At what time, between 3'o clock and 4'o clock, both the hands will coincide with each other?

$16 \frac{4}{11}$ minutes

At $3$ o'clock, the minute hand is $15$ min. spaces apart from the hour hand.

To be coincident, it must gain $15$ min. spaces.

$55$ min. are gained in $60$ min.

So, 15 mins are gained in 60/55 x 15mins => 180/11 mins

so, it will be $16 \frac{4}{11}$ minutes