Aptitude - Clock - Discussion

Agree @Abdeali Chitalwala.

You are absolutely right.

I think it's 90 min.

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.

As per the formula, it is;

((720/11) -64) * ( (60*24) /64).

Well explained & very simple. Thanks @Shivangi.

The speed is inversely proportional to time, if clock hands are fast they lose time and when clock hands are slow they gain time.

If the clock covers 60-minute spaces in 64 minutes instead of 65+ (5/11) then the clock is faster, hence losing time. (taking less time than actual time).

Use this formula,
((720/11)-M) x 24 x 60/M.
Here M is 64.

To coincide with each other space(ticks) between them should be ZERO(no space).

Consider starting from 12 noon.

in 1 hr--> min hand covers spaces(ticks) =60
in 1 hr--> hour hand covers spaces(ticks) = 5
so in 1 min --> hour hand covers 5/60=1/12 space(tick)

so after 1 hr=60 mins (1.00) spaces between them will be equal to 5
so have to cover 5 places for minute hand to meet hour hand
total time = 60+5 ... but in 5 mins hour hand will further go ahead by 5*1/12 ticks
so have to cover 5/12 ticks for minute hand to meet
total time = 60+5+5/12 ... but agin in 5/12 mins hour hand will go ahead buy 5/12*1/12= 5/12^2... and so on

So total time will be = 60+5+(5/12+5/12^2+5/12^3+.........) this GP
total time to meet = 720/11 i.e., 65.(5/11).

This time required to coincide hands in correct clock... solve accordingly.

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

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.