At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?A1341113411''B1641116411''C51115111''D1241112411''

The question is asking for the time between 3 o'clock and 4 o'clock when the minute and hour hands of a clock will overlap or coincide.

Here's how to solve it:

1. At 3 o'clock, the minute hand is at 12 and the hour hand is at 3.

2. The minute hand moves 12 times faster than the hour hand.

3. So, the minute hand will catch up to the hour hand at some point between 3 o'clock and 4 o'clock.

4. To find out when, we can set up an equation. Let's say that "m" is the number of minutes past 3 o'clock when the hands coincide.

5. In "m" minutes, the minute hand will move 12m degrees (since it moves at a rate of 12 degrees per minute).

6. The hour hand moves at a rate of 0.5 degrees per minute, so in "m" minutes it will move 0.5m degrees.

7. Since the hour hand starts out 90 degrees ahead of the minute hand (since it's at 3 and the minute hand is at 12), we can set up the following equation to find out when the minute hand will catch up:

12m = 0.5m + 90

8. Solving for "m" gives us m = 16.36 minutes.

So, the minute and hour hands will coincide approximately 16 minutes and 22 seconds past 3 o'clock.

Therefore, the correct answer is B1641116411''.