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. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other, is

9.8 seconds
10.8 seconds
11.8 seconds
12.8 seconds

Answer: Option B

Explanation:

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

Distance = 140+160 = 300 meters

Time = Distance/Speed

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

So the time trains will take to cross each other will be 10.8 seconds

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 train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to pass a man standing at a crossing.

10 seconds
12 seconds
14 seconds
16 seconds

Answer: Option B

Explanation:

As we need to get answer in seconds, so never forget to convert speed into meter per second.

Speed = 30 km/hr = 30* 5/18 m/sec
= 25/3 m/sec

Distance = length of train = 100 meter

Required time =
\begin{aligned}
\frac{Distance}{Speed} \\
= \frac{100}{\frac{25}{3}} \\
= 100* \frac{3}{25} = 12 sec \\
\end{aligned}

4. Length of train is 130 meters and speed of train is 45 km/hour. This train can pass a bridge in 30 seconds, then find the length of the bridge.

230 meters
235 meters
240 meters
245 meters

Answer: Option D

Explanation:

Let the length of bridge is X [as always we do :)]
Speed of train is = 45*(5/18) m/sec = 25/2 m/sec
Time = 30 seconds

Total distance = 130+x
We know Speed = distance/time
so,
\begin{aligned}
\frac{130+x}{30} = \frac{25}{2} \\
=> 2(130+x) = 750 \\
x = 245 \text{ meters}
\end{aligned}

So length of the bridge is 245 meters

5. A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform.

310 meter
335 meter
345 meter
350 meter

Answer: Option D

Explanation:

Speed = Distance/time = 300/18 = 50/3 m/sec

Let the length of the platform be x meters
then
\begin{aligned}
Distance = Speed*Time \\
x+300 = \frac{50}{3}*39 \\
=>3(x+300)= 1950 \\
=> x = 350 \text{ meters}
\end{aligned}