A train overtakes two persons who are walking in the same direction in

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A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 seconds and 10 seconds respectively. The length of the train (in metres) is

A. 45
B. 50
C. 54
D. 62
E. 72

A. 45
B. 50
C. 54
D. 62
E. 72

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freedom128 · Answer

Train speed = v m/s
Train length = L m

Person #1 (2km/h)  
After 9 secs, train travels 9v meter and person #1 travels (2*5/18*9)=5 meter. -->  9v= 5+ L ... Eq.(1)

Person #2 (4km/h)  
After 10 secs, train travels 10v meter and person #2 travels (4*5/18*10)=100/9 meter. -->  10v= 100/9 + L ... Eq.(2)

(2)-(1)  --> v=55/9 m/s

(1)  --> 9v - 5 = L = 9(55/9) - 5 = 50m

FINAL ANSWER IS (B)

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lacktutor · Answer

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 seconds and 10 seconds respectively. The length of the train (in metres) is
 
 1st :  2kmph=(\frac{5}{9})  meter per second
 2nd : 4kmph=(\frac{10}{9})  meter per second
--> Let  x  and  y  be the speed and length of the train:  y = ????

if the train passes  1st  person in  9  seconds:
-->  x*9= y+ \frac{5}{9}*9 
 9x= y+ 5

if the train passes  2nd  person in  10  seconds: 
-->  x*10= y+ (\frac{10}{9})*10 
 10x= y+ \frac{100}{9} 
-----------------------------------------
-->  10x -9x = y+ \frac{100}{9} -y -5 
 x= \frac{55}{9}  
-->  y = 55-5 =50

Answer (B)

CareerGeek · Answer

Let the length of the train =  L  kms & speed =  v  kmph

train overtakes them in 9 & 10 seconds respectively
-->  \frac{9}{3600} = \frac{L}{v - 2}  -->  L = \frac{9(v - 2)}{3600}  ....... (1)
&  \frac{10}{3600} = \frac{L}{v - 4}  -->  L = \frac{10(v - 4)}{3600}  ....... (2)

From (1) & (2),
 \frac{9(v - 2)}{3600} = \frac{10(v - 4)}{3600} 
-->  9v - 18 = 10v - 40 
-->  10v - 9v = 40 - 18 
-->  v = 22 kmph

From (2),
 L = \frac{10(v - 4)}{3600} = \frac{10*18}{3600} = \frac{1}{20} kms = \frac{1}{20}*1000 meters = 50 meters

Option B

exc4libur · Answer

same direction: subtract rates

d/(t-2)=9, d=9t-18
d/(t-4)=10, d=10t-40
9t-18=10t-40, t=22kmh
d/(t-2)=9 secs
d/(t-2)=9/3600 hrs
d=1/400*(22-2)=20/400=1/20km
d=1/400*(22-2)=20/400=50m

Ans (B)

eakabuah · Answer

let t be speed of train and x be the length of the train
We know that speed = distance/time, hence distance = speed * time
Then the length of the train is (t-2)*9/3600 with respect to the person traveling at 2kmph and (t-4)*10/3600 with respect to the person traveling at 4kmph.
But the length is the same, 
hence (t-2)*9/3600 = (t-4)*10/3600
9t-18=10t-40
t=22kmph

x = (22-2)*9/3600 = 0.050km = 50m

B is the answer.

madgmat2019 · Answer

let the length of train be x
speed of train be s
 two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph which is 2*5/18 = 5/9m/sec and 4*5/18 = 10/9m/sec
x = 9(s-5/9)
x= 10(s-10/9)
from above we get 
s=55/9
then x becomes 50m

OA:B

unraveled · Answer

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 seconds and 10 seconds respectively. The length of the train (in metres) is

A. 45
B. 50
C. 54
D. 62
E. 72

A. 45
B. 50
C. 54
D. 62
E. 72
Length of train = L
Speed of train = S
Speed of person 1 = 2 kmph =  \frac{5}{9}  m/s
Speed of person 2 = 4 kmph =  \frac{10}{9}  m/s

Now, 
 \frac{L}{S-5/9}  = 9 and
 \frac{L}{S-10/9}  = 10

Two Equation and two variables. Solving we have
S =  \frac{55}{9}  and L = 50

Answer B.

ScottTargetTestPrep · Answer

First, let’s convert the rates to meters per hour (m/h): 2 kmph = 2000 m/h and 4 kmph = 4000 m/h. Now, let L = the length of the train, in meters, and r = the speed of the train, in m/h. We can create the equations:

2000 x 9/3600 + L = r x 9/3600

5 + L = r x 9/3600 → Eq. 1

and

4000 x 10/3600 + L = r x 10/3600

100/9 + L = r x 10/3600 → Eq. 2

Subtracting Eq. 1 from Eq. 2, we have:

55/9 = r x 1/3600

55/9 x 3600 = r

22,000 = r

Substituting 22,000 for r in Eq. 1, we have:

5 + L = 22,000 x 9/3600

5 + L = 55

L = 50

Answer: B

Kunni · Answer

Hi,

9v= 5+ L . Could you please tell me how did you equate this?

Regards
Kunal

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