## Aptitude question and answer on Problems on trains

 1 A person standing on a platform - 160 meter long finds that a train crosses the platform in 54 seconds but himself in 30 seconds Then length of the train is A.    100 m B.    175 m C.    150 m D.    200 m Answer : D.  200 m Explanation: $v={x \over 30}$-----------------(1) Where x=length of the train  $v={x+160 \over 54}$-------------(2) From equation (1) and (2), we get  ${x\over 30}={x+160 \over 54}$ $54 x=30x+4800$ $24 x=4800$ $x= 200 m$ Discuss 2 A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train? A.    190 Metres B.    160 Metres C.    200 Metres D.    120 Metres Answer : C.  200 Metres Explanation: Speed of the train, v = 40 km/hr = $40000\over3600$m/s = $400\over36$m/s  Time taken to cross, t = 18 s  Distance Covered, d = vt = $\bigg({400\over36}\bigg) \times 18$ = 200 m  Distance covered is equal to the length of the train = 200 m Discuss 3 A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 m? A.    120 Second B.    99 Second C.    89 Second D.    80 Second Answer : C.  89 Second Explanation: v = $240\over24$ (where v is the speed of the train) = 10 m/s t =$(240+650)\over10$ = 89 seconds Discuss 4 A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is A.    270 Mtrs B.    245 Mtrs C.    235 Mtrs D.    220 Mtrs Answer : B.   245 Mtrs Explanation: Assume the length of the bridge = x meter Total distance covered = 130+x meter total time taken = 30s speed = Total distance covered /total time taken = $(130+x)\over30$ m/s => 45 × $({10\over36})$ = $(130+x)\over30$ => 45 × 10 × $30 \over36$ = 130+x => 45 × 10 × $10 \over 12$ = 130+x => 15 × 10 × $10 \over 4$ = 130+x => 15 × 25 = 130+x = 375 => x = 375-130 =245 Mtrs Discuss 5 A train has a length of 150 meters . it is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train. A.    182 km/hr B.    180 km/hr C.    152 km/hr D.    169 km/hr Answer : A.  182 km/hr Explanation: Length of the train, l = 150m  Speed of the man , Vm= 2 km/hr  Relative speed, Vr = total distance/time = $({150\over3})$ m/s = $({150\over3}) \times ({18\over5})$ = 180 km/hr  Relative Speed = Speed of train, Vt - Speed of man (As both are moving in the same direction)  => 180 = Vt - 2  => Vt = 180 + 2 = 182 km/hr Discuss 6 How many seconds will a 500 meter long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ? A.    42 Second B.    30 Second C.    50 Second D.    28 Second Answer : B.   30 Second Explanation: Distance = 500m Speed = 63 -3 km/hr = 60 km/hr = $600\over 36$ m/s = $50\over3$ m/s Time taken = $distance\over speed$=$500\over({50\over3})$ = ${500 \times 3\over 50}$=30 Second   Discuss 7 Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is A.    42 km/hr B.    20 km/hr C.    28 km/hr D.    36 km/hr Answer : D.  36 km/hr Explanation: Distance covered = 120+120 = 240 m Time = 12 s Let the speed of each train = v. Then relative speed = v+v = 2v 2v = distance/time = $240\over12$ = 20 m/s Speed of each train = v = $20\over2$ = 10 m/s  = $10 \times {36\over10}$ km/hr = 36 km/hr   Discuss 8 A train 108 m long is moving at a speed of 50 km/hr . It crosses a train 112 m long coming from opposite direction in 6 seconds. What is the speed of the second train? A.    82 km/hr B.    76 km/hr C.    44 km/hr D.    58 km/hr Answer : A.  82 km/hr Explanation: Total distance = 108+112 = 220 m Time = 6s Relative speed = distance/time = $220\over6$ m/s = $110\over3$ m/s = ($110\over3$) × ($18\over5$) km/hr = 132 km/hr => 50 + speed of second train = 132 km/hr => Speed of second train = 132-50 = 82 km/hr   Discuss