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Question Detail
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}
1. 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 :) ]
2. 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
3. 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}
4. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. Find the length of train ?
- 45 m
- 50 m
- 55 m
- 60 m
Answer: Option B
Explanation:
First person speed = 2*(5/18) = 5/9 m/sec
Second person speed = 4*(5/18) = 10/9 m/sec
Let the length of train is x metre and speed is y m/sec
then,
\begin{aligned}
\frac{x}{y-\frac{5}{9}} = 9 \\
=> 9y-5 = x \\
=> 9y-x = 5 .....(i) \\
Also, \\
\frac{x}{y-\frac{10}{9}} = 10 \\
90y-9x = 100 .....(ii)\\
\text{from (i) and (ii), we get,} \\
x=50
\end{aligned}
So length of train is 50 metre
5. 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}
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