Multiple choice

Ravi starts from his home at 9:00 a.m. and reaches his office at 10:00 a.m. He starts for his home at 5:30 p.m. and walks at a speed increased by 5 km/hr and reaches his home at 6:00 p.m. What is the distance between his home and his office?

  1. 2.5 km

  2. 5 km

  3. 0.5 km

  4. 10 km

  5. 2.14 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Morning trip: 1 hour. Evening trip: 0.5 hours. Let D be distance and v be speed in morning. v = D/1. Evening speed = v + 5 = D/0.5 = 2D. So D/1 + 5 = 2D, which means D = 5 km.

AI explanation

Let the usual speed be v and the distance be D. The time taken to reach the office at the usual speed is 1 hour, so D equals v. On the return trip, his new speed is v plus 5 and the time taken is 30 minutes, or 0.5 hours, giving the equation D equals 0.5 times the sum of v and 5. Substituting D equals v gives v equals 0.5v plus 2.5, which simplifies to 0.5v equals 2.5 and v equals 5. Since the distance equals the usual speed, the distance between his home and office is 5 kilometers.

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