Aptitude - Clock - Discussion

See, it is given in the question that the clock is initially 2 minutes slow and after 7 days and 2 hours it is 4 minutes 48 seconds fast. So in this whole journey of 7 days and 2 hours the clock has to first gain that 2 minutes which is lost initially, then only the clock will be able to gain 4 minutes 48 seconds.

So, it is asked in the question that when between the journey the clock will gain that 2minutes.

Hope it helps.

(2 min + 4 min 48 seconds)=(408 seconds).

For 170 hours.

For 1 hr (408/170)=2.4 seconds,
For 120 seconds(2 min initially),
Hours=(120/2.4)=50.

So Wednesday 2 PM.

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.

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]

@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.

Finally, I satisfied with the answers of @Akash vashista and Shashank. Thanks, both of them.

Gains uniformly is 2 minutes low. means clock is 2 min late at noon on Monday.

Now on next Monday it is 4 min 48 sec fast means it total gain is,
= ( 2 min + 4min 48sec).
The time total gain is (2+4min 48sec)i.e 2*60+4*60+48=408 Sec.
means 408 sec covered in 170 hrs (from this Monday to fallowing Monday means 7 * 24 = 168hrs + from 12.00pm to 2.00pm means 2hrs, i.e 168+2=170hrs),
In 1hrs 85/204 sec covered (170/408).
So to cover 120 sec (2mns)how many hours taken.

=(85/204)*120,
=50 hrs.

To cover 2mns it takes 50hrs. so it will show correct time on 2 days 2 hrs after (2*24+2=50)i.e Wednesday 2.00 PM.

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.

@Nitin

Initially, it is 2 min low at 12 pm so to compensate that loss 2min gain is there but at last, why do they calculate for 2 min gain individually? Explain it.

2 min late means that at some point it will show correct time and then after that it gains 4 min 48 sec. So total gain= 2min to correct time to 4 min 48 sec i.e. 2+4min48sec.