Aptitude Discussion

Q. |
Three friends $A$, $B$ and $C$ run around a circular track of length 120 metres at speeds of 5 m/s, 7 m/sec and 15 m/sec, starting simultaneously from the same point and in the same direction. How often will the three of them meet? |

✔ A. |
Every 60 seconds |

✖ B. |
Every 120 seconds |

✖ C. |
Every 30 seconds |

✖ D. |
None of these |

**Solution:**

Option(**A**) is correct

The problem can be solved as follows:

First find out when $A$ and $B$ will meet for the first time.

$A$ and $B$ will meet for the first time in:

\(\Rightarrow \left(\dfrac{\text{Circumference of track}}{\text{relative speed}}\right)\) seconds

\(\dfrac{120}{2}\) = 60 seconds.

This also means that $A$ and $B$ will continue meeting each other every 60 seconds.

Next find out when $B$ and $C$ will meet for the first time.

$B$ and $C$ will meet for the first time in \(\dfrac{120}{8}=15\) seconds

This also means that they will meet every 15 seconds after they meet for the first time i.e. $A$ and $B$ meet every 60 seconds and multiples of 60 seconds and $B$ and $C$ meet every 15 seconds and multiples of 15 seconds.

The common multiples to both these time, will be when $A$ and $B$ and $B$ and $C$ will meet i.e. when $A$, $B$ and $C$ will meet.

The common multiple of 60 and 15 will be 60,120,180 etc. i.e. they will meet every **60 seconds**

**Sandeep**

*()
*

When speeds a>b>c then time taken to meet for the first time ever (15>7>5)

LCM ( L/a-b , L/b-c)

LCM ( 120/8 , 120/2) => LCM ( 15,60) = 60.