Races And Games- Aptitude Questions and Answers

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A and B take part in 100 m race .A runs at 5 km per hour. A gives B a start of 8 m and still beats him by 8 sec. What is the speed of B?

A)

6.14 km/hr


B)

2.16 km/hr


C)

5.14 km/hr


D)

4.14 km/hr



Correct Answer :

4.14 km/hr


Explanation :

1 km/hr = 1000/60*60 =5/18 m/sec

A'speed = 5 km/hr =5*5/18 =25/18 m/s
Time taken by A to cover 100 m =100*18/25 =72 sec
B covers 100-8 m =92 m
Time taken by B to cover 92 m = Time taken by A + 8 Sec
=72 sec + 8 Sec = 80 sec

B's speed =92/80 m/s = 92*18/80*5 km/hr = 4.14 km/hr

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In a kilometer race, A can beat B by 100 m and B can beat C by 80 m. If A and C run in the same race, by how many meters will A win?

A)
172 m

B)
178 m

C)
220 m

D)
200 m


Correct Answer :

172 m


Explanation :

In a km race A can beat B by 100 m
ie A run 1000 m, B run (1000-100)=900 m
In a km race B can beat C by 80 m
ie B runs 1000 m, C runs (1000-80)=920 m

so B run 1 m, C run 920/1000 m
ie B runs 900 m, C runs (920/1000)×900=92×9=828 m

ie A run 1000 m,B runs 900 m and C run 828 m
Hence, A can beat C by (1000-828)=172 m

Raman covers 1 km in 8 min while suman covers the same distance in 10 min. By what distance does Raman beat Suman ?

A)

150 m


B)

65 m


C)

190 m


D)

200 m



Correct Answer :

200 m


Explanation :

Raman covers 1 km in 8 min and suman cover 1 km in 10 min.
If they starts together, then distance covered by suman in 8 min
= (1000/10) x 8 = 800 m
Thus, Raman will beat suman by (1000 - 800 ) m = 200 m

In 1 km race, A beats B by 18 m or 9 s. Find the A' s time over the course?

A)

391 s


B)

591 s


C)

491 s


D)

500 s



Correct Answer :

491 s


Explanation :

Clearly, B covers 18 m in 9 s.
B's time over the course = 9/18 x 1000 = 500 s
A' s time over the course = (500 - 9) = 491 s

In a 100 m race A runs at a speed of 5/3 m/s. If A give a start of 4 m to B and still beats him by 12 seconds, what is speed of B?

A)

5/4 m/s


B)

7/5 m/s


C)

4/3 m/s


D)

6/5 m/s



Correct Answer :

4/3 m/s


Explanation :

Let the distance is 100 m and speed of B be x m/s. Then, according to the question
96/x - 100/(5/3) = 12
96/x - 60 = 12
96/x = 72
x = 96/72
x = 4/3

Speed of B is 4/3 m/s.

In a 1 km race,A beats B by 28 m or 7 sec.Find A's time over the course?

A)

2 min ,2 sec


B)

3 min ,3 sec


C)

4 min ,3 sec


D)

5 min ,4 sec



Correct Answer :

4 min ,3 sec


Explanation :

B covers 28 m in 7 sec so,B's time over the course = 7/28 *1000 =250 sec
A's time over the course =250-7 =243 sec = 4 min ,3 sec.

A runs 7/4 times as fast as B.If A gives B a start of 84 m,how far must be winning post be so that A and B might reach it at the same time ?

A)

84 m


B)

121 m


C)

154 m


D)

196 m



Correct Answer :

196 m


Explanation :

If A runs 7/4 times as fast as B
⇒ A : B =7/4 :1 = 7 : 4

Define x: Let x be the constant ratio
A : B = 7x : 4x

Solve x: The difference is 84m
7x - 4x = 84
3x = 84
x = 28m

Find the distance of the winning post:
The winning post is the distance A has to run

A = 7x = 7*28m = 196 m

Winning post must be 196 m away from the starting point

A can run 1 km in 3 min ,10 sec and B can cover same distance in 3 min 20 sec. By what distance A beat B?

A)

50 m


B)

40 m


C)

60 m


D)

80 m



Correct Answer :

50 m


Explanation :

A can run 1 km in 3 min 10 sec and
B can cover same distance in 3 min 20 sec.
Clearly A beats B by 10 sec.

Distance covered by B in 3 min 20 sec ie 1000m in 2000sec
Distance covered by B in 10 sec =1000/200 *10 =50 m
A beats B by 50 meter.

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 sec,what is the speed of B?

A)

3.7 km/hr


B)

4.16 km/hr


C)

5.76 km/hr


D)

7.71 km/hr



Correct Answer :

5.76 km/hr


Explanation :

A's speed 8 km per hr
ie
8000 m -------60*60 sec
100 m ------- 60*60*1000/8000 =45 sec
Time taken by A to cover 100 m =45 sec

B covers 100-4 m =96 m
Time taken by B to cover 100m=Time taken by A + 15 Sec
=45 sec + 15 Sec = 60 Sec

B's speed =96 m/60 sec = 96*60*60 km/60*1000 hr
=5.76 km/hr

A runs 5/3 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 at the same time?

A)

200 m


B)

300 m


C)

240 m


D)

340 m



Correct Answer :

200 m


Explanation :

Ratio of the speed of A and B = 5/3 :1
⇒ A : B = 5 : 3

Let x be the constant ratio
A : B = 5x : 3x

The difference is 80 m
5x - 3x = 80
x = 40 m

The winning post is the distance A has to run
A = 5x = 5*80m = 200 m

Winning post must be 200 m away from the starting point

A, B and C are the three contestants in one km race. If A can give B a start of 40 metres and A can give C a start of 64 metres, how many metres start can B give C?

A)

20 m


B)

21 m


C)

25 m


D)

34 m



Correct Answer :

25 m


Explanation :

Ratio of the speed of A and B =
A : B = 1000:960
Ratio of the speed of A and C =
A : C = 1000:936

So ratio of the speed of B and C
=> B : C = 960:936 = (960+40):(936+40)
= 1000:975
That is, B can give C a start of 25 metres.

In a 100m race,A covers the distance in 36 sec and B in 45 sec.In this race A beats B by?

A)

20 m


B)

22 m


C)

25 m


D)

30 m



Correct Answer :

20 m


Explanation :

Distance covered by B in 9secs =100*9/45 =20 m
So, A beats B by 20m

In a 200 m race A beats B by 35 m or 7 sec.What is the A's time over the course?

A)

12 sec


B)

19 sec


C)

33 sec


D)

45 sec



Correct Answer :

33 sec


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

In a 300 m race A beats B by 22.5 m or 6 sec.What is the B's time over the course?

A)

92 sec


B)

80 sec


C)

73.5 sec


D)

65 sec



Correct Answer :

80 sec


Explanation :

B runs 22.5 m in 6 sec
B runs 300m in =6*300/22.5 =80 sec
B's time over the course =80 sec

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

A)

100 m


B)

140 m


C)

180 m


D)

200 m



Correct Answer :

100 m


Explanation :

B runs 25 m ,A runs 22.5 m
B runs 1000, A runs = 1000*25/22.5 =900 m
B beats A by (1000-900)m = 100 m

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 win by B?

A)

10 m


B)

14 m


C)

18 m


D)

20 m



Correct Answer :

20 m


Explanation :

A covers 500-140 = 360 m
Ratio of speeds of A:B = 3:4
Let us consider A covers 3m/sec & B covers 4m/sec
Time taken by A to cover 360m=(360/3)=120 sec
So,Distance covered by B in 120s =120*4=480m

Therefore,A wins by (500-480)= 20 metres

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

A)

14 m


B)

28 m


C)

42 m


D)

56 m



Correct Answer :

28 m


Explanation :

Ratio of speeds of A:B =100 :75
Ratio of speeds of B :C=100 :96
then Ratio of speeds of A :C =A/B*B/C
=100/75* 100/96 = 100/72

So, A beats C by 100 - 72 m=28 m

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