Question Detail

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

1. 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

2. 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}

3. 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}

4. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is ?

40 meter
45 meter
50 meter
55 meter

Answer: Option C

Explanation:

Let the length of each train is x meter
Distance will be x+x = 2x

Relative Speed = 46-36 = 10 km/hr
= 10*(5/18) = 25/9 m/sec

Distance = Speed*Time

\begin{aligned}
2x = \frac{25}{9}*36 \\
2x = 100 \\
=> x = 50
\end{aligned}
So length of both the trains are 50 meters

5. 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: