Aptitude - Clock - Discussion

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.

I think it's 90 min.

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).

@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.

Agree @Abdeali Chitalwala.

You are absolutely right.

@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.

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.

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.

@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.

How 1/64? Please explain.