At what time between 5 and 6 o' clock the hands of the clock be 3 minutes apart ?24 min past 512 min past 513 min past 415 min past 3

The hands of the clock will be 3 minutes apart at 24 minutes past 5.

Here's the step by step explanation:

1. We know that in 60 minutes, the minute hand gains 55 minutes on the hour hand (because in 60 minutes, the minute hand makes one full circle, which is 60 minutes, and the hour hand moves 5 minutes).

2. Therefore, in one minute, the minute hand gains 55/60 = 11/12 minutes on the hour hand.

3. We want to find out when the minute hand is 3 minutes ahead of the hour hand. So, we set up the equation: (11/12) * t = 3 + 5 * t, where t is the time past 5 o'clock.

4. Solving for t, we get t = 24 minutes.

So, the hands of the clock will be 3 minutes apart at 24 minutes past 5.