# Races and Games

Races and Games topic related multiple Choice Questions with Answers is given here. Candidates preparing for competitive exams can practice these important Races and Games Questions and Answers for scoring good marks in quantitative aptitude section. Races and Games Questions Answers with explanation are also available here, so that individuals can learn the basic concepts of Races and Games.

Races and Games MCQ Questions contain 4 options, candidate’s needs to choose the correct answer from these given options. Answers of these 15 Multiple Choice Races and Games Questions type are available at the end section, so after choosing the option candidates can match up there choice with the given answers.

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## Races and Games

Races and Games Concept

1. Races: A contest of speed in running, riding, driving, sailing or rowing is called a race.
2. Race Course: The ground or path on which contests are made is called a race course.
3. Starting Point: The point from which a race begins is known as a starting point.
4. Winning Point or Goal: The point set to bound a race is called a winning point or a goal.
5. Winner: The person who first reaches the winning point is called a winner.
6. Dead Heat Race: If all the persons contesting a race reach the goal exactly at the same time, the race is said to be dead heat race.
7. 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 100 race, ‘A can give B 12 m’ or ‘A can give B a start of 12 m’ or ‘A beats B by 12 m’ means that while A runs 100 m, B runs (100 – 12) = 88 m.
1. 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’.

Races And Games Formulas  & Tricks

1. If P is n times as fast as Q and P gives Q a start of x meters, then the length of the race course, so that both P and Q reaches the winning post at the same time = xn/(n-1) meters.
2. If P can run x meters race in t1 seconds and Q in t2 seconds, where t1 < t2, then P beats Q by a distance of x(t2 – t1)/ t2 meters.

General Statements Used In Races And Games Questions

Let A and B be two contestants in a race. Let’s examine some of the general statements and their mathematical interpretations.

 Statements Mathematical Interpretations A beats B by ttseconds A finishes the race tt seconds before B finishes. A gives B a start of tt seconds A starts tt seconds after B starts from the same starting point. A gives B a start of xx metres While A starts from the starting point, B starts xx meters ahead of the same starting point at the same time.To cover a race of 100100 metres in this case, A will have to cover 100100 metres while B will have to cover only (100−x)(100−x) metres. Game of 100100 A game in which the participant who scores 100100 points first wins. In a game of 100,100,A can give B 2020points While A needs to score 100100 points, B needs to score only (100−20)=80(100−20)=80 points.

Races and Games Questions With Explanation

Ques1: In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

A) 5.4m

B) 4.5m

C) 5m

D) 6m

 Explanation:A : B = 100 : 90.A : C = 100 : 87.B/C = (B/A*A/C) = (90/100*100/87) = 30/29When B runs 30 m, C runs 29 m.When B runs 180 m, C runs (29/30*180)m =174mB beats C by (180 – 174) m = 6 m.

Ques2: In a 1 km race, A beats B by 28 meters in 7sec. Find A’s time over the course?

A) 5min,4sec

B) 4min,3sec

C) 2min,3sec

D) 3min,4sec

 Explanation:B covers 28 meters in 7sec. So, B’s time over the course = (7/28)*100 =250 sec.Whereas A’s time over the course = 250 -7 = 243 sec.i.e A’s time over the course is 4min , 3 sec.

Ques3: In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:

A) 60m

B) 40m

C) 20m

D) 10m

 Explanation:To reach the winning post A will have to cover a distance of (500 – 140)m, i.e., 360 m.While A covers 3 m, B covers 4 m.While A covers 360 m, B covers (4/3)*360 = 480 m.Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.A wins by 20 m.

Ques4: 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 = 20mA beats B by 20 metres.

Ques5: A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:

A) 5.15 kmph

B) 4.14 kmph

C) 4.25 kmph

D) 4.4 kmph

 Explanation:A’s speed = (5*5/15)m/sec  = (25/18)m/secTime taken by A to cover 100 m = (100*18/15)sec = 72secTime taken by B to cover 92 m = (72 + 8) = 80 sec.B’s speed =(92/80*18/5)kmph =4.14kmph

Ques6: In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by

A) 21 m

B) 26 m

C) 28m

D) 29m

 Explanation:

Ques7: 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 = 90:80B can give C 10 points in a game of 90.

Ques8: 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:

Ques9: In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C

A) 18 m

B) 20 m

C) 27 m

D) 9m

 Explanation:

Ques10: A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:

A) 100 m

B) 75 m

C) 25 m

D) 50m

 Explanation:When B runs 25 m, A runs 45/2 mWhen B runs 1000 m, A runs (45/2*1/25*1000)m = 900 m.B beats A by 100 m.

Ques11: In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:

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) = 182:169When C covers 182 m, B covers 169 m.When C covers 350 m, B covers (169/180*350)m  = 325 mTherefore, C beats B by (350 – 325) m = 25 m.

Ques12: 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.

Ques13: 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.

Ques14: 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 secB covers 300m in (6*2/45*300)sec =80 sec

Ques15: 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 :3Thus, 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.

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