RS Aggarwal Quantitative Aptitude PDF Free Download: RACES AND GAMES

Contents

RACES AND GAMES

IMPORTANT FACTS

 Races: A contest of speed in running, riding, driving, sailing or rowing is called race

 Course: The ground or path on which contests are made is called a race course.

 Starting Point: The point from which a race begins is known as a starting point.

 Winning Point or Goal: The point set to bound a race is called a winning paint or a 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, then the race is said to be a 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.                        i

In a 100 m race, ‘A can give B 12 m’ or ‘A can give B a start of 12 m’ or ‘A beats  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 100m 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.

  SOLVED EXAMPLES :

Ex. 1. In a km race, A beats B by 28 metres or 7 seconds. Find A’s time over the course.

 Sol.  Clearly, B covers 28 m in 7 seconds.

:. B’s time over the course = (278 x 1000) sec = 250 seconds.

:. A‘s  time over the course = (250 – 7-) sec = 243 sec = 4 min. 3 sec.

 Ex. 2. A  runs 1 ¾  times as fast as B. if A gives B a start of 84 m, bow far must    

winning post be so that A and B might reach it at the same time?

Sol. Ratio of the rates of A and B =  7/4  : 1   = 7 : 4.

So, in a race of 7 m, A gains 3m over B.

:. 3 m are gained by A in a race of 7 m.

:. 84 m are gained by A in a race of (7/3 x 84) m = 196 m.

:. Winning post must be 196 m away from the starting point.

 Ex. 3. A can run 1 km in 3 min. 10 sec. and B can cover the same distance in  3 min. 20 sec. By what distance can A beat B ?

 Soln:Clearly, A beats B by 10 sec.

Distance covered by B in 10 sec. = (1000 x 10 )m = 50 m.    

                                                          200             

Therefore  A beats B by 50 metres.

Ex .4 . In a 100 m race, A runs at 8km  per hour. If A gives B a start of 4 m and still him by 15 seconds, what is the speed of B ?

Sol: Time taken by A to cover 100 m  =(60 X 60 / 8000)       x 100 sec = 45 sec.

B covers (100 – 4) m  =  96 m   in  (45 + 15) sec = 60 sec.

B’s speed  = (96 x 60 x 60  )km/hr = 5.76 km/hr.

                        60 x 1000

Ex. 5. A, Band C  are three contestants in a km race. If A can give B a start of 40 m

    and A can give C  a start of 64m  how many metre’s  start can B give C ?

      Sol:   While A covers 1000 m, B covers (1000 – 40) m = 960 m and

     C covers (1000 – 64) m or 936 m.

 When B covers 960 m, C covers 936 m.

 Ex 6. In a game of 80 points; A can give B 5 points  and C 15  points. Then how many points  B can give C  in a game of 60 ?

 Sol.    A: B = 80 : 75,   A : C = 80 : 65.

B/C  = ( B/ A *  A/C)  = (75 / 80 * 80 / 65)  = 15/13 = 60 /52 = 60: 5

Therfore ,In a game of 60, B can give C  8 points.

 

I can’t provide a free PDF download of RS Aggarwal’s Quantitative Aptitude book as it is copyrighted. However, I can help you with Races and Games concepts, formulas, and practice questions based on RS Aggarwal’s book.


Important Formulas & Concepts for Races & Games

Basic Terminologies

  • Race: A competition where contestants cover a fixed distance.
  • Dead Heat: When all contestants finish the race at the same time.
  • Start Advantage: If a racer gets a head start, it means they cover some distance before the race starts.

Formula for Races Between Two Persons
If A can give B ‘d’ meters in a race of ‘D’ meters, then the ratio of their speeds is:

Speed of A:Speed of B=D:(D−d)\text{Speed of A} : \text{Speed of B} = D : (D – d)

If A can give B ‘t’ seconds in a race, the ratio of their speeds is:

Speed of A:Speed of B=(D/(D−d))\text{Speed of A} : \text{Speed of B} = (D / (D – d))

Race with a Start Advantage

  • If A gives B a start of ‘d’ meters, B runs D – d meters while A runs D meters.
  • Speed ratio: Speed of A:Speed of B=D:(D−d)\text{Speed of A} : \text{Speed of B} = D : (D – d)

Games & Matches (Winning Probability Formula)
If two players A and B play a series of ‘n’ games, the probability of A winning ‘m’ times is:

P=C(n,m)×pm×(1−p)n−mP = C(n, m) \times p^m \times (1-p)^{n-m}

where p = probability of A winning a single game.


 Sample Problems & Solutions

Q1: A can run 200m in 20s, and B can run 200m in 25s. How much start should A give B in a 200m race?
Q2: In a 500m race, A beats B by 50m. Find the speed ratio of A to B.
Q3: A can give B a start of 20m in a 200m race. If their speeds remain the same, how much start can A give B in a 500m race?

Would you like detailed solutions or more practice questions? Let me know! 

RS Aggarwal Quantitative Aptitude PDF Free Download: RACES AND GAMES

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