Question 1

A train moving at the rate of 36 km per hour crosses a standing man in 10 seconds. It will cross a platform 55 meters long in?

Accepted Answer

speed of train = 36 x (5/18) = 10 m/sec. Let the length of the train be L meters Then, L/10 = 10 ⇒ L = 100 meters. ∴ Time taken to cross the platform = (100 + 55) / 10 = 151/2 sec.

Question 2

A train crosses a platform 100 metres long in 60 seconds at a speed of 45 km per hour. The time taken by the train to cross an electric pole is?

Accepted Answer

Let the length of train = L metres Speed of train = 45 x (5/18) = 25/2 m/sec. Distance covered in crossing the platform = (L + 100) m ∴ (L + 100) x (2/25) = 60 ⇒ 2L + 200 = 1500 ⇒ L = 650. Now, time taken to cross the pole = 650 x (2/25) = 52 sec.

Question 3

Two trains of equals length are running on parallel line in the same direction at the rate of 46 kmph and 36 kmph. The faster train passes the slower train in 36 seconds. The length of each train is?

Accepted Answer

Let the length of each train = L metres Relative speed = (46 - 36) = 10 km/hr. = 10 x (5/18) = 25/9 m/sec Distance covered in crossing = (L + L) = 2L metres ⇒ 2L x (9/25) = 36 ∴ L = (25 x 36)/(2 x 9) = 50 metres.

Question 4

Two trains 132 metres and 108 metres long are running in opposite directions, one at the rate of 32 kmph and another one at the rate of 40 kmph. From the moment they meet they will cross each other in?

Accepted Answer

Relative speed of both trains = (32 + 40) = 72 km/hr = 72 x (5/18) = 20 m/sec Distance covered in crossing each other = 132 + 108 = 240 m ∴ Required time = 240/20 = 12 sec.

Question 5

A train 300 m long crossed a platform 900 m long in 1 minute 12 seconds. The speed of the train in km/hr was?

Accepted Answer

Distance covered in 72 sec. = 300 + 900 m ∴ Speed = 1200/72 = 50/3 m/sec. = 60 km/hr .

Question 6

How long will a train 130 m long travelling at 40 km an hour, take to pass a kilometer stone?

Accepted Answer

Total distance = 130 m = 0.13 km Speed of the train = 40 km /hr Time taken = 0.13/40 hr = (0.13 x 60 x 60) / 40 = 11.7 sec.

Question 7

A train travelling at 30 km an hour took 13 1/ 2 sec in passing a certain point. Find the length of the train?

Accepted Answer

Speed = 30 km/hr = 30 x (5/18) = 25/3 m/sec. ∴ Length of the train = (25/3) x (27/2) = 225/2 = 1121/2 metres

Question 8

A train 160 metres long passes a standing man in 18 seconds. What is the speed of the train?

Accepted Answer

Speed of the train = (160/18) x (18/5) = 32 km/hr.

Question 9

Find the length of a bridge, which a train 130 metres long travelling at 45 km an hour, can cross in 30 seconds?

Accepted Answer

Speed of the train = 45 km/hr = 45 x (5/18) = 25/2 m/sec Let the length of the bridge be L metres ∴ (L + 130) / (25/2) = 30 ⇒ L + 130 = 15 x 25 L = 375 - 130 = 245 metres

Question 10

A column of men, extending 250 metres in length takes one hour to march through a street at the rate of 50 paces a minute, each pace being 75 cm. Find the length of the street?

Accepted Answer

Speed of the column of men = (50 x 75) / (100 x 60) = 5/8 m/sec. Let the length of the street be L metres ∵ (L + 250) = (60 x 60 x 5) / 8 = 2250 metres ⇒ L = (2250 - 250) m ∴ L = 2000 m = 2 km.

Question 11

A train 540 m long is running with a speed of 72 km/hr. In what time it pass a tunnel 160 m long?

Accepted Answer

∵ Speed of the train = 72 km/hr = 72 x (5/18) = 20 m/sec. Sum of the length of the train and tunnel = 540 + 160 = 700 metres. ∴ Required time taken to pass the tunnel = Time taken to cover 700 metres at 20 m/sec. = 700/20 = 35 sec.

Question 12

A train 200 m long is running with a speed of 72 km/hr. In what time will it pass a platform 160 m long?

Accepted Answer

Distance covered = 200 + 160 = 360. Speed of train = 72 km = 72 x (5/18) = 20 sec. Time = 360 / 20 = 18 sec.

Question 13

A train 150 m long passes a telegraphs post in 12 seconds. Find in what time, it will pass a bridge 250 m long?

Accepted Answer

∵ Speed of the train = 150/12 m/sec. Required time taken to cross the bridge = [(150 + 250) x (12/150)] = 32 sec.

Question 14

A train 280 m long is moving at a speed of 60 km/hr. The time taken by the train to cross a platform 220 m long is?

Accepted Answer

Distance covered = 220 + 280 = 500 = 0.5 km Speed = 60 kmph. Time taken = 0.5 / 60 hr = (0.5 x 60 x 60)/60 sec = 30 sec

Question 15

A train 700 m long is running at the speed of 72 km/hr. If it cross a tunnel in 1 minute, then the length of the tunnel?

Accepted Answer

length of tunnel + length of train = distances covered by train in 1 min ⇒ length of tunnel + 700 = 72/60 km = 1.2 km = 1200 m ∴ length of tunnel = 1200 - 700 = 500 m

Question 16

A train with 90 km/hr crosses a bridge in 36 seconds. Another train 100 m shorter crosses the same bridge at 45 km/hr. Find the time taken by the second train to cross the bridge?

Accepted Answer

Speed of the first train = 90 km/hr = 90 x (5/18) m/sec. = 25 m/sec Let the length of the train and bridge be L metre. ∴ L = 25 x 36 = 900 m.....(1) Again Speed of the second train = 45 km/hr = 45 x (5/18) = 25/2 m/sec. Now, putting the value from eqn. (1) we have Time taken = (900 - 100) x 2/25 = 800 x 2/25 = 64 sec

Question 17

Two trains 132 metres and 108 metres in length are running towards each other on parallel lines. One at the rate of 32 km/hr and another at 40 km/hr. In what time will they be clear of each other from the moment they meet?

Accepted Answer

Relative speed of the train = (32 + 40) = 72 km/hr = 72 x 5/18 = 20 m/sec. Sum of length of the train = 132 + 108 = 240 m time taken by the trains in passing each other = 240/20 = 12 sec .

Question 18

A train 700 m long is running at the speed of 72 km per hour. If it crosses a tunnel in 1 minute, then the length of the tunnel is?

Accepted Answer

Speed of the train = 72 x (5/18) = 20 m/sec Let the length of tunnel = L meters Then, (700 + L )/ 60 = 20 ⇒ 700 + L = 1200 ∴ L = 500 meters

Question 19

A trains 100 meters long, running at 36 kmph takes 25 second to pass a bridge. The length of the bridge is?

Accepted Answer

Speed = 36 x (5/18) = 10 m/sec Let the length of the bridge = L m Distance covered = (100 + L) m Time taken = 25 sec ∵ (100 + L ) / 25 = 10 m/sec ⇒ 100 + L = 250 ∴ L = 150 meter

Question 20

A train travelling at 48 km/h completely crosses an another train having half length of first train and travelling in opposite directions at 42 km/h in 12 s. It also passes a railways platform in 45 s . The length of the platform is?

Accepted Answer

Let the length of the first train be x m. Then, the length of second train is (x/2) m ∴ Relative speed = (48 + 42) km/h = (90 x 5/18) m/s = 25 m/s According to the question. (x + x/2) / 25 = 12 ⇒ 3x/2 = 300 ⇒ x = 200 m ∴ Length of first train = 200 m Let the length of platform be y m . Speed of the first train = (48 x 5/18) m/s = 40/3 m/s Time = Distance / Speed ∴ (200 + y) x 3/40 = 45 ⇒ 600 + 3y = 1800 ∴ y = 400 m

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