Correct Option: (A)
TECHNIQUE 1:-
For Hour Hand
1 hour = 5 places covered= 5 * (360 / 60) degree covered= 30 degree covered
=> 1 min = (30/60) degree covered = 0.5 degree covered
For Min. Hand
1 hour = 60 places covered= 60 * (360 / 60) degree covered = 360 degree covered
=> 1 min = (360 / 60) = 6 degree covered
Let, at x min. after 6:00 AM, the angle between hour and min hand be 120 degree.
At x min after 6
Angle covered by hour hand = (x * 0.5) degree
Angle covered by min hand = (x * 6) degree
Therefore, a/q
{(0.5 * x) degree + 180 degree} - {(6 * x) degree} = 60 degree ,(180 degree is added because initial angle between hour and min hand is 180 degree)
On solving the above equation, we get x = 21.81 min = 22 min(approx.)
TECHNIQUE 2:-
For Hour Hand
1 hour = 5 places covered= 5 * (360 / 60) degree covered= 30 degree covered
=> 1 min = (30/60) degree covered = 0.5 degree covered
For Min. Hand
1 hour = 60 places covered= 60 * (360 / 60) degree covered = 360 degree covered
=> 1 min = (360 / 60) = 6 degree covered
Therefore, at every 1 min, the difference between the angles covered by hour hand and min. hand is (6 - 0.5) degree = 5.5 degree
In other words, the min. hand and hour hand move in a manner such that 5.5 degree angular difference is covered every min.
Now, a/q
Initially, angle between hour and minute hand = 180 degree (At 6:00 AM, hour and min. hand are diametrically opposite)
Finally, say x min. after 6:00 AM, angle between hour and min hand = 60 degree
Therefore, angular difference covered in this interval = (180 - 60) degree = 120 degree
Also, angular difference covered in x min if 5.5 degree is covered every min is given by (5.5 * x) degree
Therefore, (5.5. * x) degree = 120 degree
=> x = 21.81 in = 22 min (approx.)