Latest Elitmus Aptitude Question SOLUTION: In a kilometer race, If A gives B a 40m start, A wins by 19sec. But if A gives B a 30 sec start, B wins by 40 m. Find the time taken by B to run 5,000m?

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(#M40157309) ELITMUS Numerical Ability question Keep an EYE

In a kilometer race, If A gives B a 40m start, A wins by 19sec. But if A gives B a 30 sec start, B wins by 40 m. Find the time taken by B to run 5,000m?

Asked In Elitmus Samjukta Das (7 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

ALOK RANJAN DAS  (7 years ago)

Let A travells 1000m in x sec and b in (x+19)sec
Therefore, speed of B is 1000/(x+19)
B travel 960m in x sec from here equation of speed=960/x
speed of B is constant so boht the speed equation for B are equal
960/x = 1000/(x+19)
On solving we get x=456sec
Time taken by B for 5000m : 5000/(960/456)=2375
The ans will be 2375

Is this solution Helpfull? Yes (9) | No (5)  

ASHISHKUMAR SINGH  (7 years ago)

If A takes x seconds and B takes y seconds to run 1km, then:
x+19=
960y
1000
and
960x
1000
+30=y
⇒ y=150 sec and x=125 sec
Answer =
150
1000
×5000
= 750 sec

Is this solution Helpfull? Yes (5) | No   

Prateek  (7 years ago)

let the speeds of A and B be v1 and v2 respectively
from 1st condition,
v1=1000/t
v2=960/(t+19) [since B starts the race from the point 40m ahead of A]
from the second condition,
v1=960/t2
v2=1000/(t2+30)[since B gets 30 sec headstart and reaches 1000m when A is 40m behind]
solving for v2 we get t2=132.24 sec
thus v2=1000/162.24
therefore for 5000m t3=811 sec

Is this solution Helpfull? Yes (3) | No (2)  

saicharan  (7 years ago)

if A takes x seconds and B take Y seconds for 1km race

so from 1st meaning x+19=960y/1000 ->y=150 seconds

from 2nd statement y-30=960x/1000 -> x=125 seconds

now the qus is How much time taken by B to cover 5000m

so 150/1000*5000=750 sec

Is this solution Helpfull? Yes (2) | No   

rishab  (7 years ago)

375sec
let x be speed of a, y be speed of b
x=1000/t, y=960/t+19
also
x=960/g, y=1000/t+30
solving 1000/t=960/g
960/t+19=1000/30+g
solving these we get t =125
hence y=960/125+19
t for next ans=5000*144/960

Is this solution Helpfull? Yes (1) | No (2)  

Raja Babu  (7 years ago)

1.A gives B a 40metre start then B runs 960m in T secs and A runs 1000m in T-19 secs.

2.A gives B a 30 second start then B runs 1000m in t secs and A runs 960m in (t-30) secs.


Assuming speed of A=X and B=Y

Then,
X = 960 ÷ T = 1000 ÷ t,
960t = 1000T


Y = 1000 ÷ (T - 19) = 960 ÷ (t - 30)
1000t - 30000 = 960T - 18240
Then 40t = -40T + 11760,
t = -T + 294.
Substituting for t in 960t = 1000T gives
-960T + 282240 = 1000T
1960T = 282240
T = 144
B 's speed is 960 ÷ T = 960 ÷ 144 = 6.67 metres per second.
to run 5000 metres the time taken is 5000 ÷ 6.67 = 750 seconds

Is this solution Helpfull? Yes (1) | No   

Subhasikta Behera  (5 years ago)

If A takes x seconds and B takes y seconds to run 1km, then:
x+19=
960y
1000
and
960x
1000
+30=y
⇒ y=150 sec and x=125 sec
Answer =
150
1000
×5000
= 750 sec

Is this solution Helpfull? Yes (1) | No   

Aanchal khurana  (7 years ago)

Please tell the correct answer

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gurdeep singh saini  (7 years ago)

750
answer

Is this solution Helpfull? Yes | No   

Abhisek Panigrahi  (7 years ago)

ravi in your ans it is coming p=7 and p=3 ....your ans is wrong also

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Manisha Kumari  (7 years ago)

I am getting 835.22sec

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SHAVALA NANDEESHWARUDU  (7 years ago)

No need of first statement because in the second statement all the required data is given
By considering the second statement,
v=d/t=>30=40/t
t=4/3
For 5000 mts, t=d/v=5000/(4/3)=3250

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rishab kumar  (5 years ago)

If A takes x seconds and B takes y seconds to run 1km, then:
x+19=
960y
1000
and
960x
1000
+30=y
⇒ y=150 sec and x=125 sec
Answer =
150
1000
×5000
= 750 sec

Is this solution Helpfull? Yes | No   

triveni  (4 years ago)

1. A can run 1000 m in T-19 sec
and B can run 960 m (1000-40) in T sec .
2 . A can run 960 m in t-30 sec
and B can run 1000 m in t sec .
then ....< speed =distance /time > .
speed=1000/T-19=960/t-30--------eqn.1
speed=960/T=1000/t---------------eqn.2

therefore,by solving both
eqn 1 & 2
T=144
t=150.

therfore ,1000-----150
5000------? 5000*150/1000= 750..
and
if , 960------144
5000------? 5000*144/960= 750...

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