A) \[\frac{25}{11}\]
B) \[\frac{3}{2}\]
C) \[\frac{5}{2}\]
D) \[\frac{11}{5}\]
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\[\frac{{{t}_{1}}}{{{t}_{2}}}=\frac{25}{\frac{18\times 36}{110}}=\frac{11}{5}\]
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