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A Deer and Rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively.P,Q,R,S are the four consecutive points on the circular track which are equidisant from each other .P is opposite to R and Q is opposite to S. After how many minutes they will meet together for the first time at the starting point,when both have started simultaneously from the same point in the same direction

Second scenario:

Also after how many minutes they will meet together for the first time,when both have started simultaneously from the same point in the same direction(in Minutes)?

I dont Know how to approach this sum? please anyone one find the solution for this

2 Answers 2

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Hint:

They will meet at the starting place the first time at a time which is the LCM of the times each one of them takes to reach the starting place.

Hope you can take it from here.

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    Do you know how to find LCM @Learning user – 2017-02-28
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    @ATHARVA for second scenario how? – 2017-02-28
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    For first scenario it is 45 Minutes and for second scenario – 2017-02-28
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    @Learninguser Take the circumference of the track = LCM of 9 and 5 = 45 m. Ratio of time of deer and rabbit = 9 : 5 $\implies $ Ratio of speed of deer and rabbit = 5 : 9 $\implies $ Relative Speed = 4 m/min They meet together for the first time other than starting point after 45/4 min – 2017-02-28
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    @Rohan how you calculated relative speed from the ratio – 2017-02-28
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    @Learninguser As speeds are in ratio of 5:9, let us the speeds are 5k and 9k respectively for some k. But as the circumference of the track is 45 m, then k equals 1. So difference in speed $=? $ – 2017-02-28
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    difference in speed is 4K @Rohan – 2017-02-28
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    How did you find the circumference of the track is 45 ,please upvote my question Rohan,guide me rohan i will learn from you – 2017-02-28
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    @Learninguser We know Time = Distance/Speed. We take the distance as the circumference of track. But what will we use for the speed? It is obvious that we cannot use either of the animals speed. That is why we take the relative velocity. – 2017-02-28
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    ok Thankyou@Rohan – 2017-02-28
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For second scenario,

Let circumference be d.

So speed of deer is $\frac{d}{5}$ and of rabbit is $\frac{d}{9}$

So the relative velocity (suppose you are the rabbit then the velocity with which you will see the deer) will be $$\frac{d}{5}-\frac{d}{9}$$. So as distance is d you will meet first time at $$\frac{d}{(\frac{d}{5}-\frac{d}{9})}$$

$$=\frac{1}{\frac{1}{5}-\frac{1}{9}}$$

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    Did you get it @Learning user – 2017-02-28
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    super @Atharva, I have understand your method,but i want Rohan explanation also As speeds are in ratio of 5:9, let us the speeds are 5k and 9k respectively for some k. But as the circumference of the track is 45 m, then k equals 1. So difference in speed =? what he suggesting explain this also – 2017-02-28
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    @Learning user You are welcome:) and don't forget to accept answers when you are satisfied with them:) – 2017-02-28
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    you also helped me and rohan also helped me , if i accept answer for you what rohan will think,i am in locked position,what i have to do now? @Atharva – 2017-02-28
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    ok, let it be as it is :) @Learninguser – 2017-02-28
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    ok Thank you @ATHARVA,for understanding my position,i want your help for learning throughout the last – 2017-02-28
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    @Learninguser you may even accepi rohans answer no offence – 2017-02-28
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    thank you i have not done , because my heart is not responding@atharva – 2017-02-28