Aptitude - Clock - Discussion

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?

Say its 12 o' clock:
The minute hand and the hour hand points towards 12

After an hour i.e at 1 o' clock:
The minute hand points at 12 and the hour hand points 1

The difference between the two hands after 60 min (1 hr) is 55 spaces but the hands did not coincide!

They will coincide when 60 spaces are covered

And to cover 60 spaces it takes = (60/55*60) = 65.4545 min (in a normal clock)

Now given in question is that the hands coincide at 64 min (defective clock)

So loss in time when the hands coincide is 65.4545 - 64 = 1.4545 min (this loss happens for every 64 min in our defective clock)

So for 1 min our loss is = 1.4545/64 min

For a day 1.4545/64*(24*60) = 32.7 min

@Naresh : just remember this

If coinciding time > 65(5/11) then our clock is going slow than normal (our watch is loosing time) and if coinciding time < 65(5/11) then its going fast than normal (or gaining time).

By 65(5/11) i mean 65.4545 and not (65*5)11

And we say loosing time in questions just to state the irregularity in time.

HOPE THIS CLEARS IT ALL

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).

Walking at 4/5 of his usual speed a man is 10 min too late. Find his usual time?