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Use the following data: A and B are running along a circular course of radius 7 km in opposite directions such that when they meet they reverse their directions and when they meet, A will run at the speed of B and vice-versa, Initially, the speed of A is thrice the speed of B. Assume that they start from $M_{0}$ and they first meet at $M_{1}$, then at $M_{2}$, next at $M_{3}$, and finally at $M_{4}$.

What is the shortest distance between $M_{1}$ and $M_{3}$ along the course?

  1. $22$ km
  2. $14 \sqrt{2}$ km
  3. $22 \sqrt{2}$ km
  4. $14$ km
asked in Quantitative Aptitude by (7.7k points) 50 149 436
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We need to find the red marked line's distance of the above picture.

Now, the circumference of the circular course $2\pi r\hspace {0.2cm} i.e.\hspace{0.2cm}2\times\dfrac{22}{7}\times{7} = 44 cm $

We're divided this circular course in $4$ equal halves.So, every half is exactly $\dfrac{44}{4}=11 km\hspace{0.1cm} long$

Or, we can say that $\color{blue}{M_{0}\Rightarrow M_{1}= 11km}$ & $\color{blue}{M_{1}\Rightarrow M_{2}= 11km}$ & $\color{blue}{M_{2}\Rightarrow M_{3}= 11km}$ & $\color{blue}{M_{3}\Rightarrow M_{4} \text{ or } M_{0}= 11km}$

$\color{green}{\text{So,The shortest distance between}}$ $\color{red}{M_{1}}$ $\color{green}{\&}$ $\color{red}{M_{3}}$ $\color{green}{\text{along the course is}}$ $\color{orange}{11+11=22\hspace{0.1cm}km}$    $\qquad\color{lightblue}{\big[∵M_{1}\rightarrow M_{3}= M_{1}\rightarrow M_{2}+M_{2}\rightarrow M_{3}\hspace{0.2cm}OR\hspace{0.2cm} M_{1}\rightarrow M_{3}= M_{1}\rightarrow M_{0}+M_{0}\rightarrow M_{3}\hspace{0.2cm} \big]}$

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For better understanding please see: https://aptitude.gateoverflow.in/4032/cat1995-88

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