Time, Speed & Distance
Aptitude

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Q.

Three athletes $A$, $B$ and $C$ run a race, $B$ finished 24 meters ahead of $C$ and 36 m ahead of $A$, while $C$ finished 16 m ahead of $A$. If each athlete runs the entire distance at their respective constant speeds, what is the length of the race?

 A.

108 m

 B.

90 m

 C.

80 m

 D.

96 m

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Solution:
Option(D) is correct

Let the length of the race be '$d$'. 

When $B$ finished the race, $A$ and $C$ would have run $(d−36)$ and $(d−24)$ meters respectively. 

When $C$ finishes the race, $A$ would have run $(d−16)$ meters.

The ratio of speeds of $C$ and $A$ is:

\(\dfrac{d-24}{d-36}=\dfrac{d}{d-16}\)

$⇒ d= \textbf{96 m}$


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