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# A wall clock gains 2 mins in 12 hrs, while a table clock

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Re: clock speed and time [#permalink]
I think your answer is correct however the times shown by both clocks will not be same after 12 days!!!

After 12 days i.e after 12X24 hours clock A will gain 48 mins and will show 12:48 noon
After 12 days i.e after 12X24 hours clock B will loose 16 mins and will show 11:44 am.

The two clocks will show same time after 135 days. The time difference has to be 12 hours between them = 720 mins.
[ A will gain 540 mins in 135 days & B will loose 180 mins in 135 days total 720 mins ]
Further if we consider only time then the problem becomes simpler:
Total difference of 8 mins between the times shown by the clocks after 36 hours
=> 16/3 min difference in 1 day => 12X60 min difference in (3/16)X(12X60)= 135 days
Please let me know what you think.
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Re: clock speed and time [#permalink]
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Clock 1 - +2mins/12hrs
Clock 2 - -2 mins/36 hrs

Clock1 - Clock2 = 8mins/36hrs difference
Both will read same when the difference is 12hrs = 720 mins. At the rate of 8mins/36hrs, you get a difference of 720mins when the real time elapsed is 720/8*36/24 days = 135 days...
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Re: clock speed and time [#permalink]
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mainhoon wrote:
Clock 1 - +2mins/12hrs
Clock 2 - -2 mins/36 hrs

Clock1 - Clock2 = 8mins/36hrs difference
Both will read same when the difference is 12hrs = 720 mins. At the rate of 8mins/36hrs, you get a difference of 720mins when the real time elapsed is 720/8*36/24 days = 135 days...

ph damn now I understand ....its a simple problem of LCM ....phew ...there is no need to get into degrees asnd all !!

understood thanx guys
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Re: clock speed and time [#permalink]
Thanks for the question.

Quote:
The time difference has to be 12 hours between them = 720 mins.

Unfortunately, I must be missing something...why does the time difference need to be 12 hours between them?

Thank you...
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Re: clock speed and time [#permalink]
Bunuel wrote:
up4gmat wrote:
Hi bunuel,
kindly explain how you got this :
A wall clock gains 2 minutes in 12 hours --> gains 6 mins in 12 hours;

Typo. Should read: A wall clock gains 2 minutes in 12 hours --> gains 6 mins in 36 hours;

Bunuel,

kindly explain "both to show the same time next wall clock should make 12 hours revolution". How can we not assume the same time 2 clocks meet will be 12:30 or 1:30.
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Re: clock speed and time [#permalink]
Bunuel wrote:
up4gmat wrote:
Hi bunuel,
kindly explain how you got this :
A wall clock gains 2 minutes in 12 hours --> gains 6 mins in 12 hours;

Typo. Should read: A wall clock gains 2 minutes in 12 hours --> gains 6 mins in 36 hours;

Bunuel,

kindly explain "both to show the same time next wall clock should make 12 hours revolution". How can we not assume the same time 2 clocks meet will be 12:30 or 1:30.

Both are set right at noon on Tuesday and we calculated that both will show the same time in exactly 135 days.

So, the correct time when they both show the same time next would be exactly after 135 days at 12 noon again.

Hope it's clear.
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Re: clock speed and time [#permalink]
Both are set right at noon on Tuesday and we calculated that both will show the same time in exactly 135 days.

So, the correct time when they both show the same time next would be exactly after 135 days at 12 noon again.

Hope it's clear.[/quote]

Bunuel,

Sorry if I am too dumb but If both the clocks have to show the same time i.e. 12 Noon, doesn't the question has the answer? Should the question be reworded and include answer choices that include the number of days they will meet again?
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Re: clock speed and time [#permalink]
Sorry I didnt see the choice 12 Night
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Re: clock speed and time [#permalink]
Bunuel wrote:
A wall clock gains 2 mins in 12 hrs, while a table clock loses 2 mins in 36 hrs; both are set right at noon on Tuesday.The correct time when they both show the same time next would be
a. 12.30 night
b. 12 noon
c. 1.30 night
d. 12 night

A wall clock gains 2 minutes in 12 hours --> gains 6 mins in 36 hours;
A table clock loses 2 minutes in 36 hours;

Relative speed is 6+2=8 minutes in 36 hours (difference in 36 hours), which means that if we consider a table clock to stay still then a wall clock will move 8 minutes in 36 hours, so both to show the same time next wall clock should make 12 hours revolution (12*60=720 minutes), which it would make in 720/8 * 36 hours = 135 days.

So, the correct time when they both show the same time next would be exactly after 135 days at 12 noon.

Hope it's clear.

Can someone please explain how you get from 8 minutes in 36 hours to 12 hours revolutions the next time they will show equal? I'm having trouble figuring this out. Thank you.
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Re: clock speed and time [#permalink]
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A wall clock gains 2 mins in 12 hrs, while a table clock loses 2 mins in 36 hrs; both are set right at noon on Tuesday.The correct time when they both show the same time next would be
a. 12.30 night
b. 12 noon
c. 1.30 night
d. 12 night

A wall clock gains 2 minutes in 12 hours --> gains 6 mins in 36 hours;
A table clock loses 2 minutes in 36 hours;

Relative speed is 6+2=8 minutes in 36 hours (difference in 36 hours), which means that if we consider a table clock to stay still then a wall clock will move 8 minutes in 36 hours, so both to show the same time next wall clock should make 12 hours revolution (12*60=720 minutes), which it would make in 720/8 * 36 hours = 135 days.

So, the correct time when they both show the same time next would be exactly after 135 days at 12 noon.

Hope it's clear.[/quote]

Hi Benuel,

Since we are setting both clocks to 12 noon and we want them to be showing the same time next, shouldnt the wall clock make 24 revolutions so that next time it shows same 12 NOON?
By taking 12 hrs as mentioned in the explanation above, the clock will show 12 Midnight.
Or is noon/midnight iirrelevant?

Thanks
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Re: clock speed and time [#permalink]
martie11 wrote:
Thanks for the question.

Quote:
The time difference has to be 12 hours between them = 720 mins.

Unfortunately, I must be missing something...why does the time difference need to be 12 hours between them?

Thank you...

Because it analog clock i.e. no demarcation between AM and PM so say 6 a.m will be equal to 6 p.m ( difference of 12 hrs)
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Re: A wall clock gains 2 minutes in 12 hours, while a table [#permalink]
Bunuel wrote:
SrinathVangala wrote:
A wall clock gains 2 minutes in 12 hours, while a table clock loses 12 minutes in 36 hours;both are set right at noon on tuesday . The correct time when they both show smae time next would be

A. 12:30 night
B. 12 noon
C. 1:30 night
D. 12 night
E. 11:30 noon

Merging similar topics.

Bunuel - Can it be answered like this?

Clock 1 gains 2 minutes in 12 hrs so it will gain 12 hrs ( 12*60 minutes) in ( 12*12*60) / 2 hrs

Similarly Clock 2 loses 2 minutes in 36 hrs so it will lose 12 hrs in (12*36*60 ) /2

For both the clock to show same time , they should have lost/gained a multiple of 12 hrs i.e LCM of the two times which is 12*36*60/2 which again is a multiple of 24 ( number of hours in a day) so they will show same time after n number of days but at same time i.e. 12:00 noon.
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Re: A wall clock gains 2 mins in 12 hrs, while a table clock [#permalink]
A wall clock gains 2 mins in 12 hrs, while a table clock loses 2 mins in 36 hrs; both are set right at noon on Tuesday.The correct time when they both show the same time next would be[/b]
a. 12.30 night
b. 12 noon
c. 1.30 night
d. 12 night

A wall clock gains 2 minutes in 12 hours --> gains 6 mins in 36 hours;
A table clock loses 2 minutes in 36 hours;

Relative speed is 6+2=8 minutes in 36 hours (difference in 36 hours), which means that if we consider a table clock to stay still then a wall clock will move 8 minutes in 36 hours, so both to show the same time next wall clock should make 12 hours revolution (12*60=720 minutes), which it would make in 720/8 * 36 hours = 135 days.

So, the correct time when they both show the same time next would be exactly after 135 days at 12 noon.

Hope it's clear.[/quote]

Hi Bunuel,

I am not able to understand how both clocks show correct time after 12hours.
Though i can understand the initial solution till relative speeds, i cant visualise the final part.
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Re: A wall clock gains 2 mins in 12 hrs, while a table clock [#permalink]
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gauravnagpal wrote:
A wall clock gains 2 mins in 12 hrs, while a table clock loses 2 mins in 36 hrs; both are set right at noon on Tuesday. The correct time when they both show the same time next would be

A. 12.30 night
B. 12 noon
C. 1.30 night
D. 12 night

CONCEPT: A faulty clock shows the correct time when the clock is either 12 hours behind the correct time of 12 hours ahead of correct time

Clock1 gains 2 mins in 12 hrs
i.e. Clock1 gains 60 mins (1 Hour) in 360 hrs(15 days)
i.e. Clock1 gains 12 hours in 15*12 = after 180 days same time

Clock2 Loses 2 mins in 36 hrs
i.e. Clock2 Loses 60 mins (1 Hour) in 1080 hrs(45 days)
i.e. Clock2 Loses 12 hours in 45*12 = 540 days same time

Both Clocks will show the same time after a time (days) that is a common multiple of 180 and 540 = 540 days and same time

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Re: A wall clock gains 2 mins in 12 hrs, while a table clock [#permalink]
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Hi Bunuel,

I am not able to understand how both clocks show correct time after 12hours.
Though i can understand the initial solution till relative speeds, i cant visualise the final part.

To understand why the clock shows the correct time after 12 hours
"Suppose your clock stops due to low battery at 10 AM then look at the clock at 10 PM same day and you will see the stopped clock showing the correct time cause it has gone 12 hours behind the correct time"

In 12 Hours gap from the correct time, AM turns into PM or vice versa but the hands of clock are found at the same position and Clock doesn't tell us whether it's AM or PM it just shows the time which looks correct.

I hope it helps!
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A wall clock gains 2 mins in 12 hrs, while a table clock [#permalink]
A wall clock gains 2 mins in 12 hrs, while a table clock loses 2 mins in 36 hrs; both are set right at noon on Tuesday. The correct time when they both show the same time next would be

A. 12.30 night
B. 12 noon
C. 1.30 night
D. 12 night

one way to look at it is as a distance/rate problem
combined distance=12 hours=720 minutes
combined rate=1/6 minute per hour+1/18 mph=2/9 mph
(720 m)/(2/9 mph)=3240 hours
3240/24=135 days
12 noon
B

Originally posted by gracie on 11 Nov 2015, 14:57.
Last edited by gracie on 11 Jun 2017, 20:38, edited 1 time in total.
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Re: A wall clock gains 2 mins in 12 hrs, while a table clock [#permalink]
Dear Bunuel,

Could you kindly explain the logic behind the following reasoning that you have made (AFter reviewing the question and answer of the same from others I am still confused):

so both to show the same time next wall clock should make 12 hours revolution (12*60=720 minutes), which it would make in 720/8 * 36 hours = 135 days

sincerely,

Anoosheh
Re: A wall clock gains 2 mins in 12 hrs, while a table clock [#permalink]
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