In a race of 500 m, L beats M by 40 seconds and beats N by 125 m. If M

Question

In a race of 500 m, L beats M by 40 seconds and beats N by 125 m. If M and N run a 500 m race, M beats N by 40 seconds. Find the time taken (in seconds) by M to run the race.

(A) 160
(B) 240
(C) 280
(D) 320

chetan2u · Answer

We can compare TIME and get to our answer..

Let the speed of M and N be m and n in meter per second
Two situtations..

1) when L finishes the race..
L...40sec..M .... in meters it will be m*40
L........125m......N
The distance between M and N is 125-40m

2) when M finishes the race..
M...40sec..N.... in meters it will be n*40
Here N travels 125-40n

So the time M takes to finish race, both M and N have traveled for 40 secs.
Thus N travels 125-40n in 40 secs..
So, 40= \frac{125-40n}{n}=\frac{125}{n}-40...........80=\frac{125}{n}............n=\frac{125}{80} m/s
Therefore, time taken by N is  \frac{Distance}{speed}=500/\frac{125}{80}=\frac{500*80}{125}=4*80=320  seconds..

But we are looking for time taken by M, who finishes race 40 secs before N => 320-40=280 seconds

C

Piyush1993 · Answer

pls give a kudos if you like the solution.

lets say M takes t time to finish the race.
 Dist Time
L 500 t-40 
M 500 t 
N 500 t+40

Also, basis L and M run, we can understand that as L beats M by 125m, it means when L finished the race (dist covered 500m), M has covered only 375m (500-125)
 Dist Time
L 500 t-40 
M 375 t-40

equating speed of M from both the tables, 500/(t+40) = 375/ (t-40)
solve for t, t= 280s

In a race of 500 m, L beats M by 40 seconds and beats N by 125 m. If M

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