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Walking time between park gates

XAT 2026 · Quantitative Ability & Data Interpretation · Medium · Geometry

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A park has two gates, Gate 1 and Gate 2. These two gates are connected via two alternate paths. If one takes the first path from Gate 1, they need to walk 80m80\text{m} towards east, then 80m80\text{m} towards south, and finally 20m20\text{m} towards west to arrive at Gate 2. The second path is a semi-circle connecting the two gates, where the diameter of the semi-circle is the straight-line distance between the two gates.

A person walking at a constant speed of 5 km/h5\text{ km/h} enters the park through Gate 1, walks along the first path to reach Gate 2 and then takes the second path to come back to Gate 1.

Which of the following is the CLOSEST to the time the person takes, from entering the park to coming back to Gate 1, if she never stops in between?

  1. A.

    4 minutes

  2. B.

    3 minutes 30 seconds

  3. C.

    4 minutes 30 seconds

  4. D.

    5 minutes 30 seconds

  5. E.

    6 minutes

Answer

A

Explanation

Path 1 length =80+80+20=180 m= 80 + 80 + 20 = 180\text{ m}. Straight line distance between Gate 1 and Gate 2: East displacement =80−20=60 m= 80 - 20 = 60\text{ m}. South displacement =80 m= 80\text{ m}. Diameter D=602+802=100 mD = \sqrt{60^2 + 80^2} = 100\text{ m}. Path 2 (semi-circle) length =πD2=50π≈157 m= \frac{\pi D}{2} = 50\pi \approx 157\text{ m}.

Total distance =180+157=337 m= 180 + 157 = 337\text{ m}. Speed =5 km/h=500060=2503 m/min= 5\text{ km/h} = \frac{5000}{60} = \frac{250}{3}\text{ m/min}. Time taken =337250/3=1011250≈4.044 minutes≈4 minutes= \frac{337}{250/3} = \frac{1011}{250} \approx 4.044\text{ minutes} \approx 4\text{ minutes}.

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