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A, B and C run around a circular track starting from the same point

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Bunuel
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A, B and C run around a circular track starting from the same point [#permalink] A, B and C run around a circular track starting from the same point   22 Jul 2016, 03:53
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A
B
C
D
E

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65% (hard)

Question Stats:

63% (02:44) correct 37% (02:28) wrong based on 397 sessions
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A, B and C run around a circular track starting from the same point simultaneously and in the same direction at speeds of 4 kmph, 6 kmph and 8 kmph respectively. If the length of the track is 400 meters, when will A, B and C meet at the starting point for the first time after they started the race?

A. 1 minute
B. 5 minutes
C. 12 minutes
D. 20 minutes
E. 24 minutes
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C
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DensetsuNo
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Re: A, B and C run around a circular track starting from the same point [#permalink] A, B and C run around a circular track starting from the same point   22 Jul 2016, 08:55
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A: 400 metres in 6 minutes
B: 400 metres in 4 minutes
C: 400 metres in 3 minutes

LCM? 12

Answer C)
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hsbinfy
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A, B and C run around a circular track starting from the same point [#permalink] A, B and C run around a circular track starting from the same point   22 Jul 2016, 04:09
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take lcm of 4,6,8

24

ans E

till that time A will have 6 revs
b will 4revs and c will have 3 revs
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A, B and C run around a circular track starting from the same point [#permalink] A, B and C run around a circular track starting from the same point   22 Jul 2016, 04:49
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4 kmph, 6 kmph and 8 kmph is equal to 4000/60 mtrs/min, 6000/60 mtrs/min and 8000/60 mtrs/min or 200/3, 100, 400/3 mtrs/min respectively.

Seeing this we can infer that the answer should be at least divisible by 3. (minutes in options are integers. So if the answer is not divisible by 3, we will have 200/3*answer = distance traveled by A in fractions whereas 100*answer = distance traveled by A as integer)

So, A,B and D are out.

At 12 min A,B and C will travel 800, 1200 and 1600 mtrs respectively. Length of the circle is given as 400 mtrs.

As 800, 1200 and 1600 are divisible by 400, we can say that A,B and C will be at starting point after 12 min.

Hence, C will be the answer.
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Re: A, B and C run around a circular track starting from the same point [#permalink] A, B and C run around a circular track starting from the same point   22 Jul 2016, 08:41
hsbinfy wrote:
take lcm of 4,6,8

24

ans E

till that time A will have 6 revs
b will 4revs and c will have 3 revs


we are given values in hour & answers in mins :)
do convert

Ans 12
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Re: A, B and C run around a circular track starting from the same point [#permalink] A, B and C run around a circular track starting from the same point   22 Jul 2016, 09:54
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time taken by A ,B and C to complete a round will be 6,4,3 mins respectively.
LCM of 6,4,3= 12
so they will meet at starting point after 12 mins

ANS C
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Re: A, B and C run around a circular track starting from the same point [#permalink] A, B and C run around a circular track starting from the same point   28 Jul 2016, 13:36
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Bunuel wrote:
A, B and C run around a circular track starting from the same point simultaneously and in the same direction at speeds of 4 kmph, 6 kmph and 8 kmph respectively. If the length of the track is 400 meters, when will A, B and C meet at the starting point for the first time after they started the race?

A. 1 minute
B. 5 minutes
C. 12 minutes
D. 20 minutes
E. 24 minutes


Respective speed of A, B and C= 4000/60 , 6000/60, 8000/60 km/h

Time required by A= 400 *60/4000= 6 mins
Time required by B= 400*60/6000= 4 mins
Time required by C = 400 *60/8000= 3 mins

Time when these three first meet= LCM of 6, 4 and 3= 12 mins

C is the answer
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Re: A, B and C run around a circular track starting from the same point [#permalink] A, B and C run around a circular track starting from the same point   25 Oct 2018, 02:39
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Please suggest if my method to solve this question is right.

Distance is same for A, B and C= 400 meters.
Since they are going in same direction, relative speed can be calculated: 8-6-4= 2kmph

Time = (400/2*1000)*60= 12 min.
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Re: A, B and C run around a circular track starting from the same point [#permalink] A, B and C run around a circular track starting from the same point   23 Sep 2020, 08:27
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Rate A = 4, 000 meters per hour

Time to complete 1 Lap for A= 400 / 4,000= 1/10 hr = 6 min


Rate B = 6, 000 meters per hour

Time to complete 1 Lap for B = 400/6,000 = 4/60 hr = 4 min


Rate C = 8,000 meters per hour

Time to complete 1 Lap for C = 400/8,000 = 1/20 hr = 3 min

All 3 will meet at the starting point again at the LCM of the times it takes for each to complete 1 Lap

LCM ( 6 min ; 4 min ; 3 min) = 12 min


Answer: 12 minutes

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Re: A, B and C run around a circular track starting from the same point [#permalink] A, B and C run around a circular track starting from the same point   03 May 2024, 13:25
Ananya1919 wrote:
Please suggest if my method to solve this question is right.

Distance is same for A, B and C= 400 meters.
Since they are going in same direction, relative speed can be calculated: 8-6-4= 2kmph

Time = (400/2*1000)*60= 12 min.

­ Bunuel can you tell us if this is a correct way ?
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Re: A, B and C run around a circular track starting from the same point [#permalink] A, B and C run around a circular track starting from the same point   15 May 2024, 09:07
hsbinfy wrote:
take lcm of 4,6,8

24

ans E

till that time A will have 6 revs
b will 4revs and c will have 3 revs 
 

A is the slowest and C is the quickest, therefore A will have 3 revs and c will have 6 revs. 
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Re: A, B and C run around a circular track starting from the same point [#permalink]
15 May 2024, 09:07
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