APTITUDE TECHNIQUES ON RACES AND GAMES

26. 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.

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sty� Q f n P� �z� .0pt'>:Let the speed of the train be x kmph.

       Speed of the train relative to man = (x + 5) kmph = (x + 5) *5/18 m/sec.

      Therefore 100/((x+5)*5/18)=6 <=> 30 (x + 5) = 1800 <=> x = 55

      

        Speed of the train is 55 kmph.

Ex9. A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes.12 sec  to pass a man walking at 6 kmph in the same direction in which the train is going . Find the length of the train and the length of the platform.

Sol:Let the length of train be x metres and length of platform be y metres.

     Speed of the train relative to man = (54 - 6) kmph = 48 kmph

      = 48*(5/18) m/sec = 40/3 m/sec.

     In passing a man, the train covers its own length with relative speed.

     Length of train = (Relative speed * Time) = ( 40/3)*12 m = 160 m.

     Also, speed of the train = 54 *(5/18)m / sec = 15 m / sec.

   (x+y)/15 = 20 <=> x + y = 300 <=> Y = (300 - 160) m = 140 m.

Ex10. A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?

Sol: Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph.

      Speed of goods train = (112 - 50) kmph = 62 kmph.

         

in;lI � h i P� �z� t;mso-pagination:none;mso-layout-grid-align: none;text-autospace:none'>Adding (i) ,(ii) and (iii), we get:  2 (x + y + z ) = 50 or  (x + y + z) = 25.

Thus, x= (25 - 19) = 6;  y = (25 - 21) = 4;  z = (25 - 10) = 15.

Hence, the required numbers are 6, 4 and 15.

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