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

Question

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

This question has already been discussed no conclusive answer as yet ....
I tried this way but I got stuck ..
since in one minute clock cover = 360/60 = 6 degrees 
degree gained by clock in 12 hours = 2 min = 2*6 = 12 
simlarly degrees lost by the other clock = 12 degrees
hence after 24 hours ....difference in time .. 8 min = 8*6 = 48 degreses

distance between two hands = 360- 48 = 312 degrees .. ...

time when this distance will be 0 = 312/ 24 = 12 ( complete cycle of watch) i.e it will take complete 12 days to time to be same and hence the time will be 12 noon....

kindly see if this is the correct ...

Source of question : GMAT club ....

Oa - Sorry was not mentioned 
regards

Bunuel · Accepted Answer

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.

Answer: B.

Hope it's clear.

jlgdr · Answer

This problem tests the concept of relative rates We have that a wall clack gains 2 min every 12 hours Another one loses two minutes every 36 hours First we need to get the rates to be equivalent so multiplying the first by three we get 6 min every 36 hours Now, if they move 8 min apart in 36 hours, how much will it take them to show the same time. Well one has to imagine that one of the needles is fixed and the other will move 8 min every 36 hours until it makes a whole turn and reaches the same point. That is the basic concept of relative rates. To do so, since it is a wall clock, we will need it to turn a distance equivalent to 12 hours. Now 12*60 = 720 minutes. So by direct proportionality we get 720*36/8 that is the time it will take in minutes, divide by 60 to get the time in hours. One will get 54 hours Now since its 54 hours therefore, it will show exactly the same time cause we have no remainder. So B is our best answer here Is this clear? Hope it helps Cheers! J

soumanag · Answer

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.
 
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.

mainhoon · Answer

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...

gauravnagpal · Answer

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

martie11 · Answer

Thanks for the question.

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

Thank you...

maaadhu · Answer

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.

Bunuel · Answer

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.

maaadhu · Answer

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.

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?

maaadhu · Answer

Sorry I didnt see the choice 12 Night

grant1377 · Answer

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.

ShripadRS · Answer

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.

Answer: B.

Hope it's clear.

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?
Please help to clear my doubt.

Thanks

himanshujovi · Answer

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)

himanshujovi · Answer

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.

sharadjhaver · Answer

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.

Answer: B.

Hope it's clear.

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.
Please explain.

GMATinsight · Answer

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

Answer: option B

GMATinsight · Answer

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!

gracie · Answer

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

anooshehka · Answer

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

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

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

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