John runs on a circular track A at 6 kmph and Mary runs on a circular

Question

John runs on a circular track A at 6 kmph and Mary runs on a circular track B at 7.5 kmph. The total length of tracks A and B is 325 metres. John covers 9 rounds on track A in the same time as Mary covers 5 rounds on track B. How many seconds does Mary need to make one round on track A?

A. 42
B. 44
C. 46
D. 48
E. 50

A. 42
B. 44
C. 46
D. 48
E. 50

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DeusTacitus22 · Accepted Answer

John = 6kmph = 5/3mps
Mary = 7.5kmph = 25/12mps

We know, A+B=325m

Acc. to Question,
=> (9A)*3/5 = (5B)*12/25
=> 9A = 4B => B = 9A/4

Substituting in above eqn.
=> A = 100m

Total time taken by Mary
=> 100*12/25 => 48 sec

The Answer - D

eakabuah · Answer

The total length of tracks A and B is 325m, hence A+B=0.325km ----(1)
John covers 9 rounds of track A in the same time that Mary covers 5 rounds on track B. 
Hence  \frac{9A}{6}=\frac{5B}{7.5} 
 9*7.5A=30B 
 B=2.5A 
Substitute  B=2.5A  into (1)
 3.25A=0.325 
 A=0.1km

Time taken by Mary in seconds to make 1 round on track A  = \frac{0.1}{7.5}*3600 = \frac{3600}{75} = 12*4 = 48 sec.

The answer is D.

Archit3110 · Answer

given
speed of John = 6kmph and speed of Mary 7.5kmph
Da+Db=325
Db=325-Da
also we know about the time comparison of both
i.e
9*Da/6 = 5*Db/7.5
we can write as
1.5Da= 325-Da/1.5
solve for Da = 100
so time which Mary would take to cover 100 mtrs
100/7.5 * 3600*1/1000 = 48 seconds
OPTION D

GMATinsight · Answer

Step By step approach to the question has been demonstrated in the video.

Answer: Option D

https://www.youtube.com/watch?v=z9s1vYQ1PIg

Kinshook · Answer

Given:
1. John runs on a circular track A at 6 kmph and Mary runs on a circular track B at 7.5 kmph.
2. The total length of tracks A and B is 325 metres.
3. John covers 9 rounds on track A in the same time as Mary covers 5 rounds on track B.

Asked: How many seconds does Mary need to make one round on track A?

John's speed = 6kmph = 6*5/18 = 5/3 m/s
Mary's speed = 7.5kmph = 7.5*5/18 = 15*5/36 = 25/12 m/s

Let the length of circular track A be x metres and length of circular track B be (325-x) metres

Let the common time be t

9x = 5t/3;
5(325-x) = 25t/12

9x/5(325-x) = 5*12/3*25 = 4/5
x/(325-x) = 4*5/5*9 = 4/9
x/325 =4/13
x = 325 * 4/13 = 25*4 = 100 metres

Time Mary need to make one round on track A = 100/(25/12) = 48 seconds

IMO D

HamP95 · Answer

A very challenging question here, with numerous places to go wrong and information not readily presenting an easy starting point.

Firstly, I found the speed ratio of John and Mary by doing 6/7.5 = 0.8
So John is 80% as fast as Mary, or 0.8:1.

Therefore, John would do 0.8 * 5 or 4 rounds of B in the same time it takes Mary to do 5 rounds, which as we know is also the same time John would take to do 9 rounds of A

The length ratio of A to B, therefore, is 4:9 (don't make the error of putting it 9:4, John does more rounds of A because its shorter!)

To calculate the distance of each track, 325/4+9 = 25, so A is 100m, B is 225m

Now to calculate how long it takes Mary to run 100m:

7500/60 = 125m per minute 
100/125 = 0.8 minutes or 48 seconds - D

John runs on a circular track A at 6 kmph and Mary runs on a circular

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John runs on a circular track A at 6 kmph and Mary runs on a circular

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