Aptitude - Clock - Discussion

The two hands of a clock coincide after a gap of every 65 5/11 minutes.

For example, if we consider the starting time at 12 . the two hands coincide exactly at 12. Again after 65 5/11 minutes both coincide. Means exactly at 1 5/11 minutes.

In the problem, the two hands of a clock coincide after 64 minutes give.

It means the clock is faster than usual. It means it is gaining time.

For Every 64 minutes the clock gains 65 5/11- 64 = 1 5/11 = 16/11 minutes.

It GAINS not Loses.

So in the problem, for 64 mints clock gains ( faster) 16/11 minutes.

Then it gains how much per day? ( for 24*60 hrs)

Answer = {24*60 *16/11 }/64.

= 32 8/11 mints.

Imagine the hour and minute hand in case of 8:40, and divide the clock into 4 quarters (Each quarter defined from 12 to 3, 3 to 6, 6 to 9 and 9 to 12).

When u are seeing the clock, the time 8:40 is basically at the one to the left hand, bottom quarter(ie. in between 6 to 9) while its mirror image should be at the right hand bottom quarter(ie. between 3 to 6).

Since in a mirror image the one's in the left side take the position to your right, while those in the right side shifts to the left, hence 8:40 will correspond to 3:20 in the mirror image.

@ Shivangi is absolutely right. Check her explanation. Its easily explained.

Even now if you don't understand how 55 min are covered in 60 min then here is simple explanation.

Take it as a metaphor. Assume hour hand to be tortoise and minute hand to be hare. Now after 60 seconds you will see that hare had traveled 60 minute distance while tortoise had traveled only 5 minute distance. So you can say hare gained 55 minute or 55 spaces to tortoise. So finally you can say minute hand gained 55 spaces to hour hand.

Just imagine hour hand and minute hand starting at 12 O'clock. After 1 hour, the minute hand will be at 12 whereas the hour hand will be at 1. So what is the difference between them? it's 55 "Minute Space".

So, it takes 1 hour to cover 55 minute spaces, for overlapping they should cover total 60 minute space.

Thus, here is the calculation:

1 hr --> 55 minute space.

? hr --> 60 minute space.

(1*60) /55 hour = 60/55 * 60 minute // converting hr to mins.

= 65 5/11 minute.

Solution:

In 1 hour both the hands cover 55 min space.
=> 60/55 = 12/11 min space covered in 1min of the actual time.

for the hand to coincide hands have to cover 60 min space
=> 12/11 * 60 = 720/11 = 65.5/11 min in actual clock.

But the clock coincides every 64 min.
=>65.5/11 - 64 = 1.5/11 = 16/11 min loss in 64min.
=>16/11 * 1/64 = 1/44 min loss in 1min.

Loss In 24 Hrs => 1/44 * (24 *60) = 360/11 = 32.8/11 min the clock looses in a day.

Simple solution. Don't get confused.

Just remember that in normal clocks the minute hand and the hour hand universally takes. (6.5/11) minutes to coincide. But in error clock it takes only 64 mins.

Hence the time lost is 6.5/11-64 = 16/11.

Now the total mins in a day are 24*60 = 1440.

Now divide 1440 in equal parts of 64. i.e 1440/64 = 22.5.

Therefore. The error in 64 mins was 16/11.

Hence the error in 1440 mins is = 22. 5*16/11 = 32.8/11.

Simple.

The universal rule is , hands of any accurate clock meets after 65 5/11 [=(11*65+5)/11] minutes.

But here the clock is taking 64 minutes to meet !
Hence , the error is [65 5/11]-[64] mints -> 16/11 minutes .

Now , total minutes in a day is = 24 hrs* 60 minutes= 1440 minutes.

Now, we know , the error in 64 mins was --> 16/11.
Means in 1 min ---> 16/11*1/64.

So in 11440 mins---> (16/11*1/64)*11440.
Which equals to ---> 360/11 Answer.

@Harish.

To find mirror image of a given time, there are two approaches, one is to draw the clock on paper indicating the time given and then find the mirror image of the hour hand and minute hand.

This is time consuming. The other method requires you only to subtract the given time from 12:00, and result will be your answer.

For the example you've given 8:40.

Subtract it from 12:00, we'll have 3:20 which is the right answer.

Total minutes per day: 24 x 60 = 1440.

Minute and hour hands coincide 22 times per day so, 1440/22 = 720/11 = 65 5/11.

Here in question, it coincides every 64 mins.
So, loss in every coincide is;
65 5/11 - 64 = 16/11 or 1 5/11.

Therefore,
Loss per every coincide x number of coincide per day = total loss per day.
So, 16/11 x 22 = 32 mins per day.


@All
Please, anyone, explain me why divided by 64 and multiply by 24 and 60.

It is universal truth that watch does not lose any time.Every day start from 12:00 am in night, hr. and min hand positioned at 0 degree,than how lose? no lose is there..

But suppose hands coincide every 64 min.
(In really it is not possible..eg if ones they coincide it take 65+5/11 min always for next)
there will be lose of 65+5/11 - 64= 16/11 from actual or real time in 65+5/11 min.

So calculate lose in 1 day= 24*60 min