Aptitude - Problems on Trains - Discussion

@Agggy.

we add the length of the the train and tunnel because the train is said to have crossed the tunnel if and only if its entire part including the the very last end of it leaves the tunnel.

so if the train has crossed the tunnel in 1min then it would have covered the entire length of the tunnel and a certain distance outside the tunnel (the distance covered by the train until the very last end of the train leaves the tunnel).

So,
that 'certain distance' = length of the train.
.A______x______.B.______800______.C.

where x is the length of the tunnel and the length of the train is 800 m.
the total distance covered by the train is x + 800.

DISTANCE = X+800 m
SPEED = 78 km/hr
TIME = 60sec.

convert speed from km/hr to m/s.
SPEED = 78x1000/60 x 60.
SPEED = 65m/s.

distance /speed = time.
X + 800/65 = 60,
X + 800 = 60x65/3,
X + 800 = 3900/3,
X + 800 = 1300,
X = 1300 - 800,
X = 500.

Why we are adding the length of train and length of tunnel? Anyone please explain to me.

Speed = 78 * 1000/60 = 1300.
Total length = length of tunnel + length of train,
1300 = length of tunnel + 800.
Length of the train = 1300-800 = 500.

Easy way

Distance = 800 meter,
Speed = 78 km/hr,
Time =1 min,
Need to find 800+x,
speed = 78km/hr~1300 meter/minute,
800+x = 1300 *1 as per (D = S * T formula),
x = 1300 - 800.
x = 500 meters.
That's all.

3(800+x) = 1900
2400+3x = 1900
3x = 2400-1900,
3x = 500.
I understand the thing. But where the 3x goes?

Can somebody tell me?

@Pradnyashree.

How is 3900-2400 =500?

It's 1500. Can anyone explain that?

@All.

Please correct me, if my calculation is wrong.

If we convert 78 km/hr into m/s.
So,
78 * 5/18.
390/18.
21.6 m/s.

Now if we put these value.
x + 800/60=21.6,
x + 800= 60 * 21.6,
x+800= 1296,
x= 1296 - 800.
x= 496.

Anyone please clarify this and explain with the correct answer.

=> x+800/60 = 78 * 5/18,
=> x+800/60 = 65/3,
=> x+800 = 65 * 60/3,
=> x+800 = 1300,
=> x = 1300-800,
=> x = 500.

To understand why we use 5/18 so i clarify that to convert km into m we multiply with 1000 and from hours to second we divided by 60*60.

Hence we get 5/18.
Suppose to change 1 km /hr into metre /sec.
1 * 1000/60 * 60 = 5/18.

Last step:

3(800 + x) = 3900.
2400 + 3x = 3900.

3x = 3900 - 2400.
3x = 1500.

x = 1500/3.
x = 500.