Multiple choice

Travelling at $\dfrac{4}{5}^{th}$ of his usual speed a man reaches his destination $15$ minutes late. If he travels the same distance $20\%$ faster than his usual speed, he would reach his destination_____.

  1. $15$ min early
  2. $20$ min early
  3. $5$ min early
  4. $10$ min early
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Since speed and time are inversely proportional, traveling at 4/5 of the usual speed means the time taken is 5/4 of the usual time. The extra time of 1/4 of the usual time equals 15 minutes, which means the usual time is 60 minutes. Traveling 20% faster (6/5 of the usual speed) means taking 5/6 of the usual time, which is 50 minutes, resulting in arriving 10 minutes early.

AI explanation

Using the inverse proportionality of speed and time, the ratio of usual speed to slower speed is 5:4, making the ratio of usual time to slower time 4:5. Since the 4 part corresponds to the usual time and the 5 part is 15 minutes longer, 1 part equals 15 minutes and the usual time is 60 minutes. Traveling 20 percent faster makes the new speed 6/5 of the usual, so the new time becomes 5/6 of 60 minutes, which is 50 minutes; therefore, he reaches 10 minutes early.

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