer
    C 40 Correct Answer Incorrect Answer
    D 10 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Total area = 120×80 = 9600 Inner area = 9600 − 6400 = 3200 Let width = x Inner dimensions = (120 − 2x) and (80 − 2x) (120 − 2x)(80 − 2x) = 3200 9600 − 400x + 4x² = 3200 4x² − 400x + 6400 = 0 x² − 100x + 1600 = 0 x = (100 ± 60)/2 ⇒ x = 20 (valid)

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