Aptitude - Races and Games - Discussion

Discussion :: Races and Games - General Questions (Q.No.4)


In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

[A]. 5.4 m
[B]. 4.5 m
[C]. 5 m
[D]. 6 m

Answer: Option D


A : B = 100 : 90.

A : C = 100 : 87.

B = B x A = 90 x 100 = 30 .
C A C 100 87 29

When B runs 30 m, C runs 29 m.

When B runs 180 m, C runs 29 x 180 m = 174 m.

B beats C by (180 - 174) m = 6 m.

Tarun Gupta said: (Oct 8, 2011)  
I am getting 5.4 as answer. Please help.

if A runs 180 then b runs 162 (90*180/100)
if A runs 180 then C runs 156.6(87*180/100)


What is wrong in my approach. Help ?

Rohit said: (Feb 11, 2012)  
Hi friends i got the simple method

when A complete 100 m then
B (100-10)=90
and c (100-13)=87
they ask in 180m race B beat c means
if B covers 180 which is twice of 90
then C will reach 87*2 = 174

Pintu Kashyap said: (Aug 6, 2013)  
If say answer is 5.4 means we are including A also in the race but qtn asking about B & C.

In 100m race B cover 90m and c cover 87m. In another 90m B also cover 90m and c cover 87.

Total a cover 180m and c cover 174. So 180-172 = 6 m.

Manmohan Pal said: (Sep 7, 2013)  
It is given that.

B runs 90 m, C runs 87 m.

If B runs 180 m, C runs (87*180) /90.

C runs = 174 m.


B will beat C by 180-174 = 6 m.

R.Subash said: (Mar 11, 2014)  
Rohit your method is too great.

And Pintu kashyap in the last line you have one simple mistake, that's not 172 it is 174.

Akhil said: (Sep 19, 2016)  

That was an awesome trick thanks!

Pranay said: (Feb 12, 2017)  
Simple & of easy to understand @Rohit.

Ramm said: (Jun 27, 2017)  
Good explanation, Thanks @Rohit.

Sana said: (Jan 8, 2018)  
Another simple method.

B=behind A by 10m or travel-90m,
C= behind A by 13m or travel-87m,
Common difference B and C(90-87)=3m,
Now Follow the question its asked 180m.
B=90m*2=180m so, common difference=3*2=6m.
So, This 6m is the actual beating distance of C by B.

Priyaa said: (Jun 5, 2019)  
Thanks @Rohit.

Subhajit said: (Feb 5, 2020)  
In 100 m race, a beats b by 10m
a beats c by 13m

So b beats c by (13-10)=3m
Same configuration carry forward to 180m.

So if in. 100m race b beats c by 3m.
180m race b beats c by (3*180)/100.
=5.4m(probable ans).

Another method:

In 100m race a finish 100m at the same instant b finish 90m at the same time c finish 87m
The same configuration carry forwarded
180m race a finish 180m at the same time b finish at 162m at the same time c finish at 156.6m then difference between them is (162-156.6)=5.4m (corrected).

Vinay said: (Jul 13, 2021)  

Definition of defeating C for B is a time when B reachs 180m how far behind c is.

If you are getting 5.4 as an answer that means only "A" has reached the finish point of 180m, "B" is still at 162 meters, that is "B" has not completed the race.

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