Aptitude - Clock - Discussion

How many times the hour & minute hand are in opposite directions b/w 9PM & 10 PM?

Please answer it.

According to me,

Only 2 times in a day it happens mathematically. Actually, because for this there should be 180 degree difference between both hands and when hour hand travels 1 degree minute hand travels 12 degree so only 6 o clock it happens that actully difference between both hands is 180 degree. So answer is 2 times in a day.

It's not a straight line at 12:30. It's a straight line roughly around 12:33 because the hour hand will be halfway between 12 & 1 at 12:30. So 12-4 get 1 occurrence each. 5 does not get an occurrence as the hands won't line up perfectly until 6:00 sharp. 6 through 11 get 1 occurrence each. That means that in that 12-hour period, we get 11.

Repeat for the following 12 to get a 24-hr day.

@Anil Kumar.

7:5^5/11
8:10^10/11
9:16^1/11
10:54^6/11 & again
12:30 (by this 12 hrs are completed)

After 9:16, it is not at 10:54. it is at 10:21 and then 11:27.
So in total, 22 times.

No, its entirely wrong actually in 24 hrs hands will be in opposite direction only for 21 times i.e, on

12:30
1:38^2/11
2:43^7/11
3:46^1/11
4:54^6/11
6:00
7:5^5/11
8:10^10/11
9:16^1/11
10:54^6/11 & again
12:30 (by this 12 hrs are completed)
1:38^2/11
2:43^7/11
3:46^1/11
4:54^6/11
6:00
7:5^5/11
8:10^10/11
9:16^1/11
10:54^6/11 & again
12:30 (by this another 12 hrs are completed)

So, over all 24 hrs are completed and the hands will be in opposite direction in the above timings and only for 21 times not for 22 times.

A watch, which gains uniformity was observed to be 6 minutes slow at 9 am on a Wednesday and 3 minutes fast at 12 noon on the subsequent Thursday. When did the watch show the correct time?

Solve and find the answer.

7 clock in the opposite direction to rotate 180.

Similarly, the opposite direction of the clock 9 180 turned north end figure 3 to 6 are made. Please give me answer in detail.

Answer is 22. Just try by yourself. Use a clock and start rotating its hands. You'll find your answer.

See what you must be thinking there are 12 hours and you should get 12 opposite directions right in between every hour. 12-1, 1-2, 2-3, 3-4, 4-5. Now next moment will occur at 6pm (you can count it as between 5-6) , but next will occur at around 0705 that is 7-8, so there is no such thing between 6-7.

I can't understand how there is the loss of two hours? Please tell me.