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Question Detail
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}
1. 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
2. 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
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. How long does a train 110 meters long running at the speed of 72 km/hour take to cross a bridge 132 meters in length ?
- 15 seconds
- 12.1 seconds
- 10 seconds
- 8.1 seconds
Answer: Option B
Explanation:
Speed = 72 km/hour = 72*(5/18) m/sec
= 20 m/sec
Total distance to be covered = 110+132 = 142 meters
Time = Distance/Speed
= 242/20 = 12.1 seconds
5. 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 :) ]
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