# RS Aggarwal Quantitative Aptitude PDF Free Download: RACES AND GAMES

__RACES AND GAMES__

__RACES AND GAMES__

__IMPORTANT FACTS__

__IMPORTANT FACTS__

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

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

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

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**Winning Point or Goal:** The point set to bound a race is called a winning paint or a goal.

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**Winner:** The person who first reaches the winning point is called a winner.

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** 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.

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**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.

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__ ____SOLVED EXAMPLES :__

__SOLVED EXAMPLES :__

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

**over**

**the course.**

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**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.

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**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.

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**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 ****?**

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**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.

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**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

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**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 ?**

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** 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 ?**

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**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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