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# Tom and Harry started running around a circular track of length 400 me

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DS Forum Moderator
Joined: 21 Aug 2013
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Tom and Harry started running around a circular track of length 400 me  [#permalink]

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09 Jul 2018, 20:30
1
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:46) correct 48% (01:43) wrong based on 27 sessions

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Tom and Harry started running around a circular track of length 400 meters at the same time from diametrically opposite points. Tom ran clockwise while Harry ran anti-clockwise. If they kept running continuously at their own uniform speeds till they met for the second time, after how much time did they meet for the second time?

(1) Ratio of speeds of Tom and Harry is 3:2.

(2) Tom is 50% faster than Harry.
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Tom and Harry started running around a circular track of length 400 me  [#permalink]

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09 Jul 2018, 22:51
To find how much time required by Tom and Harry to meet for the second time

Since Tom and Harry run in opposite directions and they start at diametrically opposite points, they together need to cover half the circular track = 200 meters to meet for the first time.

After the first meeting point, Tom and Harry will meet again after they together complete one full go around the circular track. Therefore Tom and Harry will meet for the second time after another 400 meters.

So we need to find the time taken by Tom and Harry to complete 600(400+200) meters together.

Statement 1

Ratio of speeds of Tom and Harry is 3:2. The speed of Tom and Harry can be

Speed of Tom | speed of Harry

30 mts/sec | 20 mts/sec
60 mts/sec | 40 mts/sec
90 mts/sec | 60 mts/sec

Since we don't have a definitive values for speed of Tom and Harry, we can't find a unique value for the time taken by Tom and Harry to complete 600 meters.

Statement 1 is not sufficient

Statement 2

Tom is 50% faster than Harry. The speed of Tom and Harry can be

Speed of Tom | speed of Harry

30 mts/sec | 20 mts/sec
60 mts/sec | 40 mts/sec
90 mts/sec | 60 mts/sec

Since we don't have a definitive values for speed of Tom and Harry, we can't find a unique value for the time taken by Tom and Harry to complete 600 meters.

Statement 2 is not sufficient

Statements 1 and 2 together and independently provide the same information and we still don't have a definite values for speeds of Tom and Harry

Statements 1 and 2 together are insufficient

Hence option E
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Re: Tom and Harry started running around a circular track of length 400 me  [#permalink]

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10 Jul 2018, 01:27
amanvermagmat wrote:
Tom and Harry started running around a circular track of length 400 meters at the same time from diametrically opposite points. Tom ran clockwise while Harry ran anti-clockwise. If they kept running continuously at their own uniform speeds till they met for the second time, after how much time did they meet for the second time?

(1) Ratio of speeds of Tom and Harry is 3:2.

(2) Tom is 50% faster than Harry.

1.DIstance = 400 meters
Ratio of speed = 3/2
relative speed = 3x+2x(since they are running in opposite direction)=5x
time taken to meet for the first time t1=200/5x=40/x (The distance is 200 because they are starting diametrically opposite )
second time t2=400/5x=80/x
total time = 80/x+40/x=120/x
insufficient.

2.Restates 1.
Insufficient
combining both we get only the ratio of their respective speeds .
Insufficient.

E
Re: Tom and Harry started running around a circular track of length 400 me &nbs [#permalink] 10 Jul 2018, 01:27
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