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 question seems to be asking for the time between 5 and 6 o'clock when the minute and hour hands of a clock are exactly 3 minutes apart.

To solve this, we need to understand that the minute hand moves 12 times faster than the hour hand.

At 5 o'clock, the hour hand is at the 25 minute mark. The minute hand will catch up to the hour hand at a rate of 11 minutes per hour (since it moves 12 times faster but the hour hand is also moving).

So, we can set up the equation 25 + 11t = 60t, where t is the time in minutes past 5 o'clock.

Solving for t gives us t = 25/49 hours, which is approximately 30.6 minutes.

So, the hands will be 3 minutes apart at approximately 30.6 minutes past 5, or around 5:31.

None of the options provided (24 min past 5, 12 min past 5, 13 min past 4, 15 min past 3) are correct.