Aptitude - Problems on Trains - Discussion

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).

Thanks Ramakrishna, your answer is excellent.

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)

Excellent explanation SRI.

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.

Since both the trains are moving in opposite direction. To find total we have to add the sum of train length.

27x+17y
-------- = 23
x+y
27x+17y=23x+23y
27x-23x=23y-17y
4x=6y
3 x
- =- x:y= 3:2
2 y

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)

Can anyone how we got 3/2 since I understood till 4x=6y after that I didn't get that division step.

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