Aptitude - Clock - Discussion

My 2 cents:

So far we know that it takes 60 min for the minute hand to gain a 55 min space lead over the hour hand. We assume that a 60 min space lead actually means that the two hands coincide.

The time required for a 60 min space lead would be 60*60/55 min for a normal clock. Instead of this, the error clock has a time requirement of 64 min for the min hand to gain a 60 min space lead over the hour hand.

With this new value we now try to calculate how many minutes the error clock would take for it's min hand to gain a 55 min space lead. Basically- "how many minutes of the error clock would signify i hour for the normal clock?"

This works out to be 64*55/60 min..which is 58.6666 min.

So for a normal clock which counts 60 minutes (1 hour), the error clock has clocked up 60/58.6666 min(1.022 hours).

Over a period of 24 hours, the error clock has would gain 24*1.022 hours=24.4545 hours. The difference being 24.4545-24 hr
Which is equal to .4545 hr = .4545*60 min = 32.72 min ~32 8/11 .

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.

I am unable to understand this question what is it?

I can't understand this question please explain in easy language.

@Raman,

We know that the two hands (hour hand and min hand) of a clock coincide after 60 mins.

The question here is if the hands of the clock coincide after every 64 mins instead of 60 mins, how much time the clock/watch will lose in a day.

From the above comments, I can see many people are confused that if the hands coincide after every 64 mins instead of 60mins, then how come the clock/watch is losing time!

If the hands are coinciding after 64 mins instead of 60 mins, it means they are taking more time to coincide. The longer the hands take to coincide, the more time they lose.

Say for example, the time is 12 pm. In normal clock it will take 60 mins for the hands to coincide, that is to strike 1 pm. Now, as given in the example, if the hands coincide after 64 mins, it means the clock/watch will strike 1 pm after 64 mins instead of 60 mins. So it means where it took 60 mins to complete one hour, it is taking 64 mins. So here it is losing time.

Hope, this helps! :).

Why multiplied with 1/64 in last step?

This is gaining clock because it moves faster than original clock. Explain me.

How to find the mirror image when the time is 8:40?

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.

Generally hands will coincide every 1 hour:5min:(5/11)th of a minute.

According to the problem hands will coincide every 1hour:4min.

So the lose per 1 coincidence 1 min:(5/11)th of a minute.

Number of coincidences per day is 22.

So the lose per 1 day is 22min:(110/11) or is 32min.