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# Two persons A and B are racing along a circular track.... Read more a

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Manager
Joined: 24 Jan 2013
Posts: 92
Location: India
GMAT 1: 660 Q49 V31
Two persons A and B are racing along a circular track.... Read more a  [#permalink]

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30 Mar 2020, 12:28
00:00

Difficulty:

75% (hard)

Question Stats:

21% (02:30) correct 79% (02:46) wrong based on 14 sessions

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Two persons A and B are racing along a circular track. The speed of A is twice the speed of B. The length of the circular track is 800 m and the length of the race is 7200 m.After the start of the race, A meets B for the first time at the end of the third minute.If A and B start the race from the same point, find the time taken by A to finish the race.

a) 19 minutes
b) 9.5 minutes
c) 27 minutes
d) 13.5 minutes
e) 12 minutes
DS Forum Moderator
Joined: 19 Oct 2018
Posts: 1975
Location: India
Re: Two persons A and B are racing along a circular track.... Read more a  [#permalink]

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30 Mar 2020, 13:20
Speed of B = v
Speed of A = 2v

Relative distance travelled by A wrt B to overtake B first time = Length of the track = 800m
Relative speed of A wrt B = 2v-v=v

$$\frac{800}{v} = 3$$

v=$$\frac{800}{3}$$ m/min

time taken by A to finish the race = $$\frac{7200}{2v}= \frac{3600*3}{800}$$ = 13.5 min

zs2 wrote:
Two persons A and B are racing along a circular track. The speed of A is twice the speed of B. The length of the circular track is 800 m and the length of the race is 7200 m.After the start of the race, A meets B for the first time at the end of the third minute.If A and B start the race from the same point, find the time taken by A to finish the race.

a) 19 minutes
b) 9.5 minutes
c) 27 minutes
d) 13.5 minutes
e) 12 minutes
Senior Manager
Joined: 14 Oct 2019
Posts: 406
Location: India
GPA: 4
WE: Engineering (Energy and Utilities)
Re: Two persons A and B are racing along a circular track.... Read more a  [#permalink]

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30 Mar 2020, 16:26
Let speed of A= '2S' m/s and speed of B= 'S' m/s
Relative speed between A and B = 2s – s = s m/s
Time taken for A to meet B = (length of the track / relative speed between A and B )=( 800 / s) = 3 minutes
=> 800 / s = 180
=> s = 800/180
So, time taken by A to finish the race
= 7200 / 2*(800/180)
= (7200 * 180 )/ (2*800 )
= 9 * 90 seconds
= 810 seconds
= 13.5 minutes

So, the correct answer is D
CEO
Joined: 03 Jun 2019
Posts: 3176
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
Re: Two persons A and B are racing along a circular track.... Read more a  [#permalink]

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31 Mar 2020, 06:31
zs2 wrote:
Two persons A and B are racing along a circular track. The speed of A is twice the speed of B. The length of the circular track is 800 m and the length of the race is 7200 m.After the start of the race, A meets B for the first time at the end of the third minute.If A and B start the race from the same point, find the time taken by A to finish the race.

a) 19 minutes
b) 9.5 minutes
c) 27 minutes
d) 13.5 minutes
e) 12 minutes

Given:
1. Two persons A and B are racing along a circular track.
2. The speed of A is twice the speed of B.
3. The length of the circular track is 800 m and the length of the race is 7200 m.
4. After the start of the race, A meets B for the first time at the end of the third minute.

Asked: If A and B start the race from the same point, find the time taken by A to finish the race.

2. The speed of A is twice the speed of B.
Let speed of A be 2x m/s and B be x m/s

3. The length of the circular track is 800 m and the length of the race is 7200 m.
4. After the start of the race, A meets B for the first time at the end of the third minute.
A has moved 800m more than B at the end of the third minute.
800 = 3*60 * x ; x = 800/180 = 40/9 m/s

Speed of A = 80/9 m/s
Time taken by A = 7200/(80/9) = 810 seconds = 13.5 mins

IMO D
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Re: Two persons A and B are racing along a circular track.... Read more a   [#permalink] 31 Mar 2020, 06:31