A person observes that his minute’s hand hours hand coincide every 65 min. Does the watch gain or lose time? If so, how much?

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harsha

  • Oct 29th, 2006
 

it gains by 5/11 minutes.

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G.S.Manikandan

  • Oct 30th, 2006
 

yes

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santosh

  • Nov 1st, 2006
 

The clock is gaining by 5/11 minutes

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nitin

  • Dec 12th, 2006
 

isnt it 5/13........in 65 minutes hour hand will move (65/2) degreeand minute hand is gaining (65/2) - 30(degree) i.e. (5/2)degree........i.e in 65 minutes its gaining (5/2) degreethen in 60 minutes it will gain (30/13) degreei.e. minute hand is (30/13) degree i.e. 5/13 minutes

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sandeep tripathy

  • Dec 26th, 2006
 

when hour hand moves for 5 minutes spaces then minutes hand moves for 60minutes spaces therefore relative speed between two hands is 55 minutes space but according to question it is 65 minutes space between the two hands

hence actual difference in minutes is 60/55*65

=(1+1/11)*65

=65+65/11

=70+10/11

therefore the clock gains 10+10/11 minutes.

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shashank_tangwan

  • Mar 1st, 2007
 

Hold on folks , before doing all the  calculations just pause and think . Is the clock really out of time??!!

Well , I don't think so .  Here is how :

Assume it is 12 o clock. Now , the min & hr hand are OVERLAPPING .

Now when will they overlapp again ??

In another 60 mins ? .............. The Ans is  NO..

In 60 mins the min hand will be on 12 and the hr hand will be on 1 ......So it will take another 5 mins(approx) for the min hand to overlapp the hr hand

So, total time taken = 60 mins + 5 mins= 65 mins.  ...........  Actually every clock takes 65 mins for the min hand & hr hand to overlap successively..... Thus the clock neither loses nor gains any time... ..................... Any other confusion ? write back 

shashank_tangwan

  • Mar 1st, 2007
 

CORRECTION :

There is a discrepancy of 5/11 mins in overlapping and it gains by this much time in 65 mins ..................  Which means that :

correct clock takes 65 & 5/11 mins to overlap where this one takes 65 mins

so ,
 
correct clock takes 60 mins to complete an hour  while this one takes 59 & 7/12 mins


hence the actual gain / hr is  ---> 60 - (59 + 7/12) = 5/12 mins...

Hence the actual gain per hour  is 5/12 mins  & Not 5/11 mins

P.S. --> Please ignore my earlier post (which is incorrect), it was a hasty reply. My apologies

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kiranaar10728

  • Jun 18th, 2008
 

the time required for minute hand and hour hand to coincide is 60+5+5/12+5/12^2+............. it's a Gp and time=60+5*(1+1/12+1/12^2+........)=720/11
here it takes only 65min for it to coincide,so the clock is running fast by720/11 -65=5/11min.
i hope my answer meets ur satisfaction.

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mayank08bansal

  • Dec 21st, 2009
 

Let us suppose both hand's are on 12.
After 65 mins, i.e 1:05,   min hand is on 1 and hour hand will be littly in front of 1 because the time is 1:05.
Now if min hand covvers 60mins then hour hand covers 5 and for 5 mins,  hour hand will cover 1/6.
Right?

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