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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 distance travelled by A when they meet at $M_{3}$?

  1. $77$km
  2. $66$km
  3. $99$km
  4. $88$km
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1 Answer

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In order to meet $B$ at point $M_{3}$, $A$ travels to $M_{1}$ first, then $M_{2}$ & then $M_{3}$.

$\color{green}{\text{So, Total distances travelled by}}$ $\color{red}{A}$ $\color{green}{\text{when it meets with}}$ $\color{red}{B}$ $\color{green}{\text{at point}}$ $\color{red}{M_{3}}$ $\color{green}{is}$ $\color{blue}{33+11+33=77\hspace{0.1cm}km}$

$\big[\color{orange}{∵M_0\rightarrow M_1 =M_0\rightarrow M_3+M_3\rightarrow M_2+M_2\rightarrow M_1 = 11+11+11\hspace{0.1cm}km = 33\hspace{0.1cm}km}\big]$

&$\big[\color{orange}{M_1\rightarrow M_2 =11\hspace{0.1cm}km}\big]$

&$\big[\color{orange}{∵M_2\rightarrow M_3 =M_2\rightarrow M_1+M_1\rightarrow M_0+M_0\rightarrow M_3 = 11+11+11\hspace{0.1cm}km = 33\hspace{0.1cm}km}\big]$

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

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