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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. A train is running with a speed of 60 kmph and its length is 110 metres. Calculate the time by which it will pass a man running opposite with speed of 6 kmph.
- 2 second
- 4 second
- 6 second
- 8 second
Answer: Option C
Explanation:
From the given question,
we will first calculate the speed of train relative to man,
=> ( 60 + 6 ) = 66 km/hr ( we added 6 because man is running opposite )
Convert it in metre/second
\begin{aligned}
= 66 \times\frac{5}{18} \\
= \frac{55}{3} m/sec\\
\text{Time it will take to pass man }\\
= 110 \times \frac{3}{55} \\
= 6 \text{ seconds}
\end{aligned}
2. 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
3. Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
- 30 Km/hr
- 36 Km/hr
- 80 Km/hr
- 90 Km/hr
Answer: Option B
Explanation:
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = x.
Then relative velocity = x+x = 2x
2x = distance/time = 240/12 = 20 m/s
Speed of each train = x = 20/2 = 10 m/s
= 10*18/5 km/hr = 36 km/hr
4. 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
5. 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}
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