Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
[A].
1 : 3
[B].
3 : 2
[C].
3 : 4
[D].
None of these
Answer: Option B
Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Krutik Kansara said:
(Tue, Jun 1, 2010 01:10:48 PM)
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KRUTIK KANSARA.
Priya said:
(Sat, Jul 10, 2010 02:06:18 AM)
I hav no doubt, but I need different steps to solve this question.
Anyone can do this ?
Poornima said:
(Tue, Jul 13, 2010 05:19:19 AM)
Can anybody explain it clearly.
Rahul said:
(Wed, Jul 28, 2010 04:07:02 PM)
@Priya.
I don't think we can solve it by different method as given data is not sufficient to solve it by different method.
K.Kiran Kumar said:
(Tue, Aug 3, 2010 11:46:30 PM)
I can't get this step
(27x+17y) / (x+y) = 23
Why we have to use this? can any one explain me.
Niveditha said:
(Mon, Aug 9, 2010 06:40:53 AM)
Anyone please help me how this x+y is divided.
Arjun said:
(Wed, Aug 11, 2010 06:07:08 AM)
(27x+17y)/x+y=23 how did used that step?
Janardhan said:
(Thu, Aug 12, 2010 01:07:34 PM)
It's correct method to solve this problem.
Boomathi said:
(Tue, Aug 17, 2010 04:10:33 AM)
very good solution....
Arun said:
(Sun, Aug 22, 2010 06:21:26 AM)
Based on the below formula -- >
If two trains of length a(i.e. 27x) metres and b(i.e. 17y) metres are moving in opposite directions at x m/s and y m/s, then:
The time taken by the trains to cross each other (i.e.23 sec) =
(27x + 17y)
```````` secs
(x + y)
Therefore, the above solution is provided based on this derivation. Its given in the formulas section.
Mohit Sahu said:
(Sun, Aug 22, 2010 11:01:13 AM)
Friends its easy to undrstnd as the qustn says that d trains r moving in oppste drtn that means the total distance travveld by the trains wen they crosses the person will be equal to the total distance travlld by dem in crossng each other.
Mathematly we can also better undrstnd ths by wrtng tht equation as
27x + 17y = 23(x + y).
Vivek said:
(Mon, Aug 23, 2010 01:29:56 AM)
How the (27x+17y)/x+y=23 formula comes?
Sunny(Sunil) said:
(Tue, Aug 24, 2010 11:35:29 AM)
Look at this link then you can understand why we use x+y down there!
Sameer said:
(Sat, Sep 4, 2010 10:13:25 AM)
Can anyone explain me how he got this step 4x = 6y ?
Bhanu said:
(Sat, Sep 4, 2010 11:42:01 AM)
Take all x terms once side and why terms other side then subtract we get 4x = 6y.
Lokesh said:
(Tue, Sep 14, 2010 09:46:53 PM)
27x - 24x = 23y - 17y
4x = 6y
x/y = 3/2.
Prabhakaran said:
(Sat, Sep 18, 2010 01:18:30 PM)
Im not clear with above step can anyone give more explanation about this problem. I have doubt in (27x+17y) / (x+y) =23 what this statement mean by. Anyone help me please.
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,(length=speed*time..so length=x*27=27x metres)
and length of the second train = 17y metres.(length=speed*time..so length=y*17=17y metres)
If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:
The time taken by the trains to cross each other = (a + b)/u + v)sec.
By using above formula we get d solution for this.
Here it is given that they cross each other in 23 seconds.
So 23 = (27x+17y) / (x+y).
Sushma said:
(Mon, Oct 4, 2010 08:59:25 AM)
Thanks Ramakrishna, your answer is excellent.
Sri said:
(Wed, Oct 13, 2010 03:47:31 AM)
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,(length=speed*time..so length=x*27=27x metres)
and length of the second train = 17y metres.(length=speed*time..so length=y*17=17y metres)
If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:
Relative speed of the trains =x+y(since they are moving in opp direction)
Total distance covered = L1+L2
So time taken to cross each other = total distance /relative speed
Hence 23=(27x+17y)/(x+y)
Kartik said:
(Wed, Oct 13, 2010 03:52:45 AM)
Excellent explanation SRI.
Confused said:
(Wed, Oct 13, 2010 11:35:36 AM)
Sorry guys for pecking on the same thing again.
But Why is it necessary that total distance covered = sum of the train's length?
Isn't the above question assuming that before the collision both trains are travelling the distance only equal its own length.
Eshu said:
(Thu, Oct 14, 2010 12:24:30 PM)
Since both the trains are moving in opposite direction. To find total we have to add the sum of train length.
Satish said:
(Mon, Nov 29, 2010 12:48:28 AM)
27x+17y
-------- = 23
x+y
27x+17y=23x+23y
27x-23x=23y-17y
4x=6y
3 x
- =- x:y= 3:2
2 y
Arashan said:
(Sat, Dec 11, 2010 04:27:08 AM)
By the formula time=distance/speed.
but, we have two trains with two diferent distances and speeds.
then we use the formula,
total time = [(distance1)+(Distance2)]/[speed1+speed2]
for finding distance= speed*time.[so,distance1= 27*x....like wise.
finally we get, 27x+17y/(27+17)= 23 (given totaltime.)
at last the answer is... x:y (3:2)
Nayana said:
(Sat, Dec 11, 2010 08:41:51 PM)
Can anyone how we got 3/2 since I understood till 4x=6y after that I didn't get that division step.
Sumi said:
(Sun, Dec 12, 2010 03:41:26 AM)
hi nayana wen u cud understand till 4x=6y then wats complex there just bring y and 4 to the opp side then x/y=6/4
cancel by gcd thats it get the solution 3/2
Nayana said:
(Thu, Dec 16, 2010 07:46:35 PM)
Thank u sumi i was confused in that step now i got..
Parimala.B said:
(Wed, Dec 29, 2010 10:03:34 PM)
When u refer the important formula we can come to know that "Time taken by a train of length x metres to pass a pole or a signal post is equal to the time taken by the train to cover x metres"
This theorem indirectly show us that the length of the train is 27 metres and 17 meters respectively ok
Then according to the 8th formula that "If the train of length a metres and b metres are moving in the opposite direction at u m/s and v m/s then the time taken by the trains to cross each other = a+b/u+v sec
we don't know the value of u and v so let take it as x and y
then:
a=27x
b=17y
therefore 27x+17y/x+y = 23
take x+y to the right side though it is in division it will turn to multiplication
like this:
27x+17y = 23(x+y)
27x+17y = 23x+23y
then calculate difference between x and y
you will get 4x = 6y
2x = 3y
and x/y = 3/2
Chanti said:
(Tue, Jan 4, 2011 11:46:04 AM)
I didn't understood why x+y is divided by the term 27x+17y... can any body help to explain clearly
Ankit Choudhary said:
(Thu, Jan 6, 2011 11:04:08 PM)
As we know that,when two train of length l1 and l2 travels in opposite direction with speed let s1 km/hr and s2 km/hr respectively then time taken to cross each other is given by formula
t=(l1+l2)/(s1+s2)
So by using this formula we can easily solve the above problem.
here l1=27*s1=27s1.
l2=17*s2=17s2.
and t is given in problem equal to 23.
therefore,
23=(27s1+17s2)/(s1+s2)=>3:2
Thiyagarajan.S said:
(Sat, Jan 8, 2011 11:25:07 AM)
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:.
Its given as Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds.
So it should be taken as 27x and 17x seconds only, I don't know why it is given as 27x and 17y meters and also denoted as length of train. Please any one explain me?
Kiran said:
(Sat, Jan 8, 2011 12:32:46 PM)
X+Y is speeds of 2trains and 27x+17y is length of trains
so lenth/speed=time
Anjan Kumar said:
(Sun, Jan 16, 2011 10:22:21 AM)
@k.kiran kumar
27x+17y/x+y
here as the two trains cross each other total distance they travelled is length of them.As given in problem they cross in 23 seconds.
time=distance/speed
i.e 23=27x+17y/x+y
Can anyone tell me the formulas for relative speed ?
Jasminder said:
(Wed, Mar 2, 2011 03:34:29 AM)
27x+17y total distance.
X+y=total speed.
Total distance/total speed=total time.
Total time= 23 given.
Solve it.
Maha said:
(Fri, Mar 4, 2011 09:44:27 PM)
Distance=speed*time.
1st train time =27sec. 2nd train time =17sec.
two trains can cross the each other in opposite direction is 23 sec.
so total time=(total distance)/totalspeed;
total distance,
1st&2nd train have speed x,y;
total distance=27x+17y; total speed=x+y;
23=(27x+17y)/x+y;
23x+23y=27x+17y;
6y=4x;
6/4=x/y;
3/2=x/y;
3:2
Nick said:
(Sun, Mar 13, 2011 10:31:34 AM)
Can any one tell me how to calculate mod(23-17) : mod(23-27)
I forgot how to calculate mod and if we are calculating same mod(23-17) : mod(23-27) then how it comes to 6:4????
Avinash said:
(Wed, Mar 16, 2011 11:47:02 PM)
First you have to know that mod(positive or negative value) = positive value
So mod(23-17)=6
mod(23-27)=mod(-4)=4
Hope you understood.
Rabish Pandey said:
(Mon, Mar 21, 2011 02:00:45 AM)
Really it is helpful to get qualify related aptitude exam I thank from my side to indiabix. Com and easy to understand solution also.
Pardhu said:
(Sun, Apr 3, 2011 06:48:28 AM)
Avinash could you please explain clearly.
Ajit said:
(Sun, Apr 10, 2011 01:56:38 AM)
Dear rohit,
Your calculation right but this furmula use in every cases or limited case?
Jagadeesh said:
(Wed, Apr 27, 2011 03:40:01 AM)
Hi priya u can do like this take speed of train A is x and speed of B is Y
x(take difference between speed of train A and crossing time)=y(take difference between train B and crossing time) i.e
x(27-23)=y(23-17)
4x=6y
x/y=3/2
Riyas said:
(Tue, May 10, 2011 12:03:48 AM)
My explain,
You know 2train x and y
crossing the time =27then17 so 27x 17y
Given
Then each other train crossing 23 second.
so 23x 23y
27x+17y=23x+23y
27x-23x=23y-17y
Tf 4x=6y
x=6y/4
x/y=6/4
=3/2
Bhargav said:
(Tue, May 10, 2011 12:55:54 AM)
Why km/hr to m/sec conversion takes 5/18 ???
Nisha said:
(Wed, May 18, 2011 03:05:13 AM)
Hi friends .....
1 km =1000m
1 hr=3600s
So, km/hr = 1000/3600 = 5/18
It's clear.
Dhiraj said:
(Sun, Jun 19, 2011 07:38:24 AM)
(la+lb)/(Sa+Sb)=23
la/sa=27
la/sb=17
sa/sb=?
sa/sb=3:2
Swetha said:
(Thu, Jul 7, 2011 12:40:06 AM)
It can also be solved like this using the methods of allegation and mixture 27 17.
According to my opinion the first train crosses the man after crossing the other train i.e. 4 sec late and second train will crosses the man 6 sec earliar before it cross the other train .
Just take the ratio of 6:4 we get 3:2 i.e speed of seocnd train:speed of first train.
Rajkumar said:
(Thu, Jul 28, 2011 06:22:32 AM)
Let the speed of the two trains be a=x m/sec and b=y m/sec,
crossing time=23sec
formula :distance=speed*time
for 1st train,distance,u=x*27=27x
for 2nd train,distance,v=y*17=17x
suppose in opposite direction the formula is time=u+v/a+b
therefore,27x+17x/x+y=23
27x+17y=23(x+y)
27x+17y=23x+23y
27x-23x=23y-17y
4x=6y
x/y=6/4
x/y=3/2
x:y=3:2
Jyotirmoy said:
(Sat, Aug 27, 2011 05:01:26 PM)
Let the speed of the two trains be a=x m/sec and b=y m/sec
Length of a=27x and b=17y
So (27x+17y)=23(x+y).
So 4x=6y
So x/y=3/2
[In First sight I thought as the 1st train is taking more time to cross the man , so it will be the slower train, but as the lenght of the 1st train longer so it has taken longer time althought it is the faster train]
Shree said:
(Wed, Aug 31, 2011 08:25:00 PM)
Its simple .
T = D/S
Therefore total distance = 27x+17y and total speed = x+y
Total time = 23
23= 27x+17y/x+y
Deepak said:
(Thu, Sep 8, 2011 08:08:20 PM)
@niveditha
Since both train crossing each other in 23s, so have to multiply 23 by sum of speed of both train.
Gufran said:
(Sat, Sep 24, 2011 01:20:12 AM)
Let, the ist train speed v1=X m/s and T1=27s
2nd trin speed V2=Y m/s and T2=17s
Then S1=V1*T1=27x
S2=V2*T2=17Y
Both are in opposite dir. Then speed is S=S1-S2=27X-17Y
They cross each other means time difference 23(X-Y)=23X-23Y
now...
27X-17Y=23X-23Y
4X=-6Y
X/Y=-3/2=3/2(BECZ speed is not -ve)
X:Y=3:2
Mobarak said:
(Tue, Oct 11, 2011 09:43:03 AM)
If two trains running at the speed x & y respectively in opposit direction then their relative velocity is (x+y) m/s.
Now if two trains cross each other then they have to cross total length of two trains which is (27x+17y).
Now time taken for crssng the total length = (27x+17y)/(x+y) i.e 23.
Narayan said:
(Thu, Oct 20, 2011 07:06:04 PM)
27 17
23
23-17=6 27-23=4
Then ratio become 3:2
Dheeraj said:
(Mon, Dec 5, 2011 10:26:05 AM)
Hi Lokesh,
Can you please explain why you've said 27x-24x=23y-17y.....?
I can't see figure of 24 ain't where???
Thanks in advance....
Ankit said:
(Tue, Dec 13, 2011 09:44:03 AM)
Thanks Y.S.Rama Krishna
I understood the answer now. :)
Shahul Hameed.M said:
(Sat, Dec 24, 2011 04:33:01 PM)
Hi friends in smart way....
To find out the speed ratio so ,
formula is Length = speed*time
so,
speed = length /time
here 2 trains so two different length and speed so the formula
s1+s2=L1+L2/time
speed we don't know so we take X,Y for speed for 2 trains
respectively ....
use above formula:
X+Y=L1+L2/23
HERE
L1=speed*time (speed is not given so take it as X,time is given that is 27)
L2= speed*time (speed is not given so take it as Y,time is given that is 17)
SO L1=27X
L2=17Y
apply it,
X+Y=27X+17Y/23
SO SOLVE IT
23(X+Y)=27X+17Y
23X+23Y=27X+17Y
separate the X and Y terms so we get
23X-27X+23Y-17Y=0
WE GET:
-4X+6Y=0
6Y=4X
RATIO (means difference of X and Y)
SO FRIEND,
X/Y=6/4=3/2
SO THE RATIO IS 3:2
Ranjitha said:
(Tue, Dec 27, 2011 11:29:29 AM)
@ chanti
its length=speed*time
so length of first train=27*x mts
and length of 2nd train= 17*y mts
Fathima said:
(Tue, Jan 3, 2012 08:32:29 PM)
The 1st train sec 27-23=4.
The 2nd train sec 23-17=6.
So both are divide by 2.
4/2=2, and 6/3=3.
So the ratio is 3:2 its right method?
Taiwo said:
(Fri, Jan 6, 2012 05:19:34 PM)
I think I am contented with fathima explanation thank you all.
Ravi said:
(Fri, Jan 6, 2012 07:19:30 PM)
I can't get this step
(27x+17y) / (x+y) = 23
Why we have to use this? can any one explain me.
Ankit said:
(Thu, Jan 19, 2012 07:48:00 PM)
Let Speed of Train A= x m/s
And Speed of Train B= y m/s
Time taken by Train A to cover distance equals to its length = 27 s
Time taken by Train B to cover distance equals to its length = 17 s
Total distance covered
---------------------- = Time taken to Cross each other
Total speed
(Length of train A)+ (Length of train B)
so, --------------------------------------- = 23 seconds
(Speed of train A) + (Speed of train B)
(Speed x time) of Train A + (Speed x time) of Train B
----------------------------------------------------- =23
(Speed of train A) + (Speed of train B)
27x + 17y
--------- = 23
x + y
27x + 17y = 23x + 23y
4x =6y
x/y= 3/2
Nidhi said:
(Sun, Jan 22, 2012 03:01:43 AM)
Lets speed of 1st train = x and of 2nd = y.
when they cross man then.....
so length of 1st = 27x and second 17y.
total length = 27x + 17y
now when they cross each other in opp direction they take 23 sec and we know when 2 object run in opp direction their rel speed is
speed of 1st + speed of 2nd = x+y so now length = time * speed = 23(x+y)
If Two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then the time taken by the trains to cross each other=(a+b)/(u+v)sec.
27x + 17y = 23x + 23y