RACES AND GAMES OF SKILL - Education Point

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

STARTING POINT : The point from which a race begins is known as a starting point.

FINISHING POINT OR WINNING POST: 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.

FORMULA
WINNER'S DISTANCE = LENGTH OF RACE
LOSER'S DISTANCE = WINNER'S DISTANCE-(BEAT DISTANCE + START DISTANCE)
WINNER'S TIME = LOSER'S TIME-( BEAT TIME + START TIME)
WINNER'S TIME/LOSER'S DISTANCE= LOSER'S TIME/WINNER'S DISTANCE =
 BEAT TIMES+ START TIME/BEAT DISTANCE+ START DISTANCE

Results

#1. In one kilometre race, A beats B by 36 metres or 9 seconds. Find A’s time over the course.

250 Seconds

240 Seconds

241 Seconds

None of these

In one kilometre race, A beats B by 36 metres or 9 seconds. Find A’s time over the course.

Here A is the winner and B is the loser

using the formula

WINNER'S TIME/LOSER'S DISTANCE= BEAT TIMES  START TIME/BEAT DISTANCE  START DISTANCE
A's time/1000-36= 9 plus 0 /36 plus 0 
A's time = 9/36*964s
=241s

#2. In a 500 metres race, A beats B by 50 metres or 8 seconds. Find A’s time over the course.

2 minutes

1 minutes 12 seconds

2 minutes 35 seconds

1 minutes

In a 500 metres race, A beats B by 50 metres or 8 seconds. Find A’s time over the course.

B’s cover 50 metre in 8 seconds

B’s speed = 50/8

= 6.25m/s

Time taken by B= 500/6.25

= 80

80 seconds A beats B by 8 seconds

time A= 80-8

= 72

1 min 12 sec.

#3. In 300 metre race A beats B by 5 seconds or 15 metres. A ‘s time over the couse is

95 seconds

100 seconds

85 seconds

90 seconds

In 300 metre race A beats B by 5 seconds or 15 metres. A ‘s time over the course is

B covers 15 metre in 5 seconds

B’s speed = 15/5

= 3 seconds

300/3=100

100 seconds A beats B by 5 seconds

Time by A’s = 100-5

= 95 seconds

#4. X can run 20 metres while Y runs 25 metres. In a kilometres race, Ybeats X by

150 metres

200 metres

250 metres

175 metres

X can run 20 metres while Y runs 25 metres. In a kilometres race, Y beats X by

y beats X by = 200 metres

#5. In a 200 meter race, A beats B by 20 metres, While in 100 metres race,B beats C by 5 metres. A beats C n a kilometre race by

105 metres

25 metres

150 metres

145 metres

In a 200 meter race, A beats B by 20 metres, While in 100 metres race,B beats C by 5 metres. A beats C in a kilometre race by

A beats C in a kilometre race by= 145 metres

#6. In a km race, A beats B by 28 metres or 7 seconds. Find A’s time over the course.

100 seconds

200 seconds

243 seconds

None of these

In a km race, A beats B by 28 metres or 7 seconds. Find A’s time over the course.

B covers 28 m in 7 seconds

B’s time over the course = (7/28* 1000) sec

= 250 seconds

A’s time over the course = ( 250-7 ) sec = 243 seconds

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

30 points

20 points

10 points

12 points

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

A : B = 60 : 45 and A : C = 60 : 40

B/C=(B/A*A/C)=(45/60*60/40)

45/40

90/80

90 : 80

B can give C 10 points in a game of 90

#8. In a game of 80 point , A can give B 5 point and C 15 point . Then how many point B can give C in a game of 60 ?

60 : 52

44 : 90

65 : 90

None of these

In a game of 80 point , A can give B 5 point and C 15 point . Then how many point B can give C in a game of 60 ?

A : B = 80 : 75

A : C = 80 : 65.

B/C = (B/A*A/C)

= ( 75/80 * 80/65 )

= 15 / 13

= 60 / 52

= 60 : 52

#9. 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 ?

80 M

60 M

50 M

None of these

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 ?

A beats B by 10 sec.

Distance covered by B in 10 sec= ( 1000/200*10 )m

= 50 m

A beats B by 50 meter

#10. 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 :

345 m

365 m

325 m

None of these

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 : B = 200 : 169 and 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 / 182 * 350 )m

= 325 m

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

20 points

10 points

30 points

None of these

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

A : B = 100 : 80 and A : C = 100 : 72

B/C = ( B/A *A/c )

= ( 80 /100 * 100 /72 )

= 10/9

= 100/90

= 100 : 90

B can give C 10 points

#12. 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 :

23 m

65 m

28 m

None of these

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 : B =100 : 75 and B : C = 100 : 96

A : C = ( A/B * B/C )

= ( 100/75 * 100/96 )

= 100/72

= 100 : 72

A beats C by ( 100 – 72 )m

= 28 m

#13. In a 100 m race , A cover the distance in 36 seconds and B in 45 seconds . In this race A beats B by :

40 m

34 m

20 m

None of these

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

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

= 20 m

A beats B by 20 meter

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

45 sec.

33 sec.

80 sec.

None of these

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

B runs 45/2 m in 6 sec

B cover 300 m in ( 6 * 2/45 *300 ) sec.

= 80 sec.

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

100 m

445 m

145.9

None of these

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

When B runs 25 m a runs 45/2 m

When B runs 1000 m , A runs ( 45/2 * 1/25 *1000 ) m

= 900 m

B beats A by 100 m

#16. In a 200 meter race A beats B by 35 m or 7 seconds . A’s time over the course is :

44 sec.

33 sec.

334 sec.

None o these

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

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.

#17. A and B take part in a 100 m race . A runs at 5 Km per hour . A gives B a start of 8 m and still beats him by 8 seconds . The speed of B is :

4.14 Kmph

5.87 Kmph

88.0 Kmph

None of these

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

A’s speed = ( 5 * 5/18 )m/sec.

= 25/18 m/sec

Time taken by A to cover 100 m = ( 100 * 18/25 ) sec

= 72 sec

Time taken by B to cover 92 m

= (72 plus 8 )sec.

= 80 sec.

B’s speed = (92/80 * 18/5 ) Kmph

= 4.14 Kmph

#18. A runs 1 3/4 times fast as B . If A gives B start of 84 m, how far must the wining post be so that A and B might reach i at the same time ?

123 m

234 m

196 m

None of these

A runs 1 3/4 times fast as B . If A gives B start of 84 m, how far must the wining post be so that A and B might reach i at the same time ?

Ratio of the rate of A and B = 7/4

=7 : 4

So , in the race f 7 m , A gain 3 m 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 * 84 ) m

= 196 m

#19. In a 100 m race , A runs at 8 km per hour . If a gives B a start of 4 m and still beats him by 15 seconds , What is the speed of B ?

5.78 Km/hr

5.76 Km/hr

33.8 Km/hr

None of these

In a 100 m race , A runs at 8 km per hour . If a gives B a start of 4 m and still beats him by 15 seconds , What is the speed of B ?

Time taken by A cover 100 m = (60*60/8000*100 ) sec

= 45 sec

B covers ( 100 – 4 ) m = 96 m in (45 plus 15 ) sec

= 60 sec

B’s speed = ( 96*60*60/60*1000 ) Km/hr

= 5.76 Km/hr

#20. A,B and C are three contestants in a km race .If A can give B a start of 40 Km and A can give C a start of 64 m., how many meter’s start can B give C ?

45 m

44 m

25 m

None of these

A,B and C are three contestants in a km race .If A can give B a start of 40 Km and A can give C a start of 64 m., how many meter’s start can B give C ?

While A covers 1000 m, B covers ( 1000 – 40 ) = 960 m and

C covers ( 1000 – 64 ) m or 936 m

When B covers 960 m , c covers 936 m.

When B covers 1000 m ,C covers (936/960 * 1000)m

= 975 m

B can give c a start of ( 1000 – 975 )

=25 m

Finish

Results

#1. In one kilometre race, A beats B by 36 metres or 9 seconds. Find A’s time over the course.

#2. In a 500 metres race, A beats B by 50 metres or 8 seconds. Find A’s time over the course.

#3. In 300 metre race A beats B by 5 seconds or 15 metres. A ‘s time over the couse is

#4. X can run 20 metres while Y runs 25 metres. In a kilometres race, Ybeats X by

#5. In a 200 meter race, A beats B by 20 metres, While in 100 metres race,B beats C by 5 metres. A beats C n a kilometre race by

#6. In a km race, A beats B by 28 metres or 7 seconds. Find A’s time over the course.

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

#8. In a game of 80 point , A can give B 5 point and C 15 point . Then how many point B can give C in a game of 60 ?

#9. 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 ?

#10. 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 :

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

#12. 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 :

#13. In a 100 m race , A cover the distance in 36 seconds and B in 45 seconds . In this race A beats B by :

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

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

#16. In a 200 meter race A beats B by 35 m or 7 seconds . A’s time over the course is :

#17. A and B take part in a 100 m race . A runs at 5 Km per hour . A gives B a start of 8 m and still beats him by 8 seconds . The speed of B is :

#18. A runs 1 3/4 times fast as B . If A gives B start of 84 m, how far must the wining post be so that A and B might reach i at the same time ?

#19. In a 100 m race , A runs at 8 km per hour . If a gives B a start of 4 m and still beats him by 15 seconds , What is the speed of B ?

#20. A,B and C are three contestants in a km race .If A can give B a start of 40 Km and A can give C a start of 64 m., how many meter’s start can B give C ?

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