Multiple choice

Starting from his home, Mohan reaches his office 5 minutes late when he drives his bike at 24 km/hr. If he drives 25% faster on an average, he reaches his office 4 minutes earlier than the scheduled time. What is the distance of his office from his home?

  1. 15 km

  2. 18 km

  3. 20 km

  4. 23 km

  5. 27 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let d be distance, t be scheduled time. d/24 = t + 5/60. New speed = 24 * 1.25 = 30 kmph. d/30 = t - 4/60. Subtract equations: d/24 - d/30 = 9/60. d(5-4)/120 = 9/60. d/120 = 9/60 => d = 18 km.

AI explanation

Increasing the speed by 25% makes the new speed 24 km/hr * 1.25 = 30 km/hr. Using the constant distance formula where the ratio of speeds is inversely proportional to the ratio of times, the speed ratio of 24:30 simplifies to 4:5, making the time ratio 5:4. The difference in time is 5 minutes late minus 4 minutes early, resulting in a total difference of 9 minutes, which corresponds to one part in the ratio; since 5 parts equal 45 minutes (0.75 hours), the distance is 24 km/hr * 0.75 hr = 18 km.

Keep practicing — related questions