Races and Games of Skill

Races and Games

A race or a games of skill includes the contestants in a contest and their skill in the concerned contest/game.

Important Terms

1. Races: A contest of speed in running, riding, driving, sailing or rowing is called a race.
2. Race Course: The ground or path on which contests are made is called a race course.
3. Starting Point: The exact point/place from where a race begins, is called starting point.
4. Finishing Point: The exact point/place where a race ends, is known as finishing point
5. Winning Point or Goal: A person who reaches the finishing point first, is called the winner.

6. Note: For a winner, finishing point is as same as the winning point/goal.

7. Winner: The person who first reaches the winning point is called a winner.
8. Dead Heat Race: If all the persons contesting a race reach the goal exactly at the same time, the race is said to be dead heat race.
9. Start: Suppose A and B are two contestants in a race. If before the start of the race, A is at the starting point and B is ahead of A by 12 metres, then we say that 'A gives B, a start of 12 metres'.

10. To cover a race of 100 metres in this case, A will have to cover 100 metres while B will have to cover only (100 - 12) = 88 metres.

    In a 100 race, 'A can give B 12 m' or 'A can give B a start of 12 m' or 'A beats B by 12 m' means that while A runs 100 m, B runs (100 - 12) = 88 m.

11. Games:'A game of 100, means that the person among the contestants who scores 100 points first is the winner'.

12. If A scores 100 points while B scores only 80 points, then we say that 'A can give B 20 points'.

TIPS on cracking Aptitude Questions on Races and Games

Tip #1: Acquaint yourself with the terms

• Dead Heat Race: A race in which all the contestants reach the Goal at the same time.
• Start: If A and B are two contestants in a race, such that before the start of the race, A is at the starting point and B is ahead of A by 12 meters, then we say that 'A gives B a start of 12 meters'.
• Game: A game of 100, means that the person among the contestants who scores 100 points first is the winner. If A scores 100 points while B scores only 80 points, then we say that 'A can give B 20 points'. This implies that if A actually gave B a start of 20 points, then the contest would result in a dead heat.

Tip #2: Assume that the speed or the scoring rate for each player is constant

Question: In a game of 100 points, A can give B 20 points and C 28 points. How many points can B give C?
Solution:
By the time A scores 100 points, B scores only 80 and C scores only 72 points.
Let the Scoring Rate of A be Sa. (Scoring Rate = score/ time)
Scoring Rate of B, Sb = 80/100 x Sa = 0.8 Sa
Scoring Rate of C, Sc = 72/100 x Sa = 0.72 Sa
Time taken for B to get 100 points = 100/Sb = 100/ (0.8 x Sa)
Score taken by C in this time period = Sc x 100/ (0.8 x Sa) = 72/0.8 = 90
Thus, B can give C 10 points.

Question: In a 200 m race A beats B by 35 m or 7 sec. Find A's time over the course.
Solution:
By the time A completes the race, B is 35m behind A and would take 7 more seconds to complete the race.
=> B can run 35 m in 7 s. Thus, B's speed = 35 / 7 = 5 m/s.
Time taken by B to finish the race = 200 / 5 = 40 s.
Thus, A's time over the course = (40 - 7)s = 33 s.

Tip #3: If A runs x times faster than B, A's speed is actually 1+x the speed of B

Question: A runs 1? times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?
Solution:
Speed of A, Sa = 5/3 x Sb
Let the distance of the course be 'd' meters
Time taken by A to cover distance 'd' = Time taken by B to cover distance'd-80'
d/[5/3 x Sb] = (d-80)/Sb
3d = 5d - 400
⇒ 2d = 640 ⇒ d = 200m

Question: A runs 1? times faster than B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?
Solution:
Speed of A, Sa = (1 + 5/3) x Sb = 8/3 x Sb
Let the distance of the course be 'd' meters
Time taken by A to cover distance 'd' = Time taken by B to cover distance 'd-80'
d/[8/3 x Sb] = (d-80)/Sb
3d = 8d - 640
⇒ 5d = 640 ⇒ d = 128m
Note: Here, A 5/3 times faster than B, i.e., A's speed = B's speed + 5/3 times B's speed = 8/3 times B's speed.