Aptitude - Races and Games - Discussion

Discussion :: Races and Games - General Questions (Q.No.3)


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]. 60 m
[B]. 40 m
[C]. 20 m
[D]. 10 m

Answer: Option C


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 x 360 m = 480 m.

Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.

A wins by 20 m.

Kriti said: (Dec 3, 2010)  
Hi, when 3:4 is the ratio of speeds how can we use it
as 3m and 4m for A and B resp.?

Sudheer said: (May 19, 2011)  
Hi kriti here speed and distance are directly proportinal. If his speed is 10km/hr he cover 10km distance. If speed is 20km/hr he can cover 20 km distance. Thus speed and distance are directly proportinal. So here distance ratios also become3:4. But the time ratio will become4:3 because time and speed are inversly proportinal.

Vamsi said: (Jul 5, 2011)  
I didn't understand how it can be 4/3. ?

Malli said: (Sep 30, 2011)  
Hai, my dout is same that of vamsi.

Why we had taken 4/3 in problem?

Manojit said: (Feb 9, 2012)  
While A covers 3 m, B covers 4 m.
While A covers 1m, B covers 4/3 m.
While A covers 360 m, B covers (4/3* 360)m =480 m.
Here time is same in case of speed.we count different distance in same time.

Rajesh said: (Feb 7, 2013)  
Can be solved by simple calculation.

A covers 360m (ie) 500-140.

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)=120seconds.

So,Distance covered by B in 120s =120*4=480m.

Therefore,A wins by 20 metres which is (500-480).

Srinu said: (Feb 8, 2015)  
Time = dis\speed.

T = 360\3 = 120sec.
Now dis = sxT = 4x120 = 480m.

So 500-480 = 20m.
This is the answer.

Newstein Faraday . said: (Jul 1, 2015)  
A has to travel 360 meters therefore Time =distance/ speed. So 360/3 = 120 seconds.

The same 120 seconds b has to travel so distance = speed x time = 4 x 120 = 480.

The remaining distance that b has to travel is 500-480 = 20.

Damini.Arora said: (Aug 25, 2015)  
Here, because A has a start of 140, he has already covered 140 m when B starts. So when A covers rest of 360, B covers 480.

Hence B loses race by 20 m.

Ash said: (Jan 19, 2016)  
Speed is directly proportional to distance.

3/4 = (500-140)/(500-x).

3/4 = 360/(500-x).

Hence x = 20.

Anand said: (Sep 1, 2019)  
Here is the simplest method,

Speed ratio is 3:4 SO let consider 3m & 4m for both A & B.
A travels 360 and B travels 500.
This means A takes 120 seconds and B takes 125 seconds.
5 seconds more than A is travelled by B.
In one B travels 4m.
So in 5 seconds, 5*4=20m.
B travels 20m more than A.
That is A win by 20m.

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