Aptitude - Clock - Discussion

Please help me to know the completion of the problem within 1 minute.

Hands coincide every 65 min 27 secs (google it for proof) but here it happens every 64 min.

So it runs behind by 1 min 27s so for every 65 min 27 secs (3927s) there's delay of 1 min 27s (87).
Hence, for 24 hrs (86400s) there will be 87 * 86400/3927 = 1914.1329s = 31.90221 min, that's roughly 31 9/10min.

These type of questions won't be asked anyway.

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 a 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.

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

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

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

WHETHER THE CLOCK HAS GAINED OR LOST TIME?

We know from the calculation above that the two hands of the clock coincide every 65.45 mins.

But here it is mentioned that they meet every 64mins in the defective clock.

=> the clock is going fast.
=> in 24 hours it would be actually showing more than 24hours.
=> the clock has gained time!

I guess it is the wrong question because when hands coincide after 64 min I, e < 64 5/11 then clock will gain.

@Harish.

To find mirror time jus subtract given time as ==>hour time by 11 and min time by 60. You'll get the answer for ex 10.25.11- 10 = 1 & 60 - 25 = 35 so the time will be 1.35.

I can't get the question what it means? Please someone try to explain it.

Use this you will get any problem solved from clock M * 6° ~ (h + m/60) * 30°= Angle.

It actually does not cover 55 min space in 1 hr it covers 56.25 min space in 1 hr.

How could you all get 720/11 - 64 = 16/11? Please explain.