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Cross Roads Width in Park

XAT 2013 · Quantitative Ability & Data Interpretation · Medium · Mensuration

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The central park of the city is 40 metres long and 30 metres wide. The mayor wants to construct two roads of equal width in the park such that the roads intersect each other at right angles and the center of the rectangle co-incides with the center of the rectangle formed by the intersection of the two roads . Further, the mayor wants that the area of the two roads to be equal to the remaining area of the park. What should be the width of the roads?

  1. A.

    10 metres

  2. B.

    12.5 metres

  3. C.

    14 metres

  4. D.

    15 metres

  5. E.

    16 metres

Answer

A

Explanation

Area of park = 40×30=120040 \times 30 = 1200. Area of roads = 30T+40T−T2=70T−T230T + 40T - T^2 = 70T - T^2. Area of roads = half of park area = 600600. T2−70T+600=0  ⟹  (T−10)(T−60)=0T^2 - 70T + 600 = 0 \implies (T - 10)(T - 60) = 0. Since T<30T < 30, T=10T = 10 metres.

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