Aptitude Discussion

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 |

**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:

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

$⇒ d= \textbf{96 m}$