Aptitude - Clock - Discussion

Gain means the clock's hands are moving fast than actual time (i.e it takes less than 60minutes for minute's hand to complete 360 degrees).

Initially, the time in given clock is 11:58am but the actual time is 12 pm (this might be because someone changed the time to 11:58 in given clock).

Since the clock is moving fast it's time is 4min 48sec fast on following Monday. Now at one point in between present Monday to next Monday the given clock's time coincides with normal clock's time (i.e correct time). Now total time from 12 pm to next Monday 2pm is 170hours. Total time gain by given clock = 2+ (4min 48sec) = 34/5min in 170 hours. What we need now is 'When it shows the correct time. ' If clock gains those 2minutes which it is lagging initially then it shows the correct time. 34/5min gain in 170hours then 2min will gain in 170*2* (5/34) hours.

@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.

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]

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.

A watch which "gains" uniformly is 2 minutes low at noon.

Since, gain word is used hence we will add on all the gains (i.e 2+4 min 48 sec = which turns on to be 24/5 min).

Total gain=> 2+24/5 = 34/5 min.

Hence, 34/5 mins are gained in 170 hrs (7*24+2).

Then, 2 mins will be gained in x hrs.

We get x hrs = 50 hrs (from cross multiplying above two equations).

Now, 2 mins are gained in 50 hrs which can be written as 2*24+2 (i.e 2 days and 2 hrs).

After Monday if we calculate 2 days and 2 hrs we get Wednesday and 2 hrs which is the answer to the question.

Cheers!

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.

Here, the clock was late by 2 min. And then it gains 4 min 48 sec. Means we have to cover 2 min time as well as 4 min 4 sec time also.

Therefore total gain = 2 + 24/5 = 34/5 min in 7 days 2 hrs (170 hrs).

Here, extra 2 min of which we are a late need to be covered to make the time correct are gained in.

Therefore 34/5 min = 170.

1 min = 170 * (5/34),

2 min = 2 * 170 * (5/34),

2 min = 50 hrs.

i.e 2 days 2 hrs from Monday which is Wednesday 2 pm.

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.

The time total gain is (2+4min 48sec)i.e 20*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 wednes day 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.