Question 1

Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

Accepted Answer

Relative speed = = (45 + 30) km/hr = ❨ 75 x 5 ❩ m/sec 18 = ❨ 125 ❩ m/sec. 6 We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train. So, distance covered = Length of the slower train. Therefore, Distance covered = 500 m. ∴ Required time = ❨ 500 x 6 ❩ = 24 sec. 125

Question 2

Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

Accepted Answer

Let the speed of the slower train be x m/sec. Then, speed of the faster train = 2x m/sec. Relative speed = (x + 2x) m/sec = 3x m/sec. ∴ (100 + 100) = 3x 8 ⟹ 24x = 200 ⟹ x = 25 . 3 So, speed of the faster train = 50 m/sec 3 = ❨ 50 x 18 ❩km/hr 3 5 = 60 km/hr.

Question 3

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

Accepted Answer

Let the speed of the second train be x km/hr. Relative speed = (x + 50) km/hr = [ (x + 50) x 5 ] m/sec 18 = [ 250 + 5x ] m/sec. 18 Distance covered = (108 + 112) = 220 m. ∴ 220 = 6 ❨ 250 + 5x ❩ 18 ⟹ 250 + 5x = 660 ⟹ x = 82 km/hr.

Question 4

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

Accepted Answer

4.5 km/hr = ❨ 4.5 x 5 ❩ m/sec = 5 m/sec = 1.25 m/sec, and 18 4 5.4 km/hr = ❨ 5.4 x 5 ❩ m/sec = 3 m/sec = 1.5 m/sec. 18 2 Let the speed of the train be x m/sec. 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 = ❨ 22.5 x 18 ❩ km/hr = 81 km/hr. 5

Question 5

A train runs with a speed of 200 km/hour. What will be its speed in m/sec?

Accepted Answer

Speed in km/ hour =200 Speed in m/sec = 200 x 5/18 = 500/9 m/sec = 55.55 m/sec

Question 6

A train crosses a pole in 10 sec and a 200m long platform in 20 sec. What is the length of the train?

Accepted Answer

Let the length of train be x meter and speed be y m/sec Therefore, time taken to cross the pole = x/y sec and time taken to cross the platform = ( Length of train + Length of platform) / speed of train Therefore x/y = 10 And, (x+200) / y = 20 ⇒ 10y + 200 = 20 y ∴ speed of train, y = 20 m/sec And length of rain = x = 10y = 200m

Question 7

Two trains running at 36 km/hr and 54 km/hr are running parallel in the opposite direction. If their lengths are 200m and 300m respectively. Then how much time will they take to cross each other?

Accepted Answer

Relative speed, when the trains are running in the opposite direction = Sum of the speed Therefore, Relative speed = 36 km/hr +72 km/hr = 90 km/hr Relative speed in m/sec = 90 km/hr x 5/18= 25 m/sec Distance covered = sum of the lengths of the train = 200 m+ 300 m = 500m Therefore, time taken = 500m / 25 m/sec = 20 sec

Question 8

A 200 m long train is running at a speed of 60 km/ hr. Find out the time it takes to pass a man standing at the platform

Accepted Answer

Speed of the train = (60 x 5/18) m/sec = 50/3 m/sec Distance covered in passing the standing person = 200m Required time taken= =200/(50/3) = 200 x (3/50) = 12 sec

Question 9

A train is running at the speed of 264 Km/hr. If the length of the train is 330m, then how long will it take to cross a platform which is 330m long?

Accepted Answer

Speed of the train = (264 x 5/18) m/sec = 220/3 m/sec Distance covered in passing the platform = (330+330) m= 660m Time taken= ( 660 / (220/3) ) sec = (660 x 3/ 220 ) = 9 sec

Question 10

A train which is 264 meter long passes a pole in 12 sec. Find out the speed of train?

Accepted Answer

Length of train = 264 m Time taken to cross the pole = 12 sec Speed of the train, in m/sec = Length of the train/ Time taken to cross the pole Therefore, speed in m/sec= (264 / 12) m/sec = 22 m /sec Calculating speed in km/ hour = (22 m/sec ) x 18/5 = 396/5 km/hr = 79.2 km/ hour

Question 11

A train 200 m long is running at a speed of 36 km/hr. It crosses a bridge in 30 sec. What is the length of the bridge?

Accepted Answer

Speed in m/sec = 36 km/hr x 5/18 = 10m/sec Distance covered by train in crossing the bridge = Speed of train in m/sec x time in sec = 10 m/sec x 30 sec = 300 m Now, we know that Distance covered by train in crossing the bridge= Length of train + Length of bridge Therefore, Length of bridge = 300m - 200m = 100m

Question 12

A train which 360m long takes 36 sec to cross a telegraph pole. How long will it take to cross a 600m long platform?

Accepted Answer

Speed of train in m/sec = 360m / 36 sec = 10 m/sec Distance covered by train in crossing the platform = Length of train + Length of Platform = 360m + 240m = 600m Therefore, Time taken to cover this distance = 600m /(10 m/sec) = 60 sec

Question 13

A passenger train running at a speed of 72 km/hr crosses a 400m long platform in 30 sec. What is the length of the train?

Accepted Answer

Speed of train in m/sec = 72 km/hr x 5/18 = 20 m/sec Distance covered in meter = Time taken in crossing the platform in sec x speed in meter = 30 sec x 20 m/sec = 600m Now, we know , Distance covered by train in crossing the platform = Length of train + Length of Platform Therefore, length of the train = 600m - 400m = 200m

Question 14

The length of train is equal to the length of the platform. Suppose the train is running at a speed of 72 km/hr and it crosses a platform in 2 minutes. What is then the length of the train?

Accepted Answer

Speed in m/sec = 36km/hr x (5/18) = 10 m/sec Given, Time taken by train to cross the platform = 2 min = 120 sec Therefore, the distance covered by train in crossing the platform = 10 m/sec x 120 sec = 1200 m Now, distance covered by train in crossing the platform = Length of train + Length of Platform Given, Length of train = Length of Platform = x Therefore, 2x = 1200 so, x = Length of train = 1200/2 = 600 m

Question 15

A train takes 24 sec to cross a 480 m platform and 36 sec to cover a 900 m platform. what is the length of the train?

Accepted Answer

Let the length of the train be x meter and its speed be y m/sec Then, (x + 480 m) / 24 sec = y ....(i) and , (x + 720 m) / 36 sec = y ....(ii) From Eqs (i) and (ii) (x + 480) / 24 = (x + 900) / 36 ⇒ 3x + 1440 = 2x + 1800 ∴ Length of train, x= 360m

Question 16

A 200 m long rain is running at a speed of 54 km/hr. On the parallel and a different track, another train 300 m long is running at a speed of 72 km/hr. Both the trains are running in the same direction. Find out how much will it take the train to cr…

Accepted Answer

We know that, when the trains are moving in the same direction, Relative speed= Difference between the speed of train and total distance for crossing each other = Sum of the length of train Therefore, Relative speed = 72 km/hr - 54 km /hr = 18 km/hr Relative speed in m/sec = 18 km/hr x 5/18 = 5 m/sec and Total distance = 200m + 300m = 500m and Total time taken to cross each other = Total distance in meter/ Relative speed in m/sec = 500 m / (5 m/sec) = 100 sec

Question 17

A train 400 m long is running at a speed of 54 km/hr. If it crosses a tunnel in 2 minutes. Then what is the length of tunnel?

Accepted Answer

Speed of train in m/sec = (speed of train in km/hr) x 5/18 ∴ speed of train in m/sec = 54 x 5/18 = 15 m/sec Time taken to cross the tunnel = 2 minutes = 120 sec Therefore, Total length covered by train in crossing the tunnel = Speed of train x Time taken to cross the tunnel = 15 m/sec x 120 sec = 1800 m Now, we know that Total length covered by train in crossing the tunnel = Length of train + Length of tunnel Given, Length of train =400m and Calculated above, Length covered by train in crossing the tunnel = 1800 m Therefore, Length of tunnel = 1800m- 400m = 1400m

Question 18

A and B are two stations, a train goes from A to B at 64 km/hr. and return to A at a slower speed. If its average speed for the whole journey is 56 km/hr. at what speed did it return?

Accepted Answer

Let the required speed be y km/hr. Then, ( 2 x 64 ) x [ y / (64 + y)] = 56 ⇒ 128y = 64 x 56 + 56y ∴ y= (64 x 56 ) / 72 = 49.77 km/hr.

Question 19

A train 270 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in?

Accepted Answer

Relative speed = (25 + 2) = 27 km/hr = 27 x (5/18) m/sec. = 15/2 m/sec. Time taken by the train to pass the men. = 270 / (15/2) = 36 sec.

Question 20

A train 300 meters long passes a standing man is 15 seconds. The speed of the train is?

Accepted Answer

∴ Speed = Distance / Time = (300/15) = 20 m/sec = (20 x 18) / 5 = 72 km/hr

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