# 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'.

Q:

In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:

 A) 20m B) 25m C) 22.5m D) 9m

Explanation:

Distance covered by B in 9 sec. = (100/45)*9m = 20m

A beats B by 20 metres.

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Q:

In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:

 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.

48 38099
Q:

A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?

 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

31 37166
Q:

At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?

 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.

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Q:

In a 300 m race, A beats B by 22.5 m or 6 seconds. B's time over the course is:

 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

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Q:

In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C is

 A) 8 points B) 10 points C) 14 points D) 40 points

Explanation:

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Q:

In a race of 1000 meters, A can beat B by 100 meters, in a race of 800 meters, B can beat C by 100 meters. By how many meters will A beat C in a race of 600 meters?

 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.

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Q:

A runs $123$ 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?

 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 $52*80$ m =200m

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