Problem on Trains
- A train 100 meter in length in length passes a milestone in 10 seconds and another train of the same length travelling in opposite direction in 8 seconds. The speed of the second train is ?
-
View Hint View Answer Discuss in Forum
Speed of first train = (100/10) = 10 m/sec.
Let the speed of second train be x m/sec
∴ 200/ 10 + x = 8Correct Option: C
Speed of first train = (100/10) = 10 m/sec.
Let the speed of second train be x m/sec
∴ 200/ 10 + x = 8
⇒ 200 = 80 + 8x
⇒ x = 15
∴ Speed of second train = 15 m/sec
= (15 x 18/5)
= 54 km/hr.
- Two trains A and B start from station X and Y towards Y and X respectively. After passing each other they take 4 hours 48 minutes ans 3 hour 20 minutes to reach Y and X respectively. If train A is moving at 45 km/hr, then the speed of train B is ?
-
View Hint View Answer Discuss in Forum
A's speed / B's speed = √(Time taken by B to reach X) / (Time taken by A to reach Y)
Correct Option: B
A's speed / B's speed = √(Time taken by B to reach X) / (Time taken by A to reach Y)
⇒ 45/B's speed = √(10/3) x (5/24) = 5/6
∴ B's speed = 45 x (6/5) km/hr = 54 km/hr.
- Two trains Ajanta express and Taj express simultaneously started on two parallel tracks from Meerut to Nagpur, which are 390 km a part. The ratio of the speed of Ajanta express and Taj express is 6 : 7. After how long (in kms) travelling. Taj express exchanges the speed with Ajanta express so that both the trains reach at their destination simultaneously ?
-
View Hint View Answer Discuss in Forum
Basically they will exchange their speeds just after half of the time required for the whole journey. It means after covering 210 km distance they will exchange their speeds.
Correct Option: C
Basically they will exchange their speeds just after half of the time required for the whole journey. It means after covering 210 km distance they will exchange their speeds. check it out graphically for more clarification.
- A train P start from Mokama at 5:00 pm reached Hazipur at 6:00 pm. An another train Q starts from Hazipur at 5:00 pm and reaches Mokama at 6:30 pm. At what time, two trains will cross each other ?
-
View Hint View Answer Discuss in Forum
Let the distance between Mokama and Hazipur be D km
Time taken by train P to cover D km = 1 h
Time taken by Q to cover D km = 3/2 h
∴ Speed of train P = D km/h
Speed of train Q = 2D/3 km/h .
Let they cross each other T h after 5 : 00 pm.
Then, DT + 2DT/ 3 = DCorrect Option: A
Let the distance between Mokama and Hazipur be D km
Time taken by train P to cover D km = 1 h
Time taken by Q to cover D km = 3/2 h
∴ Speed of train P = D km/h
Speed of train Q = 2D/3 km/h .
Let they cross each other T h after 5 : 00 pm.
Then, DT + 2DT/ 3 = D
⇒ T + 2T/3 = 1
⇒ T(1 + 2/3) = 1
⇒ T = 3/5h = (3/5) x 60 = 3 x 12 = 36 min.
Hence, the two trains meet 36 min after 5 : 00 pm.
∴ Meeting time = 5:36 pm
- The average speed of a train in the onward journey is 25% more than that in the return journey. The train halts for 2 h on reaching the destination. The total time taken to complete to and fro journey is 32 h, covering a distance of 1600 km. Find the speed of the train in the onward journey ?
-
View Hint View Answer Discuss in Forum
Let speed in the return journey = V
∴ Speed in onward journey = (125/100) x V = 5V/4 km/h
Average speed = (2x 5V/4 x V) / (5V/4 + V) = 10V/9 km/h
∴ 1600 x (9/10V) = 30 [∴ halts for 2 h ]
∴ V = 1600 x 9/30 x 10 = 48 km/hCorrect Option: B
Let speed in the return journey = V
∴ Speed in onward journey = (125/100) x V = 5V/4 km/h
Average speed = (2x 5V/4 x V) / (5V/4 + V) = 10V/9 km/h
∴ 1600 x (9/10V) = 30 [∴ halts for 2 h ]
∴ V = 1600 x 9/30 x 10 = 48 km/h
∴ Speed in onward journey = 5V/4 = 5/4 x 48 = 60 km/h
