# 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

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.