Race and Games

A race is a competition where participants strive to complete a task or cover a distance in the shortest time, aiming to reach the finish line first.

Games are structured activities or competitions that involve skill, strategy, or luck, played for entertainment or recreation, with established rules to follow, and can be either individual or team-based.

Terminologies used in Races and Games in Quantitative Aptitude

• A gives B a start of x meters: This means that A and B are participating in the same race, but B is given a head start of x meters. To cover the same distance, A will have to run the entire race, while B will only have to run the remaining distance after the head start.
• A beats B by x meters: This means that A and B are participating in the same race, and A finishes the race x meters ahead of B.
• A can give B a start of t minutes: This means that A and B are participating in the same race, but B is given a head start of t minutes. Both A and B start the race at different times, but reach the finish line at the same time.
• A gives B x meters and t minutes: This means that A and B start the race at the same time, but A finishes x meters ahead of B. Additionally, B takes t minutes longer than A to complete the race.
• Dead Heat: This refers to a situation where two or more participants finish the race at exactly the same time. In a dead heat, there is no clear winner.
• Handicap: This refers to a system in which participants are given a head start or other advantage in order to level the playing field. Handicaps are often used in races or other competitions where there is a large skill or experience gap between participants.

Solved Race and Games Aptitude Questions

Question 1: In a 1000-meter race, A can beat B by 100 meters, and B can beat C by 100 meters. How much distance will A beat C by in a 1000-meter race?

Solution:

A beats B by 100 meters in a 1000-meter race.
This means when A finishes 1000 meters, B covers 900 meters.
B beats C by 100 meters in a 1000-meter race.
This implies when B finishes 1000 meters, C covers 900 meters.

Now, we need to find how much distance A beats C by when A runs 1000 meters.
To connect A and C directly, we calculate the effective distance C covers when A finishes:
When B runs 900 meters, C covers \frac{900}{1000} \times 900 = 810 meters.

Therefore, when A finishes 1000 meters, C covers 810 meters. So, A beats C by: 1000 - 810 = 190 meters

So, A beats C by 190 meters.

Question 2: In a tournament, each participant plays exactly one match with every other participant. If there are 10 participants, find the total number of matches played.

Solution:

When each participant plays exactly one match with every other participant, we can calculate the total matches using combinations.

If there are n participants, the number of matches played is \binom{n}{2} = \frac{n(n-1)}{2}
Given n = 10:
\text{Total matches} = \frac{10 \times 9}{2} = 45

So, 45 matches are played in total.