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Question Detail
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is ?
- 1:3
- 3:2
- 3:5
- 3:7
Answer: Option B
Explanation:
Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
Length of the second train = 17y metres.
[because distance = speed*time]
\begin{aligned}
\frac{27x+17y}{x+y} = 23 \\
=> 27x + 17y = 23x + 23y \\
=> 4x = 6y \\
=> \frac{x}{y} = \frac{6}{4}
\end{aligned}
So ratio of the speeds of train is 3:2
1. 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
2. A train speeds past a pole in 15 seconds and a platform 100 meter long in 25 seconds. What is length of the train ?
- 140 meter
- 145 meter
- 150 meter
- 155 meter
Answer: Option C
Explanation:
Let the length of the train is x meter and Speed of the train is y meter/second
Then x/y = 15 [because distance/speed = time]
=> y = 15/x
\begin{aligned}
=> \frac{x+100}{25} = \frac{x}{15} \\
x = 150 \text{ meters}
\end{aligned}
So length of the train is 150 meters
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. A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger ?
- 30 seconds
- 32 seconds
- 34 seconds
- 36 seconds
Answer: Option D
Explanation:
Speed of train relative to jogger = (45-9) = 36 kmph
= 36*(5/18) = 10 m/sec
Distance to cover = 240 + 120 = 360 metres
Time = Distance/Speed
So,
\begin{align}
Time = \frac{360}{10} = 36 \text{ Seconds}
\end{align}
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
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