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 ?

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. 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

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. 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

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. 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