At what time between 3 & 4 Hour, Minute hand & Hour hand will coincide? 

Given: Time between 3 & 4 Hour

At 3 o’clock the hour hand is at 3 and the minute hand is at 12 i.e., they are minutes apart. If they are to be together (i.e. at 3:15), the minute hand must move 15 minutes over the hour hand.

As we know 55 min are gained in 60 min.

(Note: In a complete hour, hour hand moves 5 minute and minute hand moves 60 minutes which makes minute hand 60 - 5 = 55 minute ahead hour hand always).

Therefore, 15 min difference will be gained in = [(60 ÷ 55) × 15] = 180 ÷ 11 = \(16 {4 \over 11} \) minute past 3.

Thus, "Option 1" is the correct answer.