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} $
