Two trains A and B are moving in opposite direction in different tracks. The length of these trains

M4maths Previous Puzzles

27 Nov 2013 Speed

Two trains A and B are moving in opposite direction in different tracks. The length of these trains are 100 m. and 110 m. respectively. If speeds of A and B are in the ratio 4:5 and these two trains cross each other in 10 sec. Then speed of train B is

OPtion

1) 70/3 m/s
2) 5/3 m/s
3) 50/9 m/s
4) 55/3 m/s
5) 35/3 m/s
6) 28/3 m/s
7) 4/3 m/s
8) 40/9 m/s
9) 84 m/s
10) 105 m/s

Solution

Let the speeds of the trains are 4v and 5v. Since the trains are moving in opposite direction,
relative speed of the train is 4v + 5v = 9v
According to the formula
speed = distance / time
9v = 210/10 = 21
or v = 7/3 hence speed of B is 5v = 5*7/3
= 35/3 m/s
option 5)

Correct Option: 5 Best Solution (34)

Raisul Alam   11 years AGO

As the speeds of A and B are in the ratio 4:5, so let the speed of A=4x m/sec and the speed of B=5x m/sec.
The trains are moving in opposite direction so the relative velocity will be (4x+5x)=9x m/sec.
The length of train A=100 m and the length of train B=110m. So if they crossed each other the total distance will be covered is (100+110)=210 m as they are moving in opposite direction.
Now, 9x m goes in 1 sec (given)
1 m goes in 1/9x sec.
210 m goes 210/9x sec.
So it is given that (210/9x)=10
Hence x=21/9.
So the speed of B=5*21/9=35/3. and option 5 is the right answer.

Like? Yes (8) | No (2)  

Suman   11 years AGO

As trains are running in opposite direction so their resultant speed will be sum of their speeds...
ratio of their speed is 4:5
let us assume their speed are 4x m/s and 5x m/s
resultant speed is 9x m/s
in 10 sec they cover 9x*10 i.e 90x m
According to the question 90x=210
x=210/90 i.e 7/3
So speed of train B is 7*5/3 i.e 35/3 (ans)

Like? Yes (5) | No (2)  

Ankit Goyal   11 years AGO

Let the speed of A be 4x then speed of B=5x
Their relative speed = 9x
Total distance covered = 100 + 110 mts =210 mts(Distance/Speed) = Time
210/9x = 10
x = 7/3
speed of B = (7/3) * 5 m/s = 35/3 m/s

Like? Yes (5) | No (3)  

R.RAVIKUMAR   11 years AGO

let the speed be x m/s
so, as trains are moving in opposite direction speed is 4x+5x=9x m/s
total distance is 100+110=210m
total speed is 210/10=21 m/s
so, 9x=21 m/s
so, x=21/9=7/3 m/s
Speed of train B is 5*(7/3)=35/3 m/s

Like? Yes (3) | No (2)  

Udhaya kumar   11 years AGO

let x,y as speed of A & B respectively
then
x/y= 4/5
x+y=(100+110)/10 ;; x+y=21
by solving x=28/3
y=35/3.........

Like? Yes (4) | No (3)  

lovely verma   11 years AGO

according to the formula-t=L1+L2/(V1-(-V2))
-V2 represents movement in opposite direction
10=(100+110)/(4V2/5+V2)
10=210/(9V2/5)
V2=21*5/9=35/3m/sec
speed of train B=35/3m/sec

Like? Yes (1) | No   

marigari bhagyashree   11 years AGO

t=l1+l2/(v1+v2)
=(100+110)/(4x+5x)
10=210/9x
x=7/3
b speed=5x=35/3

Like? Yes (1) | No   

Chandni Maurya   11 years AGO

ans=35/3 m/s
let the speed of train A and B are 4x and 5x resp.
their relative speed = (4x + 5x)m/s = (100+110)m/10s
=>9x=210/10
=>x=21/9 = 7/3 m/s
=>speed of train B =7*5/3 = 35/3 m/s

Like? Yes (3) | No (3)  

Gautham Sarang   11 years AGO

tot distnc = 100+110=210
rel vel= 210/10=21
21=a+b
21=b(1+4/5)
b=35/3

Like? Yes (3) | No (3)  

mirtunjay verma   11 years AGO

total distance is 100+110=210
time 10 sec so speed will be
210/10=21 divide in ratio we get 35/3

Like? Yes (3) | No (3)  

julee verma   11 years AGO

given that-La=100m,Lb=110m
Va/Vb=4/5 so Va=4Vb/5
time(t)=10 sec
so according to the formula-
t=La+Lb/(Va-(-Vb))
(here -vb is used because trains are moving in opposite direction)
10=(100+110)/(4Vb/5+Vb)
10=210/(9Vb/5)
Vb=21*5/9=7*5/3=35/3m/sec
Hence speed of train B= 35/3m/sec

Like? Yes (3) | No (3)  

AMIT JAISWAL   11 years AGO

La=100m Lb=110m
Va/Vb=4/5 so Va=4/5Vb time t=10 sec
by using formula-
t=La+Lb/(Va-(-Vb))=La+Lb/(Va+Vb)
here -Vb is used for opposite direction movement
10=100+110/(4Vb/5+Vb)
10=210/(9Vb/5)
Vb=21*5/9=35m/sec
So correct answer is 35/3m/sec

Like? Yes (3) | No (3)  

Keshav Kishlay   11 years AGO

let ratio variable is x
then the speed of A is 4x
and the speed of B is 5x
both train are in opposite direction
so speed is 9x now
9x=210/10
x=7/3
so speed of B is 5*7/3=35/3 m/s

Like? Yes (2) | No (2)  

vinod   11 years AGO

Here relative speed=t1+t2=V;
total distance=100+110;
v=d/t;
V=210/10=21;
speed of train B=5/9(21)=35/3;

Like? Yes (2) | No (2)  

Dhanisha veligatla   11 years AGO

total distance=210(since they are travelling in opposite direction.
avg speed=210/10=21
hence speed of b=(5*21)/9=35/3

Like? Yes (2) | No (2)  

Wasim Akram Khan   11 years AGO

(total lenght)/(4x+5x)=10
210/9x=10
x=7/3
speed of B is 5*(7/3)=35/3

Like? Yes (2) | No (2)  

b.s.venkatesh   11 years AGO

210=speed *10
speed of 2nd train =5*21/9
35/3

Like? Yes (2) | No (3)  

ROHIT UPADHYAY   11 years AGO

210/9x=10
x=7/3
5x=35/3

Like? Yes (2) | No (3)  

susmit   11 years AGO

let the speed of the trains be 4x and 5x respectively.
In 10 seconds they travel 100+110= 210m
so in 1 second they travel 21m
speed = distance/time
so 9x=21/1 m/s
so x=21/9m/s
so 5x=(21/9)*5=35/3m/s
option no. 5

Like? Yes (1) | No (2)  

Devendra Marghade   11 years AGO

Speed of train A & B are 4x & 5x m/s respectively
Relative speed=4x+5x=9x
Time taken to cross dist.of(100+110)=210m is 10sec
So in 1 sec, distance travelled=210/10= 21 m.
Spped/sec=9x=21/1 m/s,x=21/9=7/3
So speed of train B=5x=5*7/3=35/3 m/s

Like? Yes (1) | No (3)  

Biren Kumar Das   11 years AGO

Given speed of A and B are in the ratio 4:5 That means if speed of A is 4x then speed of B is 5x

We Know
time taken to cross each other=(length of A+length of B)/(speed of A+Speed of B)

10=(100+110)/4x+5x)
10=210/9x
x=7/3
speed of B =5x=5 * 7/3=35/3

Like? Yes (1) | No (3)  

Dr.Dipin Singh   11 years AGO

If speeds of A and B are 4x and 5x m/sec, then
9x*10= (100+110)
x= 7/3 m/sec

speed of train B = 5x= 35/3 m/sec

Like? Yes (1) | No (3)  

Shubham Saxena   11 years AGO

total distance=210 m
total speed=9x
time in which they cross each other =10 sec
therefore,210=9x*10
x=21\9
for second train that is speed=5x
so,5*21\9
=35\3 m\sec

Like? Yes (1) | No (3)  

krishn kumar gupta   11 years AGO

let speed of train A & B are 4x and 5x m/s.
then
relative speed=(110+100)/10
=>4x+5x=21
=>x=7/3
therefore speed of Train B=35/3 m/s.

Like? Yes (2) | No (4)  

C. Veda Kumar   11 years AGO

for this condition the time== (sum of distances)/sum of speeds..

Like? Yes (2) | No (4)  

DHIRENDRA    11 years AGO

given
length of train A=100m
length of train B=110m
total length=100+110=210m
ratio of the speed of train A & B=4:5
let speed of train is x;
relative speed of train =4x+5x=9x
time=distance/speed
10=210/9x
9x=21
x=7/3
speed of train A=(7/3)*4=28/3 m/s
speed of train B=(7/3)*5=35/3 m/s

Like? Yes (1) | No (3)  

prem singh   11 years AGO

logic-

l1=100
l2=110
t=10
ratio=4/5
let x is total speed then 4x/5x
speed=distance/time
4x+5x=(110+100)/10=210/10
9x=21
x=21/9=7/3

now speed of B=5x=5*7/3=35/3

Like? Yes (1) | No (3)  

KRISHNAN   11 years AGO

Let the speed of train A be x and train B be y
Thus x:y = 4:5 or x = 4/5y
Now the length of train A is 100m and train b is 110m
Time to cross each other travelling in opposite direction is (100+110)/(x+y) = 10 sec
or 210/(4/5y+y)=10
or 210= 18y or y= 35/3 m/s

Thus option 5 is correct

Like? Yes (1) | No (3)  

Satyendra Singh   11 years AGO

because if trains are moving in opposite directions than relative speed of trains
4x+5x = 9x
time taken to cross each other is 10 second
total distance is 210 meter
10 = 210/9x
x= 7/3
train B speed 5*7/3=35/3

Like? Yes (1) | No (3)  

rohit kumar   11 years AGO

Speed =distance/time
i.e speed=(110+100)/10
i.e speed=21 m/s
As given the speeds of A & B are in the ratio 4:5
So,speed of B=(5/9)*21=35/3 m/s...ANS

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ARJYA HALDER   11 years AGO

Let,x be the common ratio.
So, relative speed of both the train is=(4x+5x)=9x.
relative distance of both the train to be covered=(110+100)=210
From question,
9x*10=210
which implies x=(7/3)
So, speed of train B is [(7/3)*5]=(35/3).
So, option 5 is right.

Like? Yes (1) | No (3)  

maninder singh bajwa   11 years AGO

let speed of Train A and Train B be 4x and 5x resp.
since trains moving in same direction therefore relative speed becomes 4x+5X=9x

now s=d/t therefore 9x=100+110/10
9x=210/10=21
x=21/9 or 7/3
hence speed of train B be 5x=5*7/3
=35/3 ANS

Like? Yes (1) | No (3)  

pavan   11 years AGO

train length, A=100
train length,B=110
speed ratio=4:5
speeds A=4x, B=5x
time=10sec
den
(100+110)/(4x+5x)=10
x=21/9
speed of B= (21/9)*5=35/3

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RAKESH   11 years AGO

(100+110)/(4x+5x)=10
x=21/9
so 5x=35/3

Like? Yes (1) | No (3)