Time, Speed & Distance
Aptitude

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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

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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


(1) Comment(s)


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.