Problems on Trains- Aptitude Questions and Answers

 A 500 ft long train crosses a platform 700 feet in 10 seconds. So what is the speed of that train? A) 70 ft/s B) 85 ft/s C) 100 ft/s D) 120 ft/s Correct Answer :120 ft/s Explanation :Speed of the train = Length of (train+platform)/Time = 500+700 / 10 = 120 ft/ sec A passenger train departs from Delhi at 6 p.m. for Mumbai. At 9 p.m. an express train, whose average speed exceeds that of the passenger train by 15 km / hour leaves Mumbai for Delhi. Two trains meet each other mid-route. At what time do they meet, given that the distance between the cities is 1080 km? A) 4 p.m. B) 2 a.m. C) 12 mid-night D) 6 a.m. Correct Answer :6 a.m. Explanation :Let the speed of passenger train= x km/hr Speed of express train = (x + 15) km/hr Then, As is given 6pm#-----540-----#-----540-----#9pm (540 / x) - (540 / x + 15) = 3 [6 pm - 9 pm ] 540( 1/x - 1/x + 15) = 3 540( x + 15 - x / x*(x + 15) ) = 3 540*15 = 3x*(x + 15) x2 + 15X - 2700 = 0 (x + 60)(x - 45) = 0 x = 45 [∵ x ≠ 60] Time taken by passenger train to reach the meeting point = 540/x = 540/45 = 12 Hrs Therefore, Both train will meet at (6 pm + 12 Hrs) = 6 a.m. A 225 m long train is running at a speed of 30 km / hour. How much time does it take to cross a man running at 3 km / hour in the same direction? A) 40 seconds B) 30 seconds C) 25 seconds D) 15 seconds Correct Answer :30 seconds Explanation :Relative Speed, in the same direction= Speed of train - Speed of man =(30 - 3) km/h =(27*1000/3600) m/s =(27*5/18) =15/2 m/s Time taken to cross the man = Distance/ Relative Speed = 225 / (15/2) = 225*2 / 15 = 30 sec The distance between two cities (M and N) is 569 km. A train starts from city M at 8 am and travel towards city N @ 53 km per hour. Another train starts from city N at 9 am and travel towards city M @ 76 km per hour. At what time will the trains meet? A) 12:30 pm B) 1:00 pm C) 2:30 pm D) 1:00 pm Correct Answer :1:00 pm Explanation :Total distance between M and N= 569 km First train leaves station at 8:00 am and second at 9:00 am. So first train i.e., from M to N has covered 53 km distance in 1 hour. So, distance left between the stations = 569 − 53 = 516 km trains are travelling in opposite directions. So, relative speed of trains = 53 + 76 = 129 km/h Now, Time taken to cover 519 km = 519/129= 4 hours Hence the time, at which both the trains will meet, is 4 hour after second train left i.e., 9:00 am + 4 h = 1:00 pm