The time between 7 and 8 O'clock when the minute hand is 5 minutes behind the hour hand is

According to the question:

Minute hand moves:

1 minute → 6˚

5 minutes → 5 × 6˚ → 30˚

Here, A1 = 7 × 30 = 210˚

A2 = 30˚

Time = 2/11(210˚- 30˚)

Time = 2/11 × 180˚

Time = 360˚/11 → \(32\frac{8}{11}\)m past 7 O'clock

Hence, "Option 2" is the correct answer.

Important PointsAs we know, every angle made two times in every one hour, except 0 degree and 180 degree.

1. Before meeting both the hands.

2. After meeting both hands.

To, find Time we use formula:

Time = 2/11 (A1± A2), Where A1 = (Smaller number × 30) and A2 = (Given angle)

Note: We take Plus (+) sign when time is after the meeting both hands and we take minus (-) sign when time is before meeting both the hands.

Here, 5 minutes behind means before meeting both the hands, Thus, we take only minus (-) sign.

Additional InformationMovement of Hour head

12 hr = 360º

1 hr = 30º

60 min = 30º

1 min = 0.5º

Movement of  Minute head       

1 hr =  360º

60 min = 360º

1 min = 6º   

5 min = 30º     

Movement of Seconds head       

1 min =  360º

60 sec = 360º

1 sec = 6º   

5 sec = 30º

Gapping between hour head and minute head

​55 min = 60 min       

1 min = 60/55