Races and Games Tips and Tricks for Government Exams

Races and games in government exams test quantitative skills, requiring candidates to apply mathematical concepts such as speed, distance, and time. They evaluate analytical thinking and decision-making abilities, essential for data analysis and logistical tasks in government roles.

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

• Races: A contest of speed in running, riding, driving, sailing or rowing is called a race.
• Race Course: The ground or path on which contests are made is called a race course.
• Starting Point: The exact point/place from where a race begins, is called starting point.
• Finishing Point: The exact point/place where a race ends, is known as finishing point
• Winning Point or Goal: A person who reaches the finishing point first, is called the winner.
• Note: For a winner, finishing point is as same as the winning point/goal.
• Winner: The person who first reaches the winning point is called a winner.
• 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.
• 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'.
  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.
• Games: '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'.

TIPS to Crack Questions

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

Q1: In a game of 100 points, A can give B 20 points and C 28 points. How many points can B give C?
Sol:
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.

Q2: In a 200 m race A beats B by 35 m or 7 sec. Find A's time over the course.
Sol:
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

Q1: 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?
Sol:
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

Q2: 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?
Sol:
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.