A) 16 s
B) 18 s
C) 12 s
D) 13.07 s
E) 10 s
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 |
| \[=\frac{\text{length}\,\text{of}\,(TrainA+TrainB)}{\text{Relative}\,\text{speed}\,\text{of}\,\text{train}\,(A+B)}\] |
| \[=\frac{168+257}{\left( \frac{35}{2}+15 \right)}=\frac{425\times 2}{35+30}=\frac{850}{65}=13.076\] |
| Therefore, time taken by train A to cross train |
| \[B=13.07\,s.\] |
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