A clock's hour hand and min hand overlap each other at 12:00pm i,e, angle of overlap is 0 degrees. what is the next closet time at which the hour hand and minute hand are aligned in a straight line(180 degrees between each other)
Answers
Question: A clock's hour hand and min hand overlap each other at 12:00pm i,e, angle of overlap is 0 degrees. what is the next closet time at which the hour hand and minute hand are aligned in a straight line(180 degrees between each other)
Answer: If someone is thinking of 6:00 pm then you're wrong.
The hour hand and the minute hand will align straight to each other at 12:32 pm. i.e. 12 hrs 32 mins and 40 seconds. [6 degree makes a minute, so 4 degree makes 40 seconds]
Logic: For 1 degree change in minute hand the hour hand moves (1/12) degree.
So, at 180 degree of minute hand the hour hand will move by 15 degree.
The time will be 12:30pm.
Similarly, at 12:31 pm the minute hand will make an angle of 186 degree and the hour hand will make 15.5 degree. Angle difference = 170.5 degree
Similarly, at 12:32 pm the minute hand will make an angle of 192 degree and the hour hand will make 16 degree. Angle difference = 176 degree
Similarly, at 12:33 pm the minute hand will make an angle of 198 degree and the hour hand will make 16.5 degree. Angle difference = 181.5 degree
For 196 degree of minute hand the hour hand will have covered 16.34 degree. So, angle difference = 179.66 degree i.e. approx 180 degree. [192+4 degree = 196 degree]; The hour hand and the minute hand will align straight to each other at 12:32 pm. i.e. 12 hrs 32 mins and 40 seconds. [6 degree makes a minute, so 4 degree makes 40 seconds]
Therefore, the required time lies in between 12:32 pm and 12:33 pm; closer to 12:33 pm.