Aptitude - Clock - Discussion

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

55 min. Spaces are gained by minute hand in 60 min period.

To find how many spaces it has actually gained, we need to fix a standard point first. !

With respect to it, we need to see the difference by how much is it actually varying. !

So let us assume the standard point to be the place where the minutes hand and hours hand has been coincided. !

I may be 12:00, 1.06, 2.11, 3.17. etc. from there. 60 minutes implies the minute hand must come back to the same point where it has started. !

Is it not. ?

Now, 60 minute passed and so minute hand covers 60 minute spaces.

And the hour hand advances by 5 minute spaces. !

So from the standard point fixed initially (we assumed the standard point is where the minute point and hours hand were coinciding. Also. 60 minutes will be passed when the minute hand comes back to the same position from where it started).

Now, there is.

An absolute 60 min spaces covered by minute hand in 60 min and then there is 5 min spaces advanced by hour hand in 60 min period. !

So on total.

Total advancement is 60-5 = 55 minute spaces. !

Pleaes clarify, whether the clock looses or gain in this question?

A watch which gains uniformly, is 5 minutes slow at 8 o' clock in the morning on Sunday and it is 5 min. 48 sec fast at 8 p. M. On following Sunday. When was it correct?

Well said Konxie.

I can't understand this problem 65*5/11-64

First consider in how many minutes, hands should coincide.
55 min. spaces are covered in 60 min.
60 min. spaces will be covered in, 65 (5/11) i.e. 65.45 minutes.

But this clock is taking 64 minutes to coincide hence it is 1.45 min slow to actual time (65.45-64=1.45).

In 64 min of journey clock is 1.45 min slow, then
in 24*60 min it will 32.62 min slow.

=(24*60*1.45*1)/64= 32.62 or 32(8/11).

I am not able to understand how 55 min. Spaces are gained by minute hand in 60 min period. Can anybody explain?

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.

Why does everybody say that the minute hand does a complete circle in exactly 1 hour, when it is evidently not so (since the clock is losing time)?

The solution should be like this:

Let Wm be the angular speed of the minute hand, in radians per astronomical minute, and Wh be the angular speed of the hour hand. The constraint of the clock mechanism requires that Wh=Wm/12 (per each full revolution of the hour hand, the minute hand makes 12 full revolutions).

The requirement that the hands meet every 64 minutes is:

Wm*t = Wh*t + 2*pi, where t=64 astronomical minutes (astronomical minutes = actual minutes!).

Hence we have Wm*(11/12) = 2*pi/64,

or Wm = 2*pi*(12/11/64) rad/ast. minute, giving a period of revolution of (11/12)*64 = 58.6(6) astronomical minutes per revolution.

In 1 astronomical hour the minute hand covers Wm*60 = 2*pi*(60/64)*(12/11) radians, or simply 90/88=1+1/44 of a full revolution. Thus after each astronomical hour the minute hand shows 1/44*60 "clock minutes" more than the number of astronomical minutes passed.

In other words, each astronomical hour the clock GAINS 15/11 of a minute. Thus it GAINS (15/11)*24 = 32+8/11 clock minutes per astronomical day (i.e., each astronomical day it shows time which is 32+8/11 minutes more than the actual astronomical time).