Aptitude - Races and Games - Discussion

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.

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.

@ 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.

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.

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.

1.15m/sec.

1.15*3600 = 4140 mph = 4.14 kmph.

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.

@Baburaj:

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.

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?

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. !

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.