Quantitative Aptitude - Trains
A train travelling at a speed of 75 mph enters a tunnel 3½ miles long. The train is ¼mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges? A.2.5 min B.3 min C.3.2 min D.3.5 min
Answer: Option B Explanation: Total distance covered =[ (7/2) + (1/4) ] miles =( 15/4 )miles. Time taken = [(15)/(4*75)]hrs = (1/20)hrs =[ (1/20)x 60 ] min. = 3 min.
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train? A.230 m B.240 m C.260 m D.270 m
Answer: Option D Explanation: Speed =[ 72 x(5/18) ]m/sec= 20 m/sec. Time = 26 sec. Let the length of the train be x metres. Then,[ (x+250)/26 ]= 20 => x + 250 = 520 => x = 270.
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? A.230 m B.240 m C.260 m D.320 m E.None of these
Answer: Option A Explanation: Relative speed = (120 + 80) km/hr =200*(5/18)m/sec = ( 500/9 ) m/sec. Let the length of the other train be x metres. Then,[ ( x + 270)/9 ]=( 500/9 ) => x + 270 = 500 => x = 230.
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is: A.50 m B.150 m C.200 m D.Data inadequate
Answer: Option B Explanation: Let the length of the train be x metres and its speed by y m/sec. Then, (x/y)= 15 => y =(x/15) Therefore, [ (x + 100) / 25 ]=(x/15) => 15(x + 100) = 25x => 15x + 1500 = 25x => 1500 = 10x => x = 150 m.
A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? A.5 sec B.6 sec C.7 sec D.10 sec
Answer: Option B Explanation: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr. = [ 66 x ( 5 / 18) ] m/sec =( 55 / 3 ) m/sec. Time taken to pass the man = [ 110 x ( 3 / 55 ) ] sec = 6 sec.
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 Explanation: Let the speed of the slower train be x m/sec. Then, speed of the faster train = 2x m/sec. Relative speed = (x + 2x) m/sec = 3x m/sec. Therefore, [ (100 + 100) / 8 ]= 3x => 24x = 200 => x =25/3 So, speed of the faster train =(50/3)m/sec =[ (50 / 3) x ( 18/ 5 ) ] km/hr = 60 km/hr
A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is: A.130 B.360 C.500 D.540
Answer: Option C Explanation: Speed =[ 78 x ( 5/18 ) ] m/sec =( 65/3 ) m/sec. Time = 1 minute = 60 seconds. Let the length of the tunnel be x metres. Then, [ (800 + x )/(60) ]= 65/3 => 3(800 + x) = 3900 = 500
A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train? A.69.5 km/hr B.70 km/hr C.79 km/hr D.79.2 km/hr
Answer: Option D Explanation: Let the length of the train be x metres and its speed by y m/sec. Then, (x/y)=8 => x = 8y Now, [ (x + 264)/20 ] = y 8y + 264 = 20y y = 22. Speed = 22 m/sec =[ 22*(18/5) ]km/hr = 79.2 km/hr.
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is: A.9 B.9.6 C.10 D.10.8
Answer: Option D Explanation: Relative speed = (60 + 40) km/hr =[ 100 x ( 5 / 18 ) ]m/sec = ( 250 /9 ) m/sec. Distance covered in crossing each other = (140 + 160) m = 300 m. Required time = ( 300 x ( 9/250 ) ) sec = ( 54/ 5 )sec = 10.8 sec.
A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? A.320 m B.350 m C.650 m D.Data inadequate
Answer: Option B Explanation: Speed =( 300/18) m/sec = (50/3)m/sec. Let the length of the platform be x metres. Then,[(x + 300)/39]=( 50 / 3 ) => 3(x + 300) = 1950 => x = 350 m.