Question 1

A train crosses a platform in 30 seconds at a speed of 45km/hr. How much time will it take to cross an electric pole if take to cross an electric pole if the length of the platform is 100 metres?

Accepted Answer

Distance covered by the train in crossing the platform = (45 x 30) / 3600 = 3/8 km = 375 metres ∴ Length of train = (375 - 100) = 275 meters ∴ Time taken to cross the pole = 275 ÷ (375/30) = (275 x 30) /375 = 30 sec

Question 2

A 440 m long train is running at 240 km/h. In what tie will it pass a man running in the direction opposite to that of the train at 24 km/h?

Accepted Answer

Speed of the train relative to man = (240 + 24) km/h = 264 km/h = 264 x (5/18) m/s = 220/3 m/s Distance covered in passing the man = 440 m ∴ Time taken = (440/220) x 3 = 6 s

Question 3

A 280 m long train crosses a platform which is three times of its length, in 6 min 40 s . What is the speed of the train?

Accepted Answer

Length of the train = 280 m Length of the platform = 280 x 3 = 840 m Taken time = 6 min 40 s = (360 + 40) = 400 s ∴ Required speed = Distance / Time = (840 + 280)/400 = 1120/400 = 28 m/s

Question 4

Two trains of length 512 m and 528 m are running towards each other on parallel lines at 84 km/h and 60 km/h, respectively. In what time, will they be clear of each other from he moment they meet?

Accepted Answer

Relative speed = (84 + 60) km/h = 144 km/h = 144 x (5/18) m/s = 8 x 5 = 40 m/s Distance covered in passing each other = 512 + 528 = 1040 m ∴ Required time = 1040/40 = 26 s

Question 5

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?

Accepted Answer

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.

Question 6

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?

Accepted Answer

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.

Question 7

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 expres…

Accepted Answer

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.

Question 8

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?

Accepted Answer

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

Question 9

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 th…

Accepted Answer

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

Question 10

A train overtake two persons walking along a railway track. The first one walks at 4.5 km/h and the other one walks at 5.4 km/h. The train needs 8.4 s and 8.5 s respectively , to overtake them. What is the speed of the train, if both the persons are…

Accepted Answer

Speed of the person = 4 km/h = 4.5 x (5/18) = m/s = 5/4 m/s = 1.25 m/s Speed of 2nd person = 5.4 km/h = 5.4 x (5/18) m/s = 3/2 m/s = 1.5 m/s Let speed of train be x m/s. Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5 ⇒ 8.4x - 10.5 = 8.5x - 12.75 ⇒ 0.1x = 2.25 ⇒ x = 22.5 ∴ Speed of the train = 225 x (18/5 ) = 81 km/h .

Question 11

Two trains A and B starts from Howrah and Patna towards Patna and Howrah respectively at the same time. After passing each other, they take 4, h, 48 min and 3 h, 20 min to reach Patna and Howrah, respectively. If the train from Howrah is moving at 4…

Accepted Answer

Given, a = 45 km/h, y = ?, t1 = 4 h 48 min and t2 = 3 h 20 min Using y = a√t1 / t2= 45√4 h and 48 min /3 h and 20 min = 45√(24/5h) / (10/3 h) = 45√24 x 3/5 x 10 = 45 x √1.44 = 45 x 12 = 54 km/h

Question 12

A train travelling at 36 kmph completely crosses another train having half its length and travelling in the opposite direction at 54 kmph, in 12 second, If it also passes a railway platform in 1 1/ 2 minutes, the length of the platform is?

Accepted Answer

Let the length of slower train be L meters and the length of faster train be (L/2) meters Their relative speed = (36 + 54) km/hr = 90 x (5/18) = 25 m/sec ∵ 3L / (2 x 25) = 12 ⇒ 3L = 600 ⇒ L = 200 ∴ Length of slower train = 200 meters Let the length of platform by M meters Then, 200 + M/[36 x (5/18)] = 90 sec. ⇒ 200 + M = 900 ⇒ M = 700 meters Length of platform = 700 meters.

Question 13

A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?

Accepted Answer

Relative speed =280/9 m / sec = (280/9*18/5) kmph = 112 kmph. Speed of goods train = (112 - 50) kmph = 62 kmph.

Question 14

A train of length 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

Accepted Answer

6

Question 15

Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 9 hours after they passed each other the ratio of the speeds of the two trains was

Accepted Answer

Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a) Therefore, Ratio of the speeds of two trains = 9 : 4 = 3 : 2

Question 16

A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is :

Accepted Answer

Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr. Therefore, Man's rate against the current = (12.5 - 2.5) = 10 km/hr.

Question 17

Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?

Accepted Answer

24

Question 18

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

Accepted Answer

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 = 240/12 = 20 m/s Speed of each train = v = 20/2 = 10 m/s = 10 × 36/10 km/hr = 36 km/hr

Question 19

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 ?

Accepted Answer

79.2 km/hr

Question 20

A train moves with a speed of 108 kmph. Its speed in metres per second is :

Accepted Answer

108 kmph = 108*[5/18] m/sec = 30 m / s.

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