Aptitude - Clock - Discussion

If Answer Is This ( The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).) So
(The hands of a clock point in opposite directions (in the same straight line)(Because between 1 and 11 they point in opposite directions at 6 o'clcok only).

I want to ask something that at 5:59 and 6:00 o'clock the hour hand and minute hand of the clock will be in opposite direction.

If you want to check you can practically check so the answaer will be 24.

Method to solve it.

If we consider hour hand to increnment after 12 minute hand.

Then,

HH at 12:00 for MH between 12:00 to 12:11, but will be opposite directions if HM-12:00 & MM-&6:00, so condition is not satisfied.

Similarly if we calculate for 12:01, 12:02, 12:03, 12:04, 1:05, 1:06, 1:07, 1:08, 1:09, 2:10, 2:11, . So on. Till 11:59. Condition will satisfy only for 12:32, 1:38, 2:43, 4:54, 5:59, 6:00, 7:05, 8:10, 9:16, 10:21, 11:27.

11 times. Multiplied by 2 (for both a. M and p. M) =22.

Hence answer is 22.

The minute hand moves 360 degrees in 60 minutes. This means that the angle of the minute hand is given by 6t, where t is number of minutes past midnight.

The hour hand moves 30 degrees in 60 minutes. This means that the angle of the minutes hand is given by 0.5t.

The hands start together at midnight. The first time they make a 180 degree angle is when the minute hand has moved 180 degrees further than the hour hand, so this is given by the equation:

6t = 0.5t + 180
5.5t = 180
t = 360/11

So, after every t minutes there will an angle of either 180 degrees or 0 degrees alternatively.

24 hours is 1440 minutes.
1440 / (360/11) = 44.

Out of 44 times, at 22 times angle between minute hand and hour hand will be 180 degrees.

The concept is we start from 12 they are one time opposite before 1 pm.

Similarly they will be opposite one more time before 2 pm. This is the condition till 5 pm but at 6 they are opposite at exactly 6 ( minute hand at 12 hour hand at 6 ) after this they will be opposite 7 times after 7 similarly opposite 11 times after 11 and 12 times after twelve gotcha after twelve so upto twelve only 11 times.

So in 24 hours 11+11 = 22 times.

The time between 5 and 6 o'clock when two hands of a clock are in same line making angle of 180 degree?

I have a doubt. You all say the hour and minute hands are in straight line only once between 5 and 7. What about 5:55?

Which angle a clock will make if both the needles are at 6.

I'm trying to find a formula for finding the hands of clock in straight line?