Question 1

Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?

Accepted Answer

Assume both trains meet after x hours after 7 am Distance covered by train starting from P in x hours = 20x km Distance covered by train starting from Q in (x-1) hours = 25(x-1) Total distance = 110 => 20x + 25(x-1) = 110 => 45x = 135 => x= 3 Means, they meet after 3 hours after 7 am, ie, they meet at 10 am

Question 2

Two trains of equal length , running in opposite directions , pass a pole in 18 and 12 seconds. The trains will cross each other in

Accepted Answer

Let the length of the train be L metres Speed of first train = 3600 18 x L m/hour Speed of secxond train = 3600 12 x L m/hour When running in opposite directions, relative speed = 200 L + 300 L m/hour Distance to be covered = L + L = 2L metre Time taken = 2 L 500 L x 3600 sec =14.4 sec

Question 3

A train travelling at a speed of 75 mph enters a tunnel 312 miles long. The train is 14 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

Accepted Answer

Total distance covered = 7 2 + 1 4 miles = 15 4 miles Time taken = 15 4 * 75 hrs = 1 20 hrs = 1 20 * 60 m i n = 3 min

Question 4

A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

Accepted Answer

150 m

Question 5

A train is moving and crossing a man who is running on a platform of 100 m at a speed of 8 kmph in the direction of the train, in 9 sec. If the speed of the train is 74 kmph. Find the length of the train ?

Accepted Answer

Let the length of the train = L mts Relative speed of train and man = 74 - 8 = 66 kmph = 66 x 5/18 m/s => 66 x 5/18 = L/9 => L = 165 mts.

Question 6

Two trains having equal lengths, take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when traveling in opposite direction?

Accepted Answer

Speed of train 1 = 120 10 m / s e c = 12 m/sec Speed of train 2 = 120 15 m / s e c = 8 m/sec if they travel in opposite direction, relative speed = 12 + 8 = 20 m/sec distance covered = 120 + 120 = 240 m time = distance/speed = 240/20 = 12 sec

Question 7

A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train ?

Accepted Answer

Relative speed = (120 + 80) km/hr =(200*5/18)m/s = (500/9)m/s Let the length of the other train be x metres. Then, x+270/9 = 500/9 => x + 270 = 500 => x = 230.

Question 8

A passenger train covers the distance between station K and L, 40 minutes faster than a goods train. Find this distance between K and L if the average speed of the passenger train is 50 km/h and that of goods train is 30 km/h?

Accepted Answer

Let the distance be 'd' kms. According to the given data, d 30 - d 50 = 40 60 hrs = > 6 d = 300 = > d = 50 kms .

Question 9

A train travelling with a speed of 60 km/hr catches another train travelling in the same direction and then leaves it 120m behind in 18 seconds. The speed of the second train is

Accepted Answer

Given speed of the first train = 60 km/hr = 60 x 5/18 = 50/3 m/s Let the speed of the second train = x m/s Then, the difference in the speed is given by 50 3 - x = 120 18 => x = 10 m/s => 10 x 18/5 = 36 km/hr

Question 10

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

Accepted Answer

Relative speed = (60 + 40) km/hr =[ 100 x ( 5 / 18 ) ]m/sec = ( 250 /9 ) m/sec. Distance covered in crossing each other = (140 + 160) m = 300 m. Required time = [ 300 x ( 9/250 ) ] sec = ( 54/ 5 )sec = 10.8 sec.

Question 11

A train travelling at 48 kmph crosses another train, having half its length and travelling in opposite direction at 42 kmph, in 12 sec. It also covers a bridge in 45 sec. Find the length of the bridge ?

Accepted Answer

Let the length of the 1st train = L mts Speed of 1st train = 48 kmph Now the length of the 2nd train = L/2 mts Speed of 2nd train = 42 kmph Let the length of the bridge = D mts Distance = L + L/2 = 3L/2 Relative speed = 48 + 42 = 90 kmph = 90 x 5/18 = 25 m/s(opposite) Time = 12 sec => 3L/2x25 = 12 => L = 200 mts Now it covers the bridge in 45 sec => distance = D + 200 Time = 45 sec Speed = 48 x5/18 = 40/3 m/s => D + 200/(40/3) = 45 => D = 600 - 200 = 400 mts Hence, the length of the bridge = 400 mts.

Question 12

A train covers a distance between station A and station B in 45 min.If the speed of the train is reduced by 5 km/hr,then the same distance is covered in 48 min.what is the distance between the stations A and B ?

Accepted Answer

Let 'd' be the distance and 's' be the speed and 't' be the time d=sxt 45 mins = 3/4 hr and 48 mins = 4/5 hr As distance is same in both cases; s(3/4) = (s-5)(4/5) 3s/4 = (4s-20)/5 15s = 16s-80 s = 80 km. => d = 80 x 3/4 = 60 kms.

Question 13

A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

Accepted Answer

Speed =[ 72 x (5/18) ]m/sec= 20 m/sec. Time = 26 sec. Let the length of the train be x metres. Then,[ (x+250)/26 ]= 20 => x + 250 = 520 => x = 270.

Question 14

The difference between the time taken by two trains to travel a distance of 350 km is 2 hours 20 minutes. If the difference between their speeds is 5 km/hr, what is the speed of faster train ?

Accepted Answer

Let the speed of the faster train be 'S' kmph Then speed of the slower train will be '(S-5)' kmph Time taken by faster train = 350/S hrs Time taken by slower train = 350/(S-5) hrs 350 s - 5 - 350 s = 2 h r s 20 m i n = 2 1 3 = 7 3 => S = 30 km/hr.

Question 15

A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is :

Accepted Answer

500

Question 16

A train is traveling at 48 kmph . It crosses another train having half of its length , traveling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. What is the length of the platform ?

Accepted Answer

400

Question 17

A jogger is running at 9 kmph alongside a railway track is 240 meters ahead of the engine of a 120 meters long train running at 45 kmph in the same direction. In how much time will the train pass the jogger ?

Accepted Answer

36 sec

Question 18

Length of train is 170 meters and speed of train is 63 km/hour. This train can pass a bridge in 30 seconds, then find the length of the bridge.

Accepted Answer

Given speed = 63 km/hr = 63 × 5 18 = 35 2 m/s Let the length of the bridge = x mts Given time taken to cover the distance of (170 + x)mts is 30 sec. We know speed = d i s tan c e t i m e m/s ⇒ 35 2 = 170 + x 30 --> x = 355 mts.

Question 19

A train sets off at 3 p.m. at the speed of 70 kmph. Another train starts at 4:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet ?

Accepted Answer

Distance = 70 x 1 ½ = 105 km Relative Speed = 85 – 70 = 15 Time = 105/15 = 7 hrs 4:30 + 7 hrs = 11.30 p.m.

Question 20

A train running at the speed of 40 km/hr crosses a signal pole in 9 seconds. Find the length of the train ?

Accepted Answer

We know that S p e e d = d i s tan c e t i m e distance= speed * time ⇒ d = 40 × 5 18 × 9 d= 100 mts.

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