Aptitude - Clock - Discussion

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day does the clock gain or loss? Can anyone answer this?

2 mins are lost in begin but gradually as it is gaining 4 min and 48 sec, so in between, it might be on correct time at the instance,

So we do first check how much it gains, i.e

Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.

The watch gains
2 + 4 (4/5) min. or 34/5 min. in 170 hrs.

Now, 34/5 min. are gained in 170 hrs.

2 min. is gained in (170 x5/34x 2) hrs = 50 hrs. [This is which we lost in the beginning of the clock , as we lost 2 mins so we calculated how much it will take to recover]

It is 2:00 PM on Tuesday
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A watch gains uniformly is 2 min slow at 12:00 on Sunday.

On the following Sunday, it is 4 min 48 sec fast at 2 PM.

Total time between 12 AM and 2 PM on another sunday
= (24*7) + 2 hours.
= 170 hour.

Time gained = 4 min 48 sec + 2 min.
= 6 min 48 sec.
= 408 sec.

The clock will show the correct time only when it gains 2 min;

408 sec ----> in 170 hours.
120 sec ---> in x hour.
408/170 = 120/x.
x = 50 hours.
= 2 days 2 hours for noon on the Sunday.

Explain me clearly to get it.

Can you please explain the solution?

@All, According to me.

At 1st Monday noon, the clock was 2 mins low meaning 2 mins slow. Therefore to become the real clock timing, it needs to gain 2 mins here.

Gaining means the clock moves fast. So when the time is 2pm on Wednesday, the clock gives the real correct time. But the clock never stops Gaining. It continues to move faster. Therefore, the next Monday at 2pm it was already 4 mins 48 secs faster. Hence gain here will be 4 mins 48 secs.

From the start, it already gains 2 mins (as it has to keep with with the low 2 mins already stated in the beginning of the question). Hence, total time gain will be (2min+4min48sec). Hope you get the concept.

How we got 170 hrs above for 34/5?

Sir, why the clock show right time on gaining of 2 minutes?

Thank you everyone.

See, for gaining 4 mins and 48 seconds it should first gain from -2 to 0 (that is from loss to zero) so there it comes 2 mins gaining and remaining 4 minutes and 48 seconds gaining so totally 6 mins and 48 seconds gaining in 170 hours so 2 mins gaining comes in 50 hours. At 2 minutes gaining there was no error, so there the time was corrected. So 50 hours from starting time gives the answer.