Consider the following statements 1 Between 3 16 p m and 3 17 p m both hour hand and minute hand coi...........

Explanation:

From statement 1:
At 3 o’clock, the minute hand is 15 minute spaces apart from hour hand.
To be coincident, it must gain 15 minute spaces.
We know that, 55 minutes are gained in 60 minutes.
So, 15 minutes are gained in (60/55) × 15 = 180/11 minutes = 16.36 minutes
Thus, hour hand and minute hand will coincide at 3:16:36, which is between 3:16 pm and 3:17 p.m.
Hence, statement 1 is correct.
From statement 2:
At 4:58 p.m. the second hand is at 12. In the next minute, the second will definitely cross the minute hand. Thus, between 4:58 p.m. and 4:59 p.m. the minute hand and second hand will definitely coincide.
Hence, statement 2 is correct.
Thus, both statements 1 and 2 are correct.