Question Detail

A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel ?

650 meter
555 meter
500 meter
458 meter

Answer: Option C

Explanation:

Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds

Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s

Distance = Speed*Time
\begin{aligned}
=> 800+x = \frac{65}{3}*60 \\
=> 800+x = 20*65 = 1300 \\
=> x = 1300 - 800 = 500 \\
\end{aligned}

So the length of the tunnel is 500 meters.

[If you want to calculate it practically, then please have your copy and pen and take a ride of Kalka to Shimla toy train in north India. It has many tunnels on the way :) ]

1. How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr

25 Seconds
28 Seconds
30 Seconds
35 Seconds

Answer: Option C

Explanation:

Relative Speed = 63-3 = 60 Km/hr
= 60 *(5/18) = 50/3 m/sec

Time taken to pass the man will ne
\begin{aligned}
500*\frac{3}{50} = 30 \text{ seconds}
\end{aligned}

2. Two trains 140 metre and 160 metre long run at the speed of 60 km/hr and 40 km/hr respectively in opposite direction on parallel tracks. What time these will take to cross each other ?

10.7 Seconds
10.8 Seconds
10.9 Seconds
11.8 Seconds

Answer: Option B

Explanation:

Relative Speed = 60+40 = 100 Kmph
= 100*(5/18) = 250/9 m/sec

Distance to be covered = 140 + 160 = 300 metres

Time = Distance/Speed

\begin{aligned}
Time = 300*\frac{9}{250} \\
= \frac{54}{5} = 10.8\text{ seconds}
\end{aligned}

3. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

220 meter
225 meter
230 meter
235 meter

Answer: Option C

Explanation:

As trains are running in opposite directions so their relative speed will get added
So, Relative speed = 120 +80 = 200 kmph
= 200*(5/18) = 500/9 m/sec

Let the length of other train is x meter then

\begin{aligned}
\frac{x+270}{9} = \frac{500}{9} \\
=> x+270 = 500\\
=> x = 230
\end{aligned}

So the length of the train is 230 meters

4. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train ?

\begin{aligned} 27\frac{7}{9} \end{aligned}
\begin{aligned} 28\frac{7}{9} \end{aligned}
\begin{aligned} 29\frac{7}{9} \end{aligned}
\begin{aligned} 30\frac{7}{9} \end{aligned}

Answer: Option A

Explanation:

As Trains are moving in same direction,
So, Relative Speed = 40-20 = 20 kmph
= 20*(5/18) = 50/9 m/sec

Length of Train= Speed * Time

\begin{aligned}
Length = \frac{50}{9}*5 \\
= \frac{250}{9} \\
=27\frac{7}{9}
\end{aligned}

5. Speed of a goods train is 72 km/hr. This train crosses a 250 meter platform in 26 seconds. Then find the length of goods train.

250 meters
260 meters
270 meters
280 meters

Answer: Option C

Explanation:

First convert speed from km/hr to m/sec

So, Speed = 72*(5/18) = 20 m/sec
Time = 26 seconds

Let the length of the train be x meters.
We know, Distance = Speed*Time.
[you can remember this formula as remembering DUST = D*ST... Distance=Speed*Time]

x+250 = 20*26
=> x = 270 meters

So length of the goods train is 270 meter