Aptitude - Races and Games - Discussion

Discussion :: Races and Games - General Questions (Q.No.1)

1. 

In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:

[A]. 18 m
[B]. 20 m
[C]. 27 m
[D]. 9 m

Answer: Option B

Explanation:

A : B = 100 : 90.

A : C = 100 : 72.

B : C = B x A = 90 x 100 = 90 .
A C 100 72 72

When B runs 90 m, C runs 72 m.

When B runs 100 m, C runs 72 x 100 m = 80 m.
90

B can give C 20 m.


Disha said: (Jan 8, 2011)  
Why we take 90 m instead of 10 m of B?

Sanju said: (May 15, 2011)  
When we took ratio between 100:90 we get 10. So they took 90 insted of 10. I hope you understand.

Gaurav said: (Jul 3, 2011)  
100-10=90, 100-28=72;

Because according to question A can gives B 10m and A can gives C 28m. I try my best to solve your problem.

Shameer said: (Aug 8, 2011)  
Why we not use A:B:C=90:X:72 ?

Saru said: (Aug 23, 2011)  
Why we use B/AxA/c here?

Bharath Ks said: (Oct 26, 2011)  
Can anyone explain it easily please ?

Prasanna said: (Oct 29, 2011)  
Why not going the race at which the question says? That is when finish the game B is 18m ahead of C.

Manojit said: (Feb 9, 2012)  
Because it is same race. They must complete same distance so when B has completed 100 m. He will give C 20m.

Ezhilmangai said: (Aug 25, 2012)  
A can give to B as 10,so B can give two times for A.so B can give C as 20.

Gopal said: (Feb 2, 2013)  
*-------------------*
<---100m------------> A
<-----90-------> B
<-----72---> C

When A completed race(100m) then B ahead 90 and c Ahead 72, and Distance between B & c = 18m.

i.e., When B cover 90 then distance between B & c = 18.
So When B cover 100 then distance between B & c = 18*100/90 =20 m.

Lavanya said: (Jun 16, 2013)  
Why do they do reciprocal 72/90?

Kalaivani said: (Sep 2, 2013)  
Can any one please explain logic clearly. How and why 72/90?

Nadeem Pasha said: (Oct 27, 2013)  
100 --- A.
90 --- B.
72 --- C.
When B covers 90m distance between A and B is 18m,
When B covers 100m distance between B and C is,

90 --- 18
100 --- ?

By cross multiplication we get 20.

Venkat said: (Mar 11, 2014)  
Can anyone explain it easily please?

Deepika said: (Jun 5, 2014)  
A : B = 100 : 90.
A : C = 100 : 72.

So divide both this equation you get C:B = 4:5.

And now we find for same 100 m race so multiply by 5*20=100 because we Find b can give c in same race.

4*20/5*20 = 80/100 = C/B.
So B can give C = 100-80 = 20 answer

Anime said: (Oct 31, 2014)  
What is m here? Is it meter or minute?

Diya said: (Jan 6, 2015)  
It is meter.

Jklomn said: (Feb 19, 2015)  
B is 18 meters ahead of C when he is at 90 m, when he will finish the race he will be 20 m ahead.

Melvin said: (Apr 10, 2015)  
How B give C 20? Is we simply check question the right answer is 18 because 28-10=18.

Arun said: (Jun 27, 2015)  
What is the meaning of A can give start of 10 meter?

Vichu said: (Aug 7, 2015)  
A can give 10 means A can lead B by 10 meter. That's A can give a lead of 10 meter. Got t @Arun.

Melvin its just not distance calculation to simply difference the distance. Here change in velocity of the players maters. For example if you just subtract the distance means B and C are running in same velocity right?

If so how would B can beat C in the race in the beginning? Got t so there is a velocity change in players that's what you are calculating unstintingly.

Abhishek Kushwaha said: (Aug 10, 2015)  
In a 100 m race, A can give B 10 m, It means A:B=100:90.....equation (1).

In a 100 m race, A can give C 28 m, It means A:C=100:72....equation (2).

In a 100 m race, B can give C=?

{Dividing Equation (1) and Equation (2) we get}.

B:C=90:72 or B:C=5:4 (After Dividing numerator and denominator by 18).

Or B:C=100:80 (After Multiplying numerator and denominator by 20).

In the same race B can give C=20[ANS].

Aarti said: (Jan 19, 2016)  
How to solve this problems in easiest way?

Aakriti said: (May 21, 2016)  
Thanks, @Abhishek Kushwaha.

Manisha said: (May 26, 2016)  
Thank you all for helping me.

Akhil Kondaparva said: (Aug 16, 2016)  
A defeats B by 10m i.e. if A runs 100m then B runs 90m.

A defeats c by 28m i.e. if A runs 100m then C runs 72m.

If B = 90 then C = 72.

If B = 100 then C = ? (cross multiply).

=> C = (72 x 100) / 90 = 80m.

So, if B = 100 C = 80.

ie=> B defeats C by 20 metres.

Dynamo said: (Aug 29, 2016)  
We have to compare between B & C.

If B goes 90.

C goes 72.

To be 100 we have to multiply by 100 and divide by 90.

90 * 100/90 ------> 72 * 100/90.

100 ------> 80.

So, B can give C = 100 - 80 = 20.

Manoj said: (Dec 7, 2016)  
Given A 100, B 10, C 28.

A gives B means 100 - 10 = 90 = B.
A gives C means 100 - 28 = 72 = C.
A : B = 100 : 90.
A : C = 100 : 72.

B : C = 90 : 72 -------> 90/72 = B/C.


Consider given one as 100.
B gives C is

B : C = 100 : 72/90.
C/B = 72/90 * 100 = 80m.

Sayeeda said: (Mar 24, 2017)  
Thank you for your explanation @Akhil.

Siddhesh said: (Apr 14, 2017)  
They are asking when B is at 100 m, where is C?

Consider A need x seconds to reach at 100m.

Velocity of A is 100/x.

Given that when A is at 100m, B and C are at 90m and 72m respectively...

So,velocity of B is 90/x (m/sec)
velocity of C is 72/x (m/sec)

Now, For B to reach 100m, 10m again have to run
time required for B to run 10m =10/(90/x) = x/9 sec.
distance covered by C in x/9 sec =(x/9)*(72/x) = 8m.

So when B is at 90+10=100m.
C is at 72+8 = 80m.

B won race by 20m difference with C.

Ramesh said: (Apr 25, 2017)  
I am not getting it.

At last how the answers came as 20? please explain.

Jayasree said: (May 18, 2017)  
Does anyone know how can we solve this question by having the difference in distance values only( i.e, using 10 and 28)?

Please tell me.

Ammu said: (Jun 11, 2017)  
Please anyone explain this in simple way.

Anandu said: (Jul 7, 2017)  
@Ammu

I think throughout the race a, b&c have respective constant velocities.
That being said this problem can easily be solved using the concept of ratios.

Question is to find the distance btw b&c at the end of the race(when b reaches 100m).
It is given separation btw b & c when b reaches 90m is 18 (ie 90-72).
So, when b reaches 1m mark the Seperation btw them is simply 18÷90=1/5
When b reaches 100m ie end of the race the seperation is (1/5) * 100. =. 20.

I hope it is clear now.

Siddharth said: (Jul 8, 2017)  
Here, give indicates the distance that participants overtake each other.

So, A beats B by 10m in a 100m race indicates A finishes 100m whereas B finishes 10m behind A in the same time ie.) 90m.

Similiarly, A beats C by 28m indicates C covers 72m in the same time where A finishes 100m.
Now ratio of distance covered in a given time by B and C remains same ie.) 90:72 ie.) 5:4.

When, B covers 100m in a given time, C covers only 80 in the same time. So B beats C by a distance of 20m.

Raja said: (Jul 27, 2017)  
A finished 100m.
At that time.
B is 10m less than A, so B is 90.
C is 28m less than A, so C is 72.
The difference b/w in B and C is.
90-72 = 18.
When B is 90m then the difference is 18m.
When B is 1m the difference is 18/90=0.2m.
When B is 100m the difference is 0.2 * 100=20m.
At that time C will be 80m.
Ans is 20m.

Mohanagiri said: (Jun 27, 2018)  
@Raja.

Clear explanation. Thanks for that.

Prince Priyadarshi said: (Aug 18, 2018)  
@All.

The solution is;

In same time A,B and C travel 100,90,72 meters respectively hence we can write:
100:VA = 90:VB = 72:VC where VA,VB,VC are velocities of A, B, C respectively.
Hence;
VB:VC = 90x:72x that means time taken by B to travel 100m is tb= 100/90x.
In this time C travel ( 100/90x)*72x = 80 m implies B gives C by 20m.

Aksh said: (Sep 9, 2018)  
A gives B 10m means A beats B by 10m, A wins the race, by completing 100m, ie B will be at 10.

Gauri said: (Jun 7, 2020)  
Thank you for the explanation @Akhil.

Ngawa said: (Oct 19, 2020)  
Difference between B and C
28 - 10 =18.
Now,
18 /90 * 100= 20.
Thus give 20m in 100 game.

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