# Quantitative Aptitude - Problem On Races - Formula & Concept Tutorial

**Linear Track**

- X beats Y by 10 m in a 100 m race

i.e X covered 100 m in the same time when y covered 90 m

- X beats Y by 10 sec in a 100 m race

i.e X took 10 sec to cover a distance that y took t + 10 sec to cover.

- X gives a head start of 10 seconds to Y

i.e Y starts 10 seconds before X.

- X gives a head start of 10 meters to Y

i.e Y is ahead of X by 10 m at the start of the race.

- Dead-heat race

If all the contestant reaches the goal exactly at the same time is known as dead heat race.

**Circular Track**

- If two runner starts at the same time and from the same point and runs in the same direction, when they meet for the first time, the faster runner would have run one round more than the slower runner.

Time is taken for the first meeting =

- If two runners start at the same time and from the same point, the time taken for them to meet at the starting point for the first time is the LCM of the duration. They take to complete one round. The direction in which the runner is immaterial.
- When three runners start from the same point at the same time, the time taken for their first meeting is the LCM of the time taken by the fastest runner to get a lead of one computer round over each of the other two.