Aptitude Discussion

Q. |
Two friends $A$ and $B$ run around a circular track of length 510 metres, starting from the same point, simultaneously and in the same direction. $A$ who runs faster laps $B$ in the middle of the $5^{th}$ round. If $A$ and $B$ were to run a 3 km race long race, how much start, in terms of distance, should $A$ give $B$ so that they finish the race in a dead heat? |

✖ A. |
545.45 metres |

✔ B. |
666.67 metres |

✖ C. |
857.14 metres |

✖ D. |
Cannot be determined |

**Solution:**

Option(**B**) is correct

$A$ and $B$ run around a circular track. $A$ laps $B$ in the middle of the $5^{th}$ lap. i.e. when $A$ has run four and a half laps he has covered a distance which is 1 lap greater than that covered by $B$'s.

Therefore, when $A$ runs \(\dfrac{9}{2}\) laps, $B$ runs \(\dfrac{7}{2}\) laps

This is same as saying when $A$ runs 9 laps, $B$ runs 7 laps.

i.e in a race that is 9 laps long, $A$ can give $B$ a start of 2 laps.

So, if the race is of 3000 metres long, then $A$ can give $B$ a start of

\(\left(\dfrac{2}{9}\right)\times 3000=\)**666.67 metres.**

The information with regard to the length of the circular track is redundant information.