At what time, between 3 and 4 o'clock, will the hands of a clock be together?

When the time of the clock is 3 o'clock, the hour hand is at 3, and the minute hand is at 12, making an angle of 90 degrees. We know that the relative velocity of the minute hand w.r.t the hour hand is 5.5 degrees per minute.

Hence, it will take (90/5.5) minutes to make the angle between the hands 0 degrees.(the hands will be together)

(90/5.5)= (180/11) minutes past 3. => $$16\frac{4}{11}$$ minutes past 3.

The correct option is C.