Multiple choice

The ratio between the rates of walking of $A$ and $B$ is $2 : 3$ and therefore $A$ takes $10$ minutes more than the time taken by $B$ to reach the destination. If $A$ had walked at double the speed, then in what time would he have covered that distance?

  1. $10$ minutes
  2. $12$ minutes
  3. $15$ minutes
  4. $18$ minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio of speeds A:B = 2:3, so ratio of times A:B = 3:2. Let times be 3t and 2t. 3t - 2t = 10, so t = 10. A's time = 30 minutes. If speed is doubled, time is halved: 30 / 2 = 15 minutes.

AI explanation

Since the ratio of speeds of A and B is 2:3, the ratio of their times for the same distance is 3:2. Let the time taken by B be 2x minutes, so the time taken by A is 3x minutes, and the difference is 3x - 2x = 10 minutes, meaning x = 10. A originally takes 3x minutes, or 30 minutes, to complete the journey. If A walks at double the speed, his new time becomes exactly half of his original time, which is 15 minutes.

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