Aptitude - Clock - Discussion

In every hour, the two hand are once in opposite direction like:

12:30.
1:35.
2:40.
3:45.
4:50.
5:55.
6:00.
7:05.
8:10.
9:15.
10:20.
11:25.

Which means in 12 hrs, it is 12 times and in 24 hours its 24 times.

In 60 min. 55 minute spaces are covered.

So lose of 5 min.

That is in 1 hour we lose 5 min.

So in 12 hour we will lose 12*5 = 60 min.

In 1 hour we will get only once when both the hands of watch will be in a straight line in opposite direction.

So we expect in 12 hour we should get 12 times both the hands be in a single straight line in opposite direction.

But unfortunately we have to minus the 1 hour that we have lost. That is one time we have to minus from 12 time.

That is in 12 hour we will have 12-1=11 time both the hand in straight line.

So finally in 24 hour we will get 22 times.

@Rajneesh.

The hands are not in a straight line at 5.55. Take a hand watch and see for yourself. This is the point being made. From 4:50, the next occurrence happens only at 6:00.

So in total, for every 12 hours, we have 11 such instances. For 24 hours, the number of instances is 11*2=24.

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.

@Nitesh Nandwana,

What is that due to the loss of 2 hour?

I don't know why its answer is 22. I think it should be 24.

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.

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.

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.

Following are the time when they are straight.

12:30.
1:35.
2:40.
3:45.
4:50.
5:55.
6:00.
7:05.
8:10.
9:15.
10:20.
11:25.

And they are all 12.

Is I am missing something? How it is 11?