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

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

Answer: Option C

Explanation:

Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 360+140 = 500 meter

Time = Distance/speed
\begin{aligned}
= 500*\frac{2}{25} = 40 seconds
\end{aligned}

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

Answer: Option D

Explanation:

First convert speed into m/sec

Speed = 144*(5/18) = 40 m/sec

Time = Distance/speed
= 100/40 = 2.5 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}