### JEE Main 12 Jan 2019 Morning Question 9

##### Question: A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr, The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite direction is [JEE Main Online Paper Held On 12-Jan-2019 Morning]

#### Options:

A) $ \frac{25}{11} $

B) $ \frac{3}{2} $

C) $ \frac{5}{2} $

D) $ \frac{11}{5} $

## Show Answer

#### Answer:

Correct Answer: D

#### Solution:

The total distance to be travelled by the train is 60+120=180 m.

When the trains are moving in the same direction, relative velocity is

$ v _1-v _2=80-30=50km,h{r^{-1}} $ so time taken to cross each other.

$ t _1=\frac{180}{50\times \frac{10^{3}}{3600}}=\frac{18\times 18}{25}s $

When the trains are moving in opposite direction relative velocity,

$ |v _1-(-v _2)|=80+30=110km,h{r^{-1}} $

So time taken cross each other $ t _2=\frac{180}{110\times \frac{1000}{3600}}=\frac{18\times 36}{110}s $ Ration $ \frac{t _1}{t _2}=\frac{25}{\frac{18\times 36}{110}}=\frac{11}{5} $