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At 3:00 PM, Monday clock was showing the right time 1st clock gains 5 mins in every 1 hour. 2nd clock loses 5 mins in every 1 hour. After how many hours both will show same time again? I know that the time difference between the two clock will be 10 minutes. 1st clock will show the time 4:05 PM and the 2nd clock will show the time 3:55 PM. But how come after exactly 12 hours both will show the same time again? I didn't understand this

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    After 12 hours, the first clock will show 4AM and the second will show 2AM. Are you sure you don't mean "after 12 days"? – 2017-01-23
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    How difference time will be 24 hours? – 2017-01-23
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    I am sure about this question. This is correct question – 2017-01-23

4 Answers 4

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It's equivalent to think of one clock going at a normal speed and the other clock gaining 10 mins every hour. The question then becomes how long before those 10 minute gains add up to 12 hours? After 6 hours the second clock will have gained an hour, so 12 lots of this will put the second clock 12 hours ahead. So the answer is $6\times 12 = 72$ hours. Double this if you're using a 24 hour clock.

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    How do we know that after 12 hours it will show the same time? – 2017-01-23
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    if you can help me with my query. How do we know that after 12 hours they will show the same time – 2017-01-23
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    If we're using a 12 hour clock, then a clock that is 12 hours fast shows the correct time. – 2017-01-23
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    How do you know that a clock that will be 12 hours fast will show the correct time. It is confusing – 2017-01-23
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    On a 12 hour clock, we know it is 6 o'clock when the big hand is pointing up and the little hand is pointing down. But you don't know if it's 6am or 6pm. So when two clocks differ by 12 hours, both will look the same. It's the same principle as with a 24 hour clock, where they will both look the same after one has gained 24 hours over the other one. – 2017-01-23
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    How it is the same in this case – 2017-01-23
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    After 12 hours also it will have a time difference of 15 minutes. How it can be same? – 2017-01-23
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    They look the same when one has gained 12 hours relative to the other one. This takes 72 hours to happen. – 2017-01-23
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Clock1 - Clock2

mon:

3:00pm - 3:00pm

4:05pm - 3:55pm ....

tue morning:

3:00am - 2:00am ...

so, through this progression we can see that every 12 hours there will be a variation of 1 hour. therefore the clocks will meet exactly at 3:00 o'clock, 3 days later.

Its supposed to meet after 6 days if you want them in 24hour clock.

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    Answer is 72 hours – 2017-01-23
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    is it better? @beginnercoder – 2017-01-23
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Look at this in tho eother pespective:

1st clock is $5$[ticks/h] faster, than normal clock. 2nd clock is $5$[ticks/h] slower, than normal clock.

We know, that the whole cycle of clock lasts $24\cdot 60$ [tics].

Let's place the boundaries of this cycle on points A and B. Now we have the question:

Cities A and B are $24\cdot 60$[ticks] away from each other. From A to B travels a train with velocity $5$[ticks/h], from B to A travels another train with velocity $5$[ticks/h]. Both trains have started at 3PM, Monday. When the trains will meet each other?

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Divide the $12$-hour clock into $144$ five-minute intervals (there are $12$ hours on the clock and $12$ five-minute intervals per hour; $12\cdot12=144$). The first clock advances $13h$ intervals every $h$ hours, and the second advances $11h$.

We want to find the smallest positive $h$ for which $13h \equiv 11h \pmod {144}$. In other words, $$2h \equiv 0 \pmod {144},$$ so $h=72$.