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      Question

      A person has to cover a fixed distance between his home

      and office. i) If he walks at 5 km/h, he reaches the office 30 minutes late. ii) If he walks at 8 km/h, he reaches the office 15 minutes early. What is the distance between his home and office?
      A 10 km Correct Answer Incorrect Answer
      B 18 km Correct Answer Incorrect Answer
      C 22 km Correct Answer Incorrect Answer
      D 32 km Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Let distance = D km Let scheduled time to reach office = T hours Case 1: Speed = 5 km/h, 30 minutes late (30 min = 1/2 hr) D / 5 = T + 1/2 ...(1) Case 2: Speed = 8 km/h, 15 minutes early (15 min = 1/4 hr) D / 8 = T − 1/4 ...(2) Subtract (2) from (1): D/5 − D/8 = (T + 1/2) − (T − 1/4) D(1/5 − 1/8) = 1/2 + 1/4 = 3/4 1/5 − 1/8 = (8 − 5)/40 = 3/40 So: D × (3/40) = 3/4 D = (3/4) × (40/3) = 40/4 = 10 km

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