Question

A train crosses a pole in 10 minutes, after this the train crosses a bridge of length 2 km in another 20 minutes. Then find in how much time it will cross a train coming from the opposite direction with a speed of 12km/hr having length 1400m.
Options

7 minutes

3.5 minutes

8.5 minutes

17 minutes

Answer 1

It will cross a train coming from the opposite direction in 1.5 minutes

Step-by-step explanation:

1. Let the length of train is $x$ meter,

so $speed$ = $\frac{Distance}{time}$,

= $\frac{x}{(10\times 60)}$ ..................(1),

2. according to second condition speed can be given as

$speed$ = $\frac{x+2000}{(20 \times 60)}$.........................(2),

On solving these two equations we can find that $x=2000  meters$

3. Now if the trains are crossing each other so relative speed will be,

= $\frac{10}{3} \textrm{(1st train speed in m/s)}+\frac{10}{3} \textrm{(opposite train speed in m/s)}$,

= $\frac{20}{3} m/s$,

4. Now the relative distance (length) which trains have to cover will be

=  $\textrm{length of 1st train }- \textrm{length of train coming from opposite side}$,

= $2000 - 1400$,

= $600 m$,

5. Now time required to cross each other will be

time = $\frac{Distance}{speed}$,

       = $\frac{600}{\frac{20}{3} }$,

       = $\frac{600 \times 3}{20}$

       = $90sec$

       = $1.5 minute$