Question Detail

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}

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 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}

3. 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}

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. 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}