Aptitude - Clock - Discussion

@Dawa Tshering.

Total minutes per day: 24 x 60 = 1440.

Minute and hour hands coincide 22 times per day so, 1440/22.
= 720/11,
= 65 5/11.

Here in question, it coincides every 64 mins.
So, loss in every coincide is;
65 5/11 - 64 = 16/11 or 1 5/11.

Till this you are correct!

However the no of coincidence per day is 22 for a normal clock.
In this peculiar clock, the coincidence happens every 64 mins.
Therefore, in 24 hours the no of coincidence is ( 24*60)/64 which is 22.5.
That means in 24 hours, this peculiar clock coincides 22.5 times.

Now, going by your logic,
Loss per every coincide x number of coincide per day = total loss.
So, 16/11 x 22.5 = 32 8/11 mins per day.

@Jess.

See for an hour the min hand has to travel 60 spaces(ticks) right?

And for the same hour, the hour hand travels only 5 spaces(ticks).
So the actual displacement by both in the same direction is = the difference between the spaces travelled.

then, the time spaces travelled is 60-5=55 min(representing each tick, not the actual minute) spaces.

And the total minute spaces travelled for a minute is 60/55 right?

then, for an hour it is (60/55)*60 which is equal to 720/11 = 65.4545 giving the time for each coincidence of the min and hour hand.

If the given value(coincidence time) is >65.4545 means your watch is losing time i.e. clock is slower.

If the given value is <65.4545 means your watch is gaining time i.e. clock is faster
Here the coincidence time is 64 hence, 65.4545 - 64 = 1.4545 this is for 64 mins.
Then for a minute, the time variation is 1.4545/64.
And to get the same for a day we multiply by 60 and 24.

Hence,
Time lost is (1.4545/64)*60*24 = 32.7272=32(8/11) min.

Total minutes per day: 24 x 60 = 1440.

Minute and hour hands coincide 22 times per day so, 1440/22 = 720/11 = 65 5/11.

Here in question, it coincides every 64 mins.
So, loss in every coincide is;
65 5/11 - 64 = 16/11 or 1 5/11.

Therefore,
Loss per every coincide x number of coincide per day = total loss per day.
So, 16/11 x 22 = 32 mins per day.


@All
Please, anyone, explain me why divided by 64 and multiply by 24 and 60.

The difference between time is 4min here.
Between 60 and 64 min, and I'd we take;
4min × 24 = 96, 96 is now common between.
60 and 64 min like 4 min, we need to find the difference for 64 min, so;
(64/24) × 96 = 256 =>32/11×8.

It's a proven fact that for a normal clock after every 720/11 = 65.4545 minutes both minute and hour hand meet.

In this case, the hour and minute hands are meeting after every 64 minutes which is less than 65.4545.

This clearly indicates the clock is going faster.

For every hour the clock is gaining 720/11 - 64 = 16/11 = 1.4545 minutes.

Hence, for 24 hours it will gain 24 * 16/11 = 34.909 = 34 10/11.

How 1/64? Please explain.

@All.

Since the Normal clock coincides after every 65.45 min. But in question, it is given that hands coincide after 64 mins. Hence, the clock is gaining time.

One day = 24 hours = 1440 minutes.
Hands meet every 65.5 minutes,
Number of times they meet = 1440 ÷ 65.5 ≈ 22 times.
Real clock: 65.5 minutes.
Your watch: 64 minutes.
Difference = 65.5 − 64 = 1.5 minutes per meeting.
Number of meetings × difference per meeting = 22 × 1.5 = 33 minutes.
Your watch loses about 32-33 minutes in one day.

The two hands of a clock coincide after a gap of every 65 5/11 minutes.

For example, if we consider the starting time at 12 . the two hands coincide exactly at 12. Again after 65 5/11 minutes both coincide. Means exactly at 1 5/11 minutes.

In the problem, the two hands of a clock coincide after 64 minutes give.

It means the clock is faster than usual. It means it is gaining time.

For Every 64 minutes the clock gains 65 5/11- 64 = 1 5/11 = 16/11 minutes.

It GAINS not Loses.

So in the problem, for 64 mints clock gains ( faster) 16/11 minutes.

Then it gains how much per day? ( for 24*60 hrs)

Answer = {24*60 *16/11 }/64.

= 32 8/11 mints.

The clock is GAINING 1 and 5/11 mins every hour and not losing.

There's an error in the question.

Hence, the clock will GAIN 32 and 8/11 mins in one day.