At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?

The minute and hour hands of a clock coincide 11 times every 12 hours. The first coincidence after 3 o'clock will occur at a time that is 12/11 of an hour after 3 o'clock.

To find the exact time, we need to convert 12/11 hours into minutes. There are 60 minutes in an hour, so we multiply:

(12/11) * 60 = 720/11 = 65.45 minutes

This is 65 minutes and approximately 27 seconds.

So, the time at which the minute and hour hands coincide after 3 o'clock is approximately 3:65, or 4:05.

Please note that this is an approximation. The exact time will be slightly different because the hour hand will have moved a bit further along in the time it takes for the minute hand to reach the same position.