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

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

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.

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

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*"Races and Games"*## 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.*