# Races and Games Questions

**FACTS AND FORMULAE FOR RACES AND GAMES QUESTIONS**

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

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

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

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

In a 100m race, 'A can give B 12m' or 'A can give B a start of 12m' or 'A beats B by 12m' means that while A runs 100m, B runs (100-12)=88m

**2. 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'.

A) 22.75 m | B) 25 m |

C) 19.5 m | D) 18.5 m |

Explanation:

A : B = 200 : 169.

A : C = 200 : 182.

C/B = (C/A*A/B) = (182/200*200/169) = 182:169

When C covers 182 m, B covers 169 m.

When C covers 350 m, B covers (169/180*350)m = 325 m

Therefore, C beats B by (350 - 325) m = 25 m.

A) 30 points | B) 20 points |

C) 10 points | D) 12 points |

Explanation:

A : B = 60 : 45.

A : C = 60 : 40.

B/C = (B/A*A/C) = (45/60*60/45) = 45/40 = 90/80 = 90:80

B can give C 10 points in a game of 90.

A) 40 sec | B) 47sec |

C) 33sec | D) none of these |

Explanation:

B runs 35 m in 7 sec.

B covers 200 m in (7/35*200) = 40 sec.

B's time over the course = 40 sec.

A's time over the course (40 - 7) sec = 33 sec.

A) 8 points | B) 10 points |

C) 14 points | D) 40 points |

A) 86 sec | B) 80 sec |

C) 76 sec | D) None of these |

Explanation:

B runs 45/2mts in 6 sec

B covers 300m in (6*2/45*300)sec =80 sec

A) 125.5 meters | B) 126.5 meters |

C) 127.5 meters | D) 128.5 meters |

Explanation:

When A runs 1000 meters, B runs 900 meters and when B runs 800 meters, C runs 700 meters.

Therefore, when B runs 900 meters, the distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 meters.

So, in a race of 1000 meters, A beats C by (1000 - 787.5) = 212.5 meters to C.

So, in a race of 600 meters, the number of meters by Which A beats C = (600 x 212.5)/1000 = 127.5 meters.

A) 110.12 meters | B) 111.12 meters |

C) 112.12 meters | D) 113.12 meters |

Explanation:

A runs 1000 meters while B runs 900 meters and C runs 800 meters.

Therefore, B runs 900 meters while C runs 800 meters.

So, the number of meters that C runs when B runs 1000 meters = (1000 x 800)/900 = 8000/9 = 888.88 meters

Thus, B can give C (1000 - 888.88) = 111.12 meters start

A) 200 m | B) 300m |

C) 270m | D) 160m |

Explanation:

Ratio of the speeds of A and B =5 : 1 = 5 :3

Thus, in race of 5 m, A gains 2 m over B.

2 m are gained by A in a race of 5 m.

80 m will be gained by A in race of $\left(\frac{5}{2}*80\right)$ m =200m

=> Winning post is 200 m away from the starting point.