Answer: B
Let after 6:00 pm and m seconds the hands of his watch form an angle of 110 degree for the first time and after 6:00 pm and n seconds the hands of his watch form an angle 110 degree for the second time.
In every one second the minutes hand covers 360/3600 = 1/10 degree
In every one second the hour's hand covers 30/3600 = 1/120 degree
(This is because the minute's hand covers one circle or 360 degree in one hour or 3600 seconds while hour's hand covers 1/12 th of a circle or 30 degree in one hour or 3600 seconds).
Initial angle formed at 6:00 pm = 180 degree.
Angle formed by the hands of his watch
=> 180 + m/120 - m/10 when minutes hand behind the hour hand.
and, n/10 - n/120 -180 when hours hand is behind the minutes hand.
So, 180 - 11m/120 = 110 or 11m/120 = 70............(i)
=> and 11n/120 - 180 = 110 => 11n/120 = 290.....(ii)
Equation(ii) - Equation(i)
=> m - n = 2400 seconds = 40 minutes.
