Aptitude - Races and Games - Discussion

Discussion :: Races and Games - General Questions (Q.No.2)


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

Answer: Option B


A's speed = 5 x 5 m/sec = 25 m/sec.
18 18

Time taken by A to cover 100 m = 100 x 18 sec = 72 sec.

Time taken by B to cover 92 m = (72 + 8) = 80 sec.

B's speed = 92 x 18 kmph = 4.14 kmph.
80 5

Naresh.Ravula said: (Dec 21, 2010)  
While finding the speed of the B, why we are using the 92m only instead of 100m?

Sanju said: (May 15, 2011)  
Out of 100m he ran 8m so we deduct 8m from 100m then we get 92m to obtain B Speed we should caluclate B Speed by using 92m instead of 100m. I hope you understand. !

Rajesh said: (Sep 18, 2011)  
We should understand the ques properly. Its in the ques that b is 8m forward than a in 100m race, am I right?

Padma said: (Sep 24, 2011)  
Here first we can find the losers time, secondly we can find losers distance[since losers distance=winners distance- (start distance+beat distance) ] and later we can find the speed of B[since speed=distance/time]. Which is the final answer.

Is this not the correct procedure. Please tell me if it is.

Baburaj said: (Dec 16, 2011)  
Why Time taken by B to cover 92 m = (72 + 8) = 80 sec. comes?
Can any one explain ?

Sudharshan Madgula said: (Jan 16, 2012)  

Because A is taking 72sec to run 100m and beats B by 8sec.
that means still B needs 8sec to complete 100m.
therefore time taken by B to complete 92m is 72+8=80sec.

Anamika Sinha said: (Jan 21, 2012)  
How did you get A's speed ? I dint understand. Please explain.

Sayed said: (Jan 21, 2012)  
How A's speed is found ?

Jaanvi said: (Jan 23, 2012)  
@anamika & sayed
A's speed is in kmph. to make it in m/s, 5 is multiplied with 1000/(60X60).
Hence, 5X5/18=25/18

Sag said: (Aug 25, 2012)  
We are adding 8 second to cmplete 100m for b. So why his speed is calulated for 92 m. It should be for 100m and answer should be 4. 25.

Mangesh said: (Sep 18, 2012)  
Since both are covering 100m finally. So why we took 92m instead 100m ?

Qwaci said: (Nov 22, 2012)  
@ Sag & Mangesh.

First of all, A gave B a start of 8m so B did not run 100m but 92m (100m-8m). Secondly, A took 72sec to cover the 100m and still won B who had only 92m to run by 8sec which means that with the 92m that B covered he used or needed 80sec (72sec+8sec). I hope my little explanation could help you understand.

Prafull Gadekar said: (Jun 24, 2013)  
Instead of taking 5/18, we solve like,

A 's speed = 5 kmph = 5000 mph = 5000/3600 = 1.38m/sec,

For 100m distance time = 72.3 sec or 72 sec,

B's require time to cover 92m distance=(72+8) = 80 sec.

80 sec- 92m then,

1 sec - 1.15m.


1.15*3600 = 4140 mph = 4.14 kmph.

Girijesh said: (Aug 4, 2013)  
Let speed of B is x meter/sec.

Speed of A is y meter/sec.

Total time to reach 100 meter by A is 100m/5kmph = 72 sec.

Total time to reach 100 meter by B is:

(8/x) + time taken by A + 8 = 100/x.

(8/x) + 72 + 8 = 100/x.

x = 92/80 m/s = 4.14 kmph.

Prasanna said: (Aug 30, 2013)  
Why can't we change the distance into km and solve?. I am not getting the answer in that way.

Buddhika said: (Dec 30, 2014)  
Forget 5 kmh.

A runs = 8 m.
B runs = 100-8 = 92 m.
B speed = 92 m/8 s = 11.5 ms.

Now we convert ms = kmh.

11.5 x 18/5 = 4.14 kmh.

That is all.

Deepali said: (May 26, 2015)  
How get 18?

Vinay said: (Sep 25, 2015)  
We have given speed of A = 5 km/h => 5x5/18 = (25/18) speed;

A takes time = 100x (18/25), Time = Distance/Speed;

=72 sec;

Since A beat B by 8 sec.

So total time taken by B = 72+8 = 80 (time);

Since A gives 8 m to B.

So total distance cover by B = 100-8 = 92 (dist);

We know that Speed = Distance/Time;

Now speed of B = 92/80 m/s;

Now converting it into km/h => (92/80) x (18/5).

=> 4.4 answer.

Manisha said: (May 26, 2016)  
I can't understand why we have to use 18/5, where it come from? Can anyone explain?

Sravs said: (Jun 22, 2016)  
18/5 is the conversion of m/s to km/hr. Because option is in km/hr. We need to convert.

Ashutosh Kumar said: (Sep 2, 2016)  
A --> 100m.

B --> 92m.

Above is the situation B covers 92m in 72 + 8 = 80s therefore we have taken 92m to calculate the speed of B.

Mariyappa said: (Mar 24, 2017)  
How get 18 came here?

Sairam said: (Mar 4, 2019)  
Actually, B has to complete 92 meters in 72 seconds but he is taking an extra 8 seconds time to complete 100 meters which can be concluded from the question. Am I right?

Sileshi said: (May 23, 2019)  
How come 5/18? Please tell me.

Rocktim said: (Jul 5, 2019)  
How come 5/18? Please tell me.

Manikanta said: (Aug 12, 2019)  
Here A runs for 100meters while B has to run only for 92Meters as B is 8meters ahead of A.

5km per hour=5000 meters per hour.

As the question is asking in seconds. Now convert for each second how many meters A is running.

Here we have 3600 seconds for one hour.

So 5000meters or 5*1000meters/3600 which comes to 5*5/18=25/18.

In how many seconds A ran the100meters =100m*25/18sec=72sec.

A has run 8seconds faster than B. Which means B took 8seconds more to complete the run. Therefore 72+8=80Sec.

Now the question is B's speed in km per hour.

Calculate for each sec how many meters he ran=92meters/80sec.

Hence=92/80*18/5 (lets say 3600sec/1000meters) =4.14kmph.

Anusha said: (Jun 18, 2020)  
Nice explanation, thanks @Buddhika.

Ramanjaneyulu said: (Apr 9, 2022)  
How 5/8 came? please explain me.

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