Two trains are running in opposite directions cross a man standing on the platform in 27 seconds

Correct Answer:

Description for Correct answer:

Length of first train = x metreLength of second train = y metrethen Speed of first train = \( \Large (\frac{x}{27}) \) m/sec& Speed of second train = \( \Large (\frac{y}{17}) \) m/secRelative Speed = \( \Large (\frac{x}{27} + \frac{y}{17} ) \) m/sec.Now, 23 = \( \Large \frac{x + y}{\frac{x}{27} + \frac{y}{17}} \)=> \( \Large \frac{x}{27} + \frac{y}{17} = \frac{x}{23} + \frac{y}{23} \)=> \( \Large \frac{x}{23} - \frac{x}{27} = \frac{y}{17} - \frac{y}{23} \)=> \( \Large \frac{27x - 23x}{23 \times 27} = \frac{23y - 17y}{23 \times 17} \)=> \( \Large \frac{4x}{27} = \frac{6y}{17} \)

=> \( \Large \frac{x}{y} = \frac{6}{17} \times \frac{27}{4} = \frac{81}{34} \)

Part of solved Time and Distance questions and answers : >> Aptitude >> Time and Distance

Comments

Discussion :: Problems on Trains - General Questions (Q.No.4)

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.

Then, length of the first train = 27x metres,

and length of the second train = 17y metres.

	27x + 17y	= 23
x+ y

27x + 17y = 23x + 23y

4x = 6y

	x	=	3	.
y	2

Poornima said: (Jul 13, 2010)

Let me explain in detail if anyone still not understood yet. Please remember the formula for finding speed. Speed = Distance/Time. Therefore, Distance = Speed x Time. If a train crosses a man/pole/post/tree in T seconds, and speed of the train is S m/s, then Then, the Length of the Train = (Speed x Time) = ST metres. Note: Here, the distance traveled by train in T seconds at the Speed of S m/s is equal to the length of the train.

Now, lets come to the given problem.

Let speed of the first train = X. Time taken taken by the first train to cross a man = 27 seconds. Therefore, Length of the first train = Speed x Time = X x 27 = 27X metres. Let speed of the second train = Y. Time taken taken by the second train to cross a man = 17 seconds. Therefore, Length of the second train = 17Y metres.

Important Formula: 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.

Given that, (a + b) / (u + v) = 23 seconds. Here, a = 27X, b = 17Y and u = X, v = Y. Therefore, (27X + 17Y)/(X + Y) = 23. => 27X + 17Y = 23X + 23Y => 4X = 6Y => X/Y = 6/4 = 3/2

=> X : Y = 3 : 2.

K.Kiran Kumar said: (Aug 3, 2010)
I can't get this step (27x+17y) / (x+y) = 23 Why we have to use this? can any one explain me.

Niveditha said: (Aug 9, 2010)
Anyone please help me how this x+y is divided.

Arjun said: (Aug 11, 2010)
(27x+17y)/x+y=23 how did used that step?

Janardhan said: (Aug 12, 2010)
It's correct method to solve this problem.

Boomathi said: (Aug 17, 2010)
very good solution....

Arun said: (Aug 22, 2010)
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: (Aug 22, 2010)
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: (Aug 23, 2010)
How the (27x+17y)/x+y=23 formula comes?

Sameer said: (Sep 4, 2010)
Can anyone explain me how he got this step 4x = 6y ?

Bhanu said: (Sep 4, 2010)
Take all x terms once side and why terms other side then subtract we get 4x = 6y.

Lokesh said: (Sep 14, 2010)
27x - 24x = 23y - 17y 4x = 6y x/y = 3/2.

Prabhakaran said: (Sep 18, 2010)
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.

Y.S.Rama Krishna said: (Sep 20, 2010)

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: (Oct 4, 2010)
Thanks Ramakrishna, your answer is excellent.

Sri said: (Oct 13, 2010)

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: (Oct 13, 2010)
Excellent explanation SRI.

Confused said: (Oct 13, 2010)
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: (Oct 14, 2010)
Since both the trains are moving in opposite direction. To find total we have to add the sum of train length.

Satish said: (Nov 29, 2010)
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: (Dec 11, 2010)
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= speedtime.[so,distance1= 27x....like wise. finally we get, 27x+17y/(27+17)= 23 (given totaltime.) at last the answer is... x:y (3:2)

Nayana said: (Dec 11, 2010)
Can anyone how we got 3/2 since I understood till 4x=6y after that I didn't get that division step.

Sumi said: (Dec 12, 2010)
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: (Dec 16, 2010)
Thank u sumi i was confused in that step now i got..

Parimala.B said: (Dec 29, 2010)

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: (Jan 4, 2011)
I didn't understood why x+y is divided by the term 27x+17y... can any body help to explain clearly

Ankit Choudhary said: (Jan 6, 2011)
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=27s1=27s1. l2=17s2=17s2. and t is given in problem equal to 23. therefore, 23=(27s1+17s2)/(s1+s2)=>3:2

Thiyagarajan.S said: (Jan 8, 2011)

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: (Jan 8, 2011)
X+Y is speeds of 2trains and 27x+17y is length of trains so lenth/speed=time

Anjan Kumar said: (Jan 16, 2011)
@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

Rohit said: (Feb 3, 2011)
Fast calculation = mod(23-17) : mod(23-27) = 6:4 = 3:2 .

Sujata said: (Feb 14, 2011)
I agreee with Rohit calculation.

Pallavi said: (Feb 25, 2011)
Can anyone tell me the formulas for relative speed ?

Jasminder said: (Mar 2, 2011)
27x+17y total distance. X+y=total speed. Total distance/total speed=total time. Total time= 23 given. Solve it.

Maha said: (Mar 4, 2011)
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: (Mar 13, 2011)
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: (Mar 16, 2011)
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: (Mar 21, 2011)
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: (Apr 3, 2011)
Avinash could you please explain clearly.

Ajit said: (Apr 10, 2011)
Dear rohit, Your calculation right but this furmula use in every cases or limited case?

Jagadeesh said: (Apr 27, 2011)
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: (May 10, 2011)
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: (May 10, 2011)
Why km/hr to m/sec conversion takes 5/18 ???

Nisha said: (May 18, 2011)
Hi friends ..... 1 km =1000m 1 hr=3600s So, km/hr = 1000/3600 = 5/18 It's clear.

Dhiraj said: (Jun 19, 2011)
(la+lb)/(Sa+Sb)=23 la/sa=27 la/sb=17 sa/sb=? sa/sb=3:2

Swetha said: (Jul 7, 2011)
It can also be solved like this using the methods of allegation and mixture 27 17. 23. 6 4. Thus ratio is 6:4 3:2.

Sachin Kamble said: (Jul 20, 2011)
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: (Jul 28, 2011)
Let the speed of the two trains be a=x m/sec and b=y m/sec, crossing time=23sec formula :distance=speedtime for 1st train,distance,u=x27=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: (Aug 27, 2011)
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: (Aug 31, 2011)
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: (Sep 8, 2011)
@niveditha Since both train crossing each other in 23s, so have to multiply 23 by sum of speed of both train.

Gufran said: (Sep 24, 2011)
Let, the ist train speed v1=X m/s and T1=27s 2nd trin speed V2=Y m/s and T2=17s Then S1=V1T1=27x S2=V2T2=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: (Oct 11, 2011)
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: (Oct 20, 2011)

27 17 23

23-17=6 27-23=4

Then ratio become 3:2

Dheeraj said: (Dec 5, 2011)
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: (Dec 13, 2011)
Thanks Y.S.Rama Krishna I understood the answer now. :)

Shahul Hameed.M said: (Dec 24, 2011)

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: (Dec 27, 2011)
@ chanti its length=speedtime so length of first train=27x mts and length of 2nd train= 17*y mts

Fathima said: (Jan 3, 2012)
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: (Jan 6, 2012)
I think I am contented with fathima explanation thank you all.

Ravi said: (Jan 6, 2012)
I can't get this step (27x+17y) / (x+y) = 23 Why we have to use this? can any one explain me.

Ankit said: (Jan 19, 2012)

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: (Jan 22, 2012)

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) Compare both : 27x + 17y = 23(x+y) 27x + 17y = 23x + 23y

4x = 6y => x/y = 3/2.

Dileep said: (Jan 22, 2012)
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. a=27x, b=27y, u=x, v=y.

Shro said: (Feb 15, 2012)
Thanku Anjan :).

Rahaman said: (Mar 20, 2012)
23-17/27-23=6:4 or 3:2 (LINK-UP METHOD)

S.K.Rao said: (Apr 21, 2012)

Step (1) Speed= (Distance/Time) meters/sec. Distance= Length here. From this formula, Length = Speed* Time So,Length of 1st Train= Speed * Time = 27* x where x=speed Likewise,length of 2nd Train .= 17* y where y=speed Step (2): Note:Imagine one train is stationary. Then the distance traveled by each train would be equal to the length of the other train + its own length.Because a train can cross the other train after the last bogie of the 1st train crosses the last bogie of the other train. So total length of both trains = 27x+17y. Now the relative speed of the trains = x+y (since both run in opposite directions). So Time = Length/speed= 27x+17y/x+y =23(given)

Cross multiply,transpose and simplify. Then you get the answer.

Nil said: (Aug 2, 2012)

Given: 1. time taken by the first train to cross a man (t1) = 27 sec 2. time taken by the second train to cross a man (t2) = 17 sec 3. Time taken by the 1st & 2nd train to cross each other (T)= 23 sec Find: Ratio 1st train's speeds (x) / 2nd train's speed (y) = x/y = ? Formula: speed = distance(or length) --------------------- time Let, Speed of 1st train to cross a man (x) = distance(d1) / time(t1) Speed of 2nd train to cross a man (y) = distance(d2) / time(t2) Thus, x = d1/27 .................I y = d2/17 .................II So, Total speed of the train (S) = speed of 1st train (x) + speed of 2nd train (y) Therefore, S = x + y Now, we can say that Total distance (D) = d1 + d2 D = 27x + 17y............from I & II Total time (T) = 23 seconds Total speed of the train (S) = Total distance (D) / Total time (T) x + y = 27x + 17y ----------- 23 23x + 23y = 27x + 17y 23y - 17y = 27x - 23x 6y = 4x x/y = 6/4 = 3/2 Thus,

1st train's speeds (x) / 2nd train's speed (y) = x/y = 3/2

Pri.. said: (Aug 10, 2012)

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). 23x + 23y = 27x + 17y 23y - 17y = 27x - 23x 6y = 4x x/y = 6/4 = 3/2 Thus,

1st train's speeds (x) / 2nd train's speed (y) = x/y = 3/2.

Karthik said: (Aug 24, 2012)
@Narayana superb.

Yogender Prashad said: (Sep 4, 2012)
Let the speed of the train is Xm/s & Ym/s resp. accordingto the qus. 27x meter is the speed of the first train 17x " " " second " finally both the the train meet =23(x+y) 27x+17y=23(x+y) 4x=6y x/y=3/2

Selvan said: (Oct 9, 2012)

Speed=distance*time or length*time Speed of the first train=X*27 Let X=distance of first train Let Y=distance of second train Speed of the second train=y*17 If train moves in opposite direction means total speed is addition of two train speed 27X+17Y Both trains meet in 23 second by crossing a man 1'st train speed=23X 2nd train speed=23Y Total speed=23X+23Y So first train speed =(27-23)*X 2nd=(23-17)*Y Equating both speed 6X=4Y

X/Y=6/4=3/2.

Shoeb said: (Nov 21, 2012)
If 2 Train are moving in opposite direction(train a 27 & train b 17)then Formula applied is The time taken by the trains to cross each other( 23 )given =(a + b)/(u + v)sec. * 27u + 17v = 23 ----------- u + v * 27u + 17v = 23u + 23v * 27u - 23u = 23v - 17v * 4u = 6v * u/v = 6/4 * 3:2 is the answer.

Gulshan said: (Feb 23, 2013)
Here concept of relative velocity is used. When objects move opposite to each other, their speed is added and when they move in same direction speed is the difference of their respective speeds.

Krishna Chavan said: (Feb 26, 2013)

Given data: l1=27 m/s. l2=17m/s. Now, we can find speed s=l/t . But speed is not given consider speeds x and y. Now easy to find lengths, l1=t*s =27x l2=t*s =17y If two trains travelling in opposite directions then we add two lengths(l1 and l2) and x and y speed m/s so that we able to find ratios. Now the time taken by train to cross each other is given i.e 23 seconds. Now formula forms like this : ( l1 + l2) ---------- = 23. ( x + y ) ( 27x + 17 y)=( 23x + 23y ). (27x - 23x ) = ( 23y - 17y ). (4x)=(6y). x 6 3 -=-=-

y 4 2

Shekharsa said: (Mar 25, 2013)
When two train s of a length a and b, of speed u, v m/sec.they move to cross each other. Time taken by the two trains cross each other is a+b(u+v). Because of these formula we have find the length of trains. I hope understood these problem.

Fatty said: (May 8, 2013)

Hai every body, The speed of one train = x, Speed of another train = y. We know that speed = length/time || length = speed*time. So we find the length of the first train = x(speed)*27(time). The length of the second train = y(speed)*17(time). Time taken by both train to cross(total time) = 23. Total length = (length of the first train)+(length of the second train) = (x*27)+(y*17). Total speed = (speed of first train) + (speed of the second train) = x+y. Total time = total length/total speed. 23 = [(x*27)+(y*17)]/(x+y). 27x+17y = 23(x+y).

27x+17y = 23x+23y ||27x-23x = 23y-17y || 4x = 6y ||x/y = 3/2.

Hardik Mistry said: (Jun 13, 2013)
@Faty how can you say total speed is (x+y). Duh the train are moving in different direction. So their total speed need to be (x-y) according to your point of view.

Harry Joshi said: (Jun 18, 2013)

@Hardik Mistry : When trains move in opposite direction their speeds are added, but when they go in the same direction their speeds are subtracted. Imagine you are going on road by bike and another bike is coming from front (i. e opposite direction) , you feel that the other bike is coming faster. But if it comes from back and tries to overtake you (i.e same direction) then it overtakes you slowly as compared to its speed.

Dileep Kumar said: (Jun 30, 2013)
27x + 17y/(x+y) = 23; 27x + 17y = 23x + 23y; 4x = 5y; x/y = 5/4.

Vipul said: (Jul 13, 2013)
First we are doing KM Hr to MS. Then Formula is a5/18. Then, 455/18=75/6 MS. Distance = SpeedTime. = 75/630. = 375. Distance = 375-130. = 245.

Carlo said: (Jul 26, 2013)
Let Train A distance = 27x Train A speed = x. Train B distance = 17y Train B speed = y. Time = distance/speed. 23 = 27x + 17y / x + y. x/y = 3/2 ----> Answer.

Askar said: (Aug 28, 2013)
:) The simple formula use for this problem is S = v*t.

Arunkumar said: (Sep 14, 2013)
Hi, Nice explanation for why we need to. 1. Add the both trains speed which were running in opposite Directions with a reference point. 2. Subtract the both trains speed which were running in Same direction with a reference point. http://en. Wikipedia. Org/wiki/Relative_velocity.

R.Abiraman said: (Sep 24, 2013)
Relative speed of train = x+y; Train 1 dis = 27x; Train 2 dis = 17y; Formula(speed = distance/time). So x+y = (27x+17y)/23. 23x+23y = 27x+17y; -4x+6y = 0; 6y = 4x; x/y = 6/4. So 3:2.

Anil Vattamwar said: (Oct 9, 2013)
Train1 time is = 27. Train2 time is = 17. Divide them = (27/17) => (3/2).

Chacko said: (Oct 30, 2013)
Can anyone say why is 27X+17Y = 23X+23Y....? Ideally if we cross multiply, it should come as 27x+17Y = 23X-23Y.

Kriti said: (Nov 7, 2013)
How can the time be taken as the ratio for length? I mean why 27x and 17y. 27 and 17 are time, then how can they be taken as ratios of length?

Anil said: (Nov 19, 2013)
If, 4x=6y. Then how to come ratio 3:2? How it possible?

Azhagarsamy said: (Nov 20, 2013)
Simple @Anil. 4x = 6y. Then x/y = 6/4. x/y = 3/2. Therefore the ratio is 3:2.

Tamil said: (Nov 28, 2013)
Hi friends. How to use mod method to calculate this problem?

Cherry said: (Dec 19, 2013)
Can any one say how does this length of the first and second trains are considered as 27x and 17y respectively?

Rajkumar said: (Dec 26, 2013)

It is very simple to understand the logic of 27x+17y/x+y=23 first we came across to know logic first of all we know the, speed=x/t in this way we assume that the sum of the two train lengths divided by assuming speeds is equal to relative crossing time is 23 seconds. One of the question arise in your mind that is why we took length s of trains in sum because they cross each other with respect to man.

Thank you.

Rajkumar said: (Dec 26, 2013)
Dear friend cherry the logic is very simple to understand we know speed = distance/time in this way 27 is the time of one train to pass a man and "x"is the assuming speed I hope to you may be understand.

Pradeep Kumar said: (Jan 4, 2014)
Also calculate as train 1 = 27sec. Train 2 = 17sec. Ratio of train 1 & train 2. 27/17 = 1.588. We have an option 3/2 = 1.5.

Bijay said: (Jan 4, 2014)
Length = speedtime. Means 27x+17y = (x+y)23. =>(27x+17x)/(x+y) = 23.

Kd Phatak said: (Jan 14, 2014)
Let the speed of the two trains bee x and y meters. Then a/c to the formula, Speed = distance/time. Distance = speed*time. Distance of one train becomes 17x. Second become 27y. a/c to formula distance + distance/speed = time. 17x+27y/x+y = 23. Now by solving you can get the answer.

Suresh Kasturi said: (Jan 20, 2014)

There are 2 trains . Here is some experiment ,one man is standing on platform. Trian 1: ========= we assume X is train 1 speed. this train cross that man in 27X meters. Trian 2: =========== We assume Y is train 2 speed. This train cross that man in 17Y meters. We concentrate trains are moving in opposite direction. So speed is X+Y. Distance is (train_1_length+trian_2_length) = 27X+17Y. Time = 23 seconds. Formule : distance = speed*time. 27X+17Y = (X+Y)*23.

X/Y = 3/2.

Karthik said: (Mar 17, 2014)
Velocity = distance/time. Let velocities are x, y m/s. x = d1/27; y = d2/17; d1 = 27x; d2 = 17y; Step 2: According to relative speed, since they are running in opposite direction their speeds are added. x+y = d1+d2/23. Sub d1 and d2; find answer.

Sidhes said: (Apr 16, 2014)

Let speed of train1: x m/s. Speed of train2: y m/s. Then relative speed of train1 = (x+y) m/s............(1). Train are crosses a man means they cross their length. Length of train1: 27x m. Length of train2: 17y m. According to Qst: Train crosses Each other in 23sec. Means train1 crosses his length & also the length of train2. => Total length crosses by train1 = Length of train1+Length of train2. =>Total length covered by train1(D)=27x+17y...........(2). We knows, Speed(s) = Distance(D)/Time(t)............Eqn(3). Put Values OF eqn(1) &(2) in eqn(3). x+y = (27x+27y)/23. => 23x+23y = 27x+17y. => 27x-23x = 23y-17y. => 4x = 6y.

=> x/y = 6/4 = 3/2..........Answer.

Grandmaster said: (May 19, 2014)
Very short form is: (27-23):(23-17), 4:6, 2:3. So the ratio is 2:3 or 3:2.

Harish said: (May 21, 2014)
I have solved it in yet simple(crude) way. Don't worry about their crossing each other in 23 seconds or whatever. On the face of it, one can make out that he has asked the simplified ration for 27:17. Simply take them to next higher level so that both of them are divisible by common highest divisor. i.e. 30/20 = 3/2. (but recommended not to follow it, as it doesn't apply to every problem?).

Swetha.T said: (Jun 7, 2014)
SPEED = DISTANCE/TIME. DISTANCE/SPEED = TIME. i.e 27X+17Y/X+Y = 23.

Het said: (Jun 23, 2014)
@Arashan has describe very well with formula of speed.

Sarath said: (Jul 12, 2014)
Lets assume, The train 1 speed= x m/sec ==> distance traveled by the train 1= 27x m. Similarly assume the speed of the train 2 is y m/sec then the train 2 has traveled a distance of 17y meter. The total distance (x+y)*23 m. Therefore, 23(x+y) = 27x+17y. 23x+23y=27x+17y. ==> 4x=6y. ==> x/y=3/2. Therefore x:y= 3:2. Answer B.

Vivek Kumar said: (Jul 17, 2014)
Hey if we follow the physics concept then relative distance should decrease while crossing each other. Then it should be (27x - 17y)/(x+y). Isn't it?

Vadivel said: (Jul 22, 2014)
Why should both trains have different length. Even sometimes they can have same length and can run in different speeds right. Then how can we do like that. Can anyone explain please?

Krishna said: (Sep 10, 2014)
If I divide speed of one train 27 divided by another its almost 1.5 can I choose 3:2. Is it a pure coincidence ?

Amit Jana said: (Sep 25, 2014)
#Vivek kumar. Here the questions is : two train of length a and b are run in opposite directions at u m/sec. and v m/sec., then the time taken by the trains to cross each other = (a+b)/(u+v). And if two train of length a and b are run in same directions at u m/sec. and v m/sec., then the time taken by the faster trains to cross the slower train = (a+b)/(u-v)

Amit Jana said: (Sep 25, 2014)
#Krishna no this is not possible as you say. Then cross each other in 23 sec. Is have no sense?

Srinivasa Raju said: (Nov 5, 2014)
Total Distance/Total Speed = Total Time; 27X+17Y/X+Y = 23.

Naveen Kumar said: (Nov 19, 2014)
Hi I have one doubt. How X and Y seconds become metres?

Param said: (Nov 25, 2014)

Another way be : Train A and B meet each other at 23 sec. It is the mean/common time of both the trains. Taking it as the reference train A will take 27-23 = 4 sec to reach end point. Similarly train B will take mod|17-23| = 6 sec to reach other end. Using Formula: If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (under root b : under root a). A:B = 6:4 =3:2.

Thanks!

Rahul said: (Nov 25, 2014)
@Vadivel. There may be possible that the lengths are same but in question given that the crossing time is 23. So we will apply the formula of crossing time (a+b)/(u+v). And for length a & b we will use the man crossing conditions. Please don't apply anything from your side only use the conditions which are given in question.

Sangeetha said: (Jan 5, 2015)
This method is easiest method I can understand this sum.

Soniya said: (Jan 9, 2015)
This is very good method to understand.

Prasanth said: (Feb 9, 2015)
Can anyone please tel me how x+y is came. They asked to find speed of that we have to use speed = length\time only know but how x+y is came.

Racha Manish said: (Feb 25, 2015)
Let we have to assume those to get ratio of that speeds.

Gaurav Singh said: (Feb 26, 2015)

Time x speed = distance. Let the speeds of two train be x and y. Then distances will be 27x for 1st train. 17y for 2nd train. Now when they both cross each other fully. Time is 23 seconds. Distance will be length of 1st train + length of 2nd train. Speed will be as we assumed above is x and y (sum of both the speed). So, 23 = (27x+17y)/x+y. 23(x+y) = 27x+17y. 23y-17y = 27x-23x. 6y = 4x. 3y = 2x.

Hence the answer 3:2.

James said: (Apr 7, 2015)
Can someone please explain to me how 27x+17y = 23x + 23y & 4x + 6y?

Sharad said: (Jun 11, 2015)
@James. 27x+17y = 23x+23y. 27x-23x = 23y-17y. 4x = 6y. 4x/2 = 6y/2. 2x = 3y. x/y = 3/2.

Adi said: (Jun 24, 2015)
Short cut: T2 = 23-17 = 6. T1 = 27-23 = 4. S1/S2 = T2/T1. = 6/4 = 3/2.

Vincent said: (Jul 10, 2015)

Let the speeds of the two trains be x m/sec and why m/sec respectively. Reference to man standing on the platform. Length of the first train = 27X metres, Length of the second train = 17Y metres. Total speed of train when crossing opposite direction is (x+y) m/s. Two trains are crossing each other in 23 seconds. So length of two trains using this condition is (x+y) 23 m. So 27X+17Y = 23X+23Y. 4X = 6Y.

X/Y = 3/2.

Rashmi said: (Jul 10, 2015)
Why is time considered as a distance or length. As per the question it is 27 seconds and 17 seconds? I see through out the discussion we consider seconds in meters. Could anyone clear my doubt please?

Sumitra said: (Jul 16, 2015)

Here the time taken by two trains itself 27 & 17 sec rt. So we know the formula that speed=d/t. Let us take the speed of the two trains is x & y. Then the corresponding distances are 27x and 17y. Then t=d/s as per formula. Time taken to cross each other is 23 sec. Equate that time as 23 sec and to cross that man by both trains. i.e (27x+17y)/(x+y) = 23.

Then solve the equation we will get the answer.

Abhijith said: (Sep 12, 2015)
One of the similar way to improve our aptitude knowledge.

Sikandar said: (Sep 13, 2015)

Two train of length a meter and b meter are moving in opposite direction at you m/s and we m/s then time taken by the faster train to cross the slower train = a+b/u+v. Or in same direction = a+b/u-v. In above problem train are in opposite direction. So a = 27x & b = 17y (x = speed of fastest train y = speed of slow train). = 27x+17y/x+y = 23. 4x = 6y.

x:y = 3:2.

Sandeep said: (Oct 5, 2015)
It is simplest form. I'm happy.

Anvesh Annu said: (Oct 6, 2015)
There is a simple method to solve this problem. ##Cross method##: 27 17 \ / \ / 23 / \ / \ 6 4 i.e, 27-23 = 4. 23-17 = 6. 6:4 so it is 3:2.

Gokulakisan S said: (Nov 18, 2015)
You can use this simple method: Time to cross men = tm. Time to cross each other = te. So 27(tm)+23(te) = 60. 17(tm)+23(te) = 40. Then 60/40 = 3/2. Therefore ratio is 3:2.

Sunil said: (Dec 15, 2015)
Hi @Gokulakisan sorry to say 27+23 = 50 not for 60.

Saurabh said: (Feb 20, 2016)
I couldn't get this part: 27x + 17y/x + y = 23. As both trains are moving in opposite directions the equation must be: 27x + 17y/x - y = 23. That is speeds must get subtracted why add both of them?

Vijendra said: (Feb 29, 2016)
The speeds of trains should be added because they are moving in opposite direction. -------------> man < ----------------. The speeds of both trains contributing to finish it in 23 seconds.

Mallikrjunrao said: (Apr 20, 2016)
In very simple method. 27 17 23 6 : 4 ................... 3:2 .................. By using mixed alligation method.

Sourabh Yadav said: (Apr 28, 2016)
An alternative answer: 27 - 23 = 4. 27 - 17 = 6. Take the square root of both 6 and 4 => 3:2.

Meenu Gopan said: (May 21, 2016)

Guys, there is an easy way to understand this question. Let us consider the SPEED of Train'A' and Train'B' as X and Y. Trains moving in opposite direction which crosses a man standing on the platform signifies the TIME of trains taken to cross the man which are 27s and 17s respectively, not the time taken by trains to cross each other(given separately in the question). Therefore, DISTANCE of the trains taken to cross the man = SPEED * TIME. D (TRAIN A)= X * 27. D (TRAIN B)= Y * 17. So, now we know that DISTANCE(LENGTH)covered by the trains and its SPEED(mentioned above). From this, it is understood that its time to find out the TIME take by the trains. But the time has already given; TIME = DISTANCE/SPEED. 23 = 27x + 17y /x + y. Cross multiply 23 (x + y) = 27x + 17y. Bring all like terms on same sides; So, 23x + 23y = 27x + 17y. 23x - 27x = 17y - 23y. - 4x = - 6y. Since both the sides have a negative sign, it will automatically get deleted)ie, 4x = 6y . Now its time to form the answer in ratio form. Ratio forms when one digit is divided by the other digit, always remember NUMERATOR should be greater than DENOMINATOR. 4x = 6y . (Bring all like terms on same sides). Then, x/y = 6/4. = 3/2 ie, 3 : 2.

Answer = 3 : 2.

Kiran Kumar said: (Jul 8, 2016)
This can be easily done by the method of allegations. 27 17 23 (23-17) : (27-23) 6 : 4 3 : 2 Or by weighted average, S1/S2 = (23-17)/(27-23) => 3/2 and that is the required ratio.

Vinod Reddy said: (Jul 13, 2016)
Here is the formula when two trains crosses each other, s1 + s2 = l1 + l2/time. According to the problem. x + y = (27x + 17y) /23. 27x + 17y = (x + y)23. x/y = 3/2.

Raj said: (Jul 24, 2016)
Short-cut : Alligation method. 27 17 23 6 4 = 6 : 4 means 3 : 2 => Answer.

Smnk said: (Jul 26, 2016)
Guys! Difference between the 23s and 27s is 4 and, Difference between the 23s and 17s is 6 of other train. So, the ratio is 4 and 6.

Mukesh said: (Aug 2, 2016)
Total distance / total speed = total time. This is the simple solution (X + Y) = relative speed. Trains comes towards each other.

P S said: (Aug 14, 2016)
Another approach by looking at answers, in question, 27 come first and 17 come later so in answer bigger number will come first and smaller later, that option is "B" only, so we can find answer without going for actual calculation.

Heisenberg said: (Aug 20, 2016)
Thanks @Narayan. => Guys use the method of mixture and allegation the answer is very much easy.

Shrikant said: (Aug 25, 2016)
@Narayan. Your answer is good it is a bit easy method.

Sarat said: (Sep 26, 2016)
TIME = DISTANCE /SPEED. We don't know how much distance apart 27x is train1 distance at which it crosses man 17y is 2nd train. We know when they meet 23 sec. 23 = 27x + 17y/ x + y.

Arifshaikh said: (Sep 29, 2016)
Try the rule of alligation. It will take 30 sec.

Harry said: (Oct 31, 2016)
I don't know its correct or not but I got the answer easily. My step-- it's not telling about the speed so what we have here is 27 sec and 17 sec so its the ratio 27:17. (27/9) = 3 : (17/9) =1.8 = 2. So I got 3 : 2. I don't know whether its right step or not, Please correct me, if it is wrong.

Phani said: (Nov 3, 2016)
23 - 17 = 6. 27 - 23 = 4. 6 : 4 = 3 : 2.

Yarasani Srinivas said: (Nov 21, 2016)
TIME = DISTANCE /SPEED. We don't know how much distance apart. 27x is train1 distance at which it crosses man. 17y is a 2nd train. We know when they meet 23 sec. 23 = 27x + 17y/ x + y.

Kripita said: (Dec 10, 2016)
Very well explained. Thanks.

Shield said: (Jan 5, 2017)
How is it possible?

Kaviarasan said: (Jan 5, 2017)
Simple method: A B 27 17 23 (Common time for A & B) 6 4 (23-17) (27-23) 3 : 2

Arunakar Reddy said: (Jan 10, 2017)
Length/speed = time. Here, Total length = 27x + 17y. Speed = x + y. Given time = 23 sec So, 27x + 17y ------------- = 23 x + y.

Kiran G said: (Jan 16, 2017)
I have another method mixture alligation. 17 27 23 ? ? (27-23) (23-17) 4 6 Answer is 2:3.

Anomoys said: (Feb 8, 2017)
There is a difference of 27-17 = 10. And we use 10 for subtracting. in 4x = 6y 10-4x=10-6x. Answer is 6x=4y. x = 3 and y=2.

Yous said: (Feb 9, 2017)
Why we should divide by x+y?

Ajay said: (Mar 9, 2017)
We know time=distance/speed, The first train length = 27x and second train length=17y. Given that two trains will cross each other in 23 sec,so applying t=d/s formula. 23 = total distance/total speed. => 23=27x+17y/x+y.

Mainul Bangladesh Khilkhet said: (May 19, 2017)
A train length= 27x. B train length= 17y. X meter goes for 1 second. 1 ---> 1/x second. 27x ---> 27x/x second. Again same as; 17y/y second for 17y. So, {(27x)/x + (17y)/y} second = 23 second. => (27x+17y) meter = (23x + 23y) meter. => 4x meter = 6y meter. => So, ratio of meter x/y = 3/2.

Kartik said: (Jun 8, 2017)
Alternative solution. Simplest of all, Train a passes the object at 27 sec. Train b passss at 17 sec. They cross each other at 23 sec. Hence , 23-17 = 6. 27-23 = 4. Hence, Ratio will be 6:4 or 3:2.

Mrk said: (Jun 21, 2017)
Yeah, I got it (x+y) say relative speed.

Gowtham said: (Jun 22, 2017)
Its very shortcut and its very simple. 27 17 2 3 6 4 The ans is 3:2 (or) 6:4.

Anil Bhadani said: (Jun 24, 2017)
Its very shortcut and its very simple. 27-23 = 4 23-17 = 6 so,4:6 = 2:3 or 3:2 also.

Hima said: (Jul 13, 2017)
Ratio of their speed = total distance travelled/total time taken= total speed. (27x+17 y)/23 = (x+y), 27x+17y = 23x+23y, 4x = 6y, x/y = 6/4, 3:2.

Rahul Tulskar said: (Jul 21, 2017)
Look at this simplest ans. Take both crossing time as an x y. 27as x 17 as y. Then, 27x+17y/x+y=23. 27x+17y=23x+23y. 27x-23x=17y-23y. 4x =6y. Or XY=4/6or 2/3 get it.

Anuj said: (Aug 9, 2017)
23-27:23-17. 4:6 2:3

Ashfaq said: (Aug 11, 2017)
Distance /time = speed. but here in solution distance /time = time (i.e 23 seconds ) How it is possible?

Udone said: (Aug 30, 2017)
27x+17y=DISTANCE. x+y=SPEED, 23=TIME.

Latz said: (Sep 5, 2017)
What if both trains will be in the same direction?

Angel said: (Sep 12, 2017)
@Latz. If both trains will be in the same direction then the equation becomes: (27x+17y)/(x-y).

Samara said: (Sep 17, 2017)
Let the distance of platform be x. Then speed1= x/27-23 and speed2= x/23-17, So, the ratio of speed is 3:2.

Pankj said: (Nov 7, 2017)
One doubt. According to this answer train taking 27 sec to cross the man having more speed than train taking 17 sec. As per my knowledge train taking more time having less speed anyone can explain this ?

Sujay said: (Dec 6, 2017)
---23------>----4-----\|27 23<--6sec---\|<---17sec----- Man Train which takes 27 sec to cross a man takes 4 more seconds to cross man(27-23) Train which takes 17 sec to cross a man takes 6 more seconds to cross train(23-17) Let distance between crossover of train and man standing to be X Speed ratio=x/4:x/6. i,e 3:2.

Pobitro Ghosh said: (Dec 30, 2017)
Relative time 1st train= 27-23=4, second train= 23-17=6, 1st:2nd= 6:4=3:2, Ans:3:2.

Mayank Yadav said: (Jan 23, 2018)
(x+y) I am not understanding that where this comes here this question, please give answer.

Sudhan Vybow said: (Feb 7, 2018)
Make it simple. 27-17 =6 :27-23 =4 6:4 or 3:2.

Vishnu said: (Feb 16, 2018)
@Sudhan. Isn't 27-17 = 10? How do you say it's 6?

Priyesh Verma said: (Feb 21, 2018)
Two trains are moving in opposite direction with the speed of 36 k.m. /h and 54 k.m. /h cross each other in 12 seconds. The length of the 2nd train is half of the 1st train. The 1st train crosses a platform in 1. 30 minutes. Then what is the length of the platform? Please solve this.

Mahesh said: (Feb 22, 2018)
860m, It consists of two cases.

Dilipreddy said: (Feb 24, 2018)
Very clear explanations. Thanks.

Naveen said: (Mar 6, 2018)

Speed=(distance/time). It rewritten as (distance/speed)=time. Same case: (relative distance/relative speed)=time We understand the only thing how to calculate relative speed and relative distance, Consider car A travel at x km/hr and car B travels at y km/hr Both A and B travel in same direction means Their relative speed=subtraction of two speed (x+y)km/hr. Relative distance= (speed1*time1)-(s2+t2). =27x-17y. Here 27 and 17 are time1 and time2. X and y are speed1 and speed2. Case2: CarA and carB travels opposite direction. Relative speed= x+y(addition of speeds) Relative distance=(speed1*time1)+(s2*t2) So we get. = 27x+17y. Finally (relative distance/relative speed)=time, Therefore (27x+17y)/(x+y)=23,

Maybe my solutions help for you

Harishankaran said: (Mar 16, 2018)
@Priyesh Verma. How can be a train, which taking time than the another, is consider as faster? In the above example, the time taken by 1 train is 23sec and the other one is 17 sec but the ratio shows that 1train is faster than second.just imagine that length of the train is 54m. Then, 54/27::54/17~=2:3.

Shyam said: (Mar 16, 2018)
T1=27-23=4,T2=23-17=6. Speed=distance/time. "Speed" inversely propotional to "time" (S1/S2)=(T2/T1)=6/4=3/2, S1:S2=3:2.

L.Santhosh Reddy said: (Apr 9, 2018)
Here, they mentioned 23sec and17sec but in answer, they took it as 23m and 17m why?

Manish said: (Apr 24, 2018)
27 and 17 are the length of the train and the speed of these train respectively x mtr/sec and y mtr/sec. So 27x+17x are there relative speed of the train. (27x+17y)/(x+y)=23. Here 23 is given time in which the Cross each other's train after solving the above eq... We get 4x=6y. x/y=2/3 that's solved.

Shree said: (May 7, 2018)
Thanks for explaining the answer. It's easy to understand the solution now.

Rekha Kondamangale said: (May 21, 2018)
Formula is The ratio of speed = ax+by /x+y.

Ramhari said: (May 31, 2018)
In this question, there is no any data that two trains are equal length. A train has passed a man in 27 seconds and another has passed in 17. The second one might be faster or short in length. So, Both can happen.

Swaminathan said: (Jun 12, 2018)
Hi, According to me, (27-23): (17-23), 4 : 6. Am I right?

Deb said: (Aug 6, 2018)
We can solve by (27-23)/(23-17).

Vidhyadhar said: (Sep 15, 2018)
Let x=speed of train 1. And y=speed of train 2. Our task=x/y. So, length of 1st train (d1)=x27(dist=speedtime) So, 2nd (d2) = y * 17. Time taken by trains to cross each other =23 sec. Time =dist/speed. 23=(d1+d2)/x+y. 23=(27x+17y)/x+y. By solving this we get. Result = x/y = 3/2

Kavya said: (Oct 3, 2018)
Good answer, Thanks @Shyam.

Ganapathi said: (Nov 22, 2018)
Time taken by 1st train is more than the 2nd train then how speed ratio of 1st train is more than second train? I am not getting this. Please tell me.

Ashis Das said: (Dec 20, 2018)
Agree @Ganapathi. Please, anyone, give clearance.

Nagendra said: (Jan 7, 2019)
@Ganapathi, @Ashish Das, The length of 1st Train is too long compared to 2nd Train. Hence even if though if it is faster, it took more time to cross the man.

Kumar said: (Jan 9, 2019)
Distance = speed * time. Time = 23 sec. Time = total distance/speed, Total distance = 27x+17y The relative speed = x+y (opposite direction). (27x+17y/x+y) = 23.

Divya. A said: (Jan 14, 2019)
Here distance is not mentioned. But you took 27 and 17 as distance. How can we take time interms of distance? Can anyone please explain?

Ruthvik said: (Apr 22, 2019)
Why we have to take x+y in denominator? Please explain.

Aditya said: (Jun 13, 2019)
Distance is not relative why we add both the lengths? We should only take either of them.

Shivam Mehta said: (Jul 16, 2019)
Let the speed of 1st train be X and 2nd be Y. So, the distance of 1st train (D= S*T) 27X and 2nd 17Y. Speed of 2 objects get added if they are in opp direction. So, speed = X+Y , T= D/S Then 23= (27X + 17Y)/ X+Y.

Kamanulla said: (Sep 27, 2019)
A = 27 - 23sec = 4sec. B = 23 - 17sec = 6sec. A:B = 4:6 = 2:3 in Sec. A:B = 3:2 in Speed.

Abraham said: (Oct 5, 2019)
The explanation are excellent, but we asked the the speed, so why we calculated the time taken?

Prasanna Kumar said: (Oct 16, 2019)
If we think let x and y be the length of the trains then, x/27,by/17 will be the speed of the trains respectively and the equation becomes x+y/23b=bx/27+y/17. Solving we get x/y=81/34. x+y = total distance. 23 = total time. Speed = x/27+y/27. Speed = distance/time. Therefore x+y/23 = x/27+y/17 is the equation, Can you tell me why this equation is wrong?

Hassan Ahmad Sheikh said: (Nov 25, 2019)

Hello there if anyone did't understood the concept behind it let me explain in my way. So, everyone know when two bodies are moving towards each other or having an velocity in opposite direction the velocity is add up (e.g you are going on car at 20 m/s and from front the other car is coming at 10 m/s so you will cross each other at 30 m/s) V1+V2. Now same concept applies here, S1+S2 = V1T1+V2T2 (S=VT). S1+S2 / V1+V2 = T1+T2. AND T1+T2 is 23. So S1+S2/V1+V2 = 23. NOW for S1= 27V1 and S2 = 17V2. Put values in eq and you will get the ratio, 27V1+17V2/V1+V2 = 23. V1/V2 = 3/2.

Thanks.

Md.Mustafijur Rahman said: (Jan 26, 2020)
s=vt. t= s/v. s= distance, v=speed.

Mahesh said: (Feb 7, 2020)
27+3 = 30. 17+3 = 20. 30/20 = 3:2.

Jay said: (May 20, 2020)
I can't understand the answer clearly. please explain how we get 3 : 2?

Rahul Raj Prasad said: (Jun 8, 2020)
Train A length=x;time A=27;speed A=x/27. Train B length=Y;time B=17;speed B=Y/17. Now relative speed between train A and B is=(x+Y)/23. Now we equating these equation through relative speed; (x+Y)/23=x/27+Y/17. => (x+Y)/23=(17x+27Y)/459, =>459x+459Y=391x+621Y, =>68x=162Y, =>x/Y=162/68, =>(x/27)/(Y/17)=(162/27)/(68/17), =>speed A/speed B=3/2, =>speed A : speed B = 3:2.

Manoj said: (Jul 19, 2020)
How possible 3:2? Because the first train takes more time than the second one. But the speed ratio is 3:2. Actually the second train moves fast than first.

Diya said: (Aug 10, 2020)
Very nice explanation, Thanks @Poornima.

Durai said: (Sep 27, 2020)
Short method is; x person 27. y person 17 add both distances and divide the total distance and multiple the same for both persons. 27+17/23 2. 37/23 = 1.6 2. 1.6*2. Ans : 3.2.

Meenu said: (Nov 8, 2020)
@Poornima. Thank you for the explanation.

Rohan said: (Mar 19, 2021)
Can the ratio be 2:3? Anyone explain me, please.

Shiv said: (Jun 30, 2021)
Here is simple solution for this question. When we take it as mixture; 23 - 17 = 6 27 - 23 = 4 6/4 i.e 3:2.

Rahul said: (Jul 29, 2021)
It's simple, speed is inversely proportional to time. so 27-23 :23-17 {alligation rule}. =6:4 (time ratio). So the speed ratio will be 4:6 =2:3.

Karma said: (Aug 24, 2021)
Isn't it like X/Y = 4/6? How come in the above solution like X/Y 6/4=3:2. X=4 and Y=6 isn't it?

Nishitha said: (Aug 25, 2021)
Given data: t1=27 sec t2=17 sec S=d/t,d=s * t. d is consider as l, l1=s1 * t1 =17 s1,l2 = s2* t2 =27 s2. In question ,it clearly move in a opposite direction,so we have to use this formula->(l1+l2) /s1+s2. Total time = (17s1+27s2)/s1 + s2, 23(s1+s2)= 17s1+27s2. Rearrange it, 23s1-17s1=27s2-23s2, 6s1 = 4s2, s1/s2 = 6/4=3/2. So,the answer is 3:2

Ebe said: (Nov 7, 2021)
I have a small doubt regarding the formula. In the question, they have said to find the ratio of speed. Not the ratio of time. So aren't we supposed to modify the formula accordingly? Please someone explain.

Nakum Pragnesh said: (May 23, 2022)

Its very easy (no need any formula). Train A speed = X m/s. Train B speed = Y m/s. For train A (Unitary method/Tri rashi method). 1sec------Xm (because train A speed =X m/s) 27sec----?. So,length of train A = 27X ----------------> P. Same For train B. So,length of train B = 17Y -----------------> Q. Train running in opposite so, Relative speed = (X+Y) m/s ---------->R. *Train cross each other in 23 sec. So total distance traavel in 23 sec = 27X+17Y. (From equations P and Q) 1sec ------------------> (X+Y)m (From eq R). 23sec ----------------(27X+17Y)m. So, 23*(X+Y) = 27X+17Y.

And we get the answer.