Races And Games- Aptitude Questions and Answers

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 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

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

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.

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.

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.
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.

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

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

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

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.

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

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

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

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

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