Question 1

A train crossed a platform in 43 s. The length of the train is 170 m. What is the Speed of the train?

Accepted Answer

Length of platform is not given. it can not be determined.

Question 2

Two train are moving in opposite direction with speed of 6 m/s and 12 m/s, respectively. Find their relative speed.?

Accepted Answer

When two trains are moving in opposite directions then their relative speed is equal to the sum of the speed of both the trains. ∴ Required relative speed = 6 + 12 = 18 m/s

Question 3

Two trains are moving in the same direction with speeds of 15 km/h and 21km/h respectively. What is the speed of trains in respect of each other?

Accepted Answer

We know that, if two trains are running in the same direction, then relative speed is equal to the difference of the speeds of both the trains. ∴ Required relative speed = 21 - 15 = 6 km/h

Question 4

The relative speed of a train in respect of a car is 90 km/h when train and car are moving opposite to each other. Find the actual speed of train . If car is moving with a speed of 15 km/h.?

Accepted Answer

Relative speed of train = Speed of train + Speed of car ⇒ 90 = Speed of train + 15 ∴ Speed of train = 90 - 15 = 75 km/h

Question 5

What is the time taken by a train running at 18 km/h to cross a man standing on a platform, length of the train is 120 m?

Accepted Answer

Speed of the train = 18 km/h = 18 x 5/18 m/s = 5 m/s Distance covered = Length of the train = 120 m ∴ Time taken by the train to cross the man = Distance/Speed = 120/5 = 24 s

Question 6

A train takes 5 seconds to pass an electric pole. If the length of the train is 120 meters, the time taken by it to cross a railway platform 180 meter long, is?

Accepted Answer

Speed of train = (120/5) = 24 m/sec. Time takes to cross the platform = (120 + 180)/24 = 121/2

Question 7

A train 120 meters long, crosses a pole in 10 seconds. The speed of the train is?

Accepted Answer

Length of train = 120 m. Total taken in crossing the pole = 10 seconds. Speed of the train = length / time = 120 / 10 = 12 m/s = 12 x (18/5) = 43.2 km/hr

Question 8

The distance between two station A and B is 220 km. A train leaves A toward B at an average speed of 80 km/hr. after half an hour another train leaves B toward A at an average speed at 100 km/hr. the distance of the point of two train meet, from A i…

Accepted Answer

Let the required distance be x km. Then, ( x/80 ) - ( 220 - x ) / 100 = 1/2 ⇒ 5x - 4( 220 - x ) = 200 ⇒ 9x = 1080 ⇒ x = 120 km ∴ Required distance = 120 km

Question 9

X and Y are two station 500 km apart. A train start from X and moves toward Y at 20 km/hr another train station from Y at the same times and moves toward X at 30 km/hr. How far from X will they cross each other?

Accepted Answer

Suppose they meet x km. from X Then, x/20 = (500 - x)/30 ⇒ 30x = 10000 - 20x ∴ x = 200 km.

Question 10

150 meter long train takes 10 second two pass a man who is going in same direction at the speed of 2 km/hr . What is the speed of the train?

Accepted Answer

Let the speed of the train be Y km/hr ∴ length of the train = 150 m = 150/1000 = 3/20 km. Time taken to cross the man = 10 seconds = 10/ (60 x 60) = 1/360 hrs . ∵ time = Length of the train /( speed of the train - speed of the man ) ∴ 1/360 = ( 3 / 20) / ( Y - 2) ⇒ (Y - 2 ) = 3/20 x 360 ⇒ (Y - 2 )= 54 ⇒ Y = 54 + 2 = 56 km/hr.

Question 11

A train running at the speed of 45 kmph took 12 seconds in passing a certain point. Then the length of the train must be?

Accepted Answer

∵ Speed = (45 x 5/18) = (25/2) m/sec Distance = (Time x Speed) = (12 x 25 / 2 ) meters = 150 meters ∴ Length of the train = 150 meters

Question 12

A train 75 meters long is running with a speed of 20 km/hr. It will pass a standing man in?

Accepted Answer

∵ Speed of the train = 20 x (5/18) = (50/9) m/sec ∴ Time taken by the train to pass the man = 75 x (9/50) = 13.5 sec

Question 13

Two stations A and B are 110 kms apart on a straight line. One train start from A at 7 a.m. and travels towards B at 20 km per hour speed. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 km per hour. At what time will th…

Accepted Answer

Suppose they meet T hrs after 7 a.m ∴ Distance covered by A in T hrs = (20 x T) km Distance covered by B in (T - 1) hrs = 25(T - 1) km ∵ 20T + 25 (T -1) = 110 ⇒ 45 x T = 135 ∴ T = 3 hours So, they meet at 10 a.m.

Question 14

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is?

Accepted Answer

Let the length of the train be L km and its speed by y km/hr Then , speed of train relative to first man = (y - 2) km/hr Speed of train relative to second man = (y - 4) km/hr ∵ L / (y - 2) = 9 /(60 x 60) and L / (y - 4) = 10/ (60 x 60) ∴ 9y - 18 = 3600 x L ...(1) and 10y - 40 = 36000 x L ... (2) So, 9y - 18 = 10y - 40 ⇒ y = 22 ∵ L/ (22 - 2) = 9/ 3600 ∴ L = (20 x 9) / 3600 = 1/20 km = (1/20) x 1000 = 50 m.

Question 15

A train 100 meter long moving at a speed of 50 kmph crosses a train 120 meters long coming from opposite direction in 6 seconds. The speed of second train is?

Accepted Answer

Let the speed of the second train be y km/hr Relative speed of both trains = (50 + y) km/hr Total distance traveled = 100 + 120 = 220 meters = 0.22 km Time = 6 sec = 6/( 60 x 60) hr. Speed = distance/time ⇒ 50 + y = (0.22 x 60 x 60)/ 6 ⇒ 50 + y = 132 ∴ y = 82 ∴ Speed of the second train = 82 km/hr

Question 16

A train speeds past a pole in 15 seconds and speeds past a platform 100 meters long in 25 second. Its length in meters is?

Accepted Answer

Let the length of the train be 'L' meters and its speed be 'v' meters/sec Then, L/v = 15 ⇒ v = L/15 ....(1) Now, (L + 100)/25 = L/15 ⇒ L = 150 m

Question 17

Two trains running in the same direction at 40 kmph and 22 kmph completely pass one another in 1 minute. If the length of the first train is 125 metres, the length of second train is?

Accepted Answer

Relative speed of the train = (40 - 22) km/hr = 18 km/hr Relative speed of the train in m/sec = 18 x (5/18) = 5 m/sec. Let the length of 2nd train be L meters. Then, (125 + L) / 5 = 60 sec. ⇒ 125 + L = 300 ⇒ L = 175 ∴ Length of second train = 175 meters

Question 18

A 150 meter long train crosses a man walking at the speed of 6 kmph in the opposite direction in 6 seconds. The speed of the train in km/hr is?

Accepted Answer

Let the speed of the train be v km/hr Relative speed of the train = (v + 6) km/hr = [(v + 6) x 5/18] m/sec ∵ 150/6 = (v + 6) x (5/18) ⇒ 5v + 30 = 450 ∴ v = 84 km/hr

Question 19

A train is running at the rate 40 kmph. A man also is going in the same direction parallel to the train at the speed of 25 kmph. If the train crosses the man in 48 sec, the length of the train is?

Accepted Answer

∵ Relative speed of the train = (40 - 25) km/hr = 15 x (5/18) = 25/6 m/sec ∴ Length of the train = (48 x 25) / 6 = 200 meters .

Question 20

A train of length 150 meters takes 10 seconds to pass over another train 100 meters long coming from the opposite direction. If the speed of the first train be 30 kmph, the speed of the second train is?

Accepted Answer

Relative speed of both trains = (150 + 100)/10 = 25 m/sec = 25 x (18/5) = 90 km/hr ∴ Speed of second train = (90 - 30) = 60 km/hr .

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