Quantitative Aptitude Ques 1085
Question: Train A travelling at 63 km/h can cross a 199.5 m long platform in 21 s. How much time would train A take to completely cross (from the moment they meet) train B, 257 m long and travelling at 54 km/h in opposite direction in which train A is travelling? [RRB (Officer Assistant) 2015]
Options:
A) 16 s
B) 18 s
C) 12 s
D) 13.07 s
E) 10 s
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] Speed of train A = 63 km/h $ =63\times \frac{5}{18}=\frac{7}{2}\times 5=\frac{35}{2}m/s $ Length of platform = 199.5 m Let length of train A = x m Train A take 21 s to cross the platform So, $ \frac{x+199.5}{\frac{35}{2}}=21 $
$ \Rightarrow $ $ 2x+399=21\times 35 $
$ \Rightarrow $ $ 2x=735-399 $
$ \Rightarrow $ $ 2x=366 $
$ \Rightarrow $ $ x=168 $
Length of train $ A=168,m $
Length of train $ B=257,m $
Speed of train $ B=54\times \frac{5}{18}=15m/s $
Since, the trains are in opposite direction.
Therefore, time to cross each other
$ =\frac{length,of,(TrainA+TrainB)}{Relative,speed,of,train,(A+B)} $
$ =\frac{168+257}{( \frac{35}{2}+15 )}=\frac{425\times 2}{35+30}=\frac{850}{65}=13.076 $
Therefore, time taken by train A to cross train
$ B=13.07,s. $
BETA
