Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
A. 30 km/hr
B. 45 km/hr
C. 60 km/hr
D. 75 km/hr
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{slower}}\,{\text{train}}\,{\text{be}}\,x\,{\text{m/sec}} \cr & {\text{Then,}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{faster}}\,{\text{train}} = 2x\,{\text{m/sec}} \cr & {\text{Relative}}\,{\text{speed}} = \,\left( {x + 2x} \right)\,{\text{m/sec}} = 3x\,{\text{m/sec}} \cr & \therefore \frac{{ {100 + 100} }}{8} = 3x \cr & \Rightarrow 24x = 200 \cr & \Rightarrow x = \frac{{25}}{3} \cr & {\text{So,}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{faster}}\,{\text{train}}\, = \frac{{50}}{3}\,{\text{m/sec}} \cr & = {\frac{{50}}{3} \times \frac{{18}}{5}} \,{\text{km/hr}} \cr & = 60\,{\text{km/hr}} \cr} $$Join The Discussion
Comments ( 1 )
Related Questions on Problems on Trains
A. 120 metres
B. 180 metres
C. 324 metres
D. 150 metres
A. 45 km/hr
B. 50 km/hr
C. 54 km/hr
D. 55 km/hr
A. 200 m
B. 225 m
C. 245 m
D. 250 m
RELATIVE SPEED=2X+X=3X
WE KNOW THAT
3X=200/8
X=25/2=50/2*18/5=60KMPH