Question 1

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

Accepted Answer

Given Data Time to pass a pole = 15 s Time to pass a 100 m platform = 25 s Required: train length Step 1: Speed from pole crossingLet train length = L m. Speed v = L ÷ 15 m/s Step 2: Use platform crossing25 = (L + 100) ÷ v = (L + 100) ÷ (L/15)⇒ 25L = 15L + 1500 ⇒ 10L = 1500 ⇒ L = 150 m Checks & Common Pitfalls For a pole, use only train length to get speed. For a platform, add train and platform lengths. Final AnswerThe train length is 150 m.

Question 2

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

Accepted Answer

Given Data Jogger is 240 m ahead of the engine Train length = 120 m Speeds: train = 45 km/hr, jogger = 9 km/hr, same direction Required: time for the train to pass the jogger completely Step 1: Relative speedvrel = 45 − 9 = 36 km/hr = 36 × (5/18) = 10 m/s Step 2: Relative distance to coverGap to cover = 240 m + train length 120 m = 360 mt = 360 ÷ 10 = 36 s Checks & Common Pitfalls Add gap + train length for complete passing. Final AnswerThe train passes the jogger in 36 s.

Question 3

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

Given Data Passing a post in 8 s Passing a 264 m bridge in 20 s Required: train speed (km/hr) Step 1: Let length = L and speed = v m/sFrom post: L ÷ v = 8 ⇒ L = 8v Step 2: Use bridge crossing(L + 264) ÷ v = 20 ⇒ (8v + 264)/v = 208 + 264/v = 20 ⇒ v = 22 m/s Step 3: Convert to km/hr22 × (18/5) = 79.20 km/hr Final AnswerSpeed of the train is 79.20 km/hr.

Question 4

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

Given Data Train A length = 270 m; speed = 120 km/hr Train B speed = 80 km/hr; length = ? Opposite directions; crossing time = 9 s Step 1: Relative speedvrel = 120 + 80 = 200 km/hr = 200 × (5/18) = 55.5556 m/s Step 2: Distance = speed × time(270 + L) = 55.5556 × 9 = 500 ⇒ L = 230 m Final AnswerOther train's length is 230 m.

Question 5

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

Accepted Answer

Given Data Train length = 110 m Train speed = 60 km/hr Man runs at 6 km/hr in opposite direction Step 1: Relative speed (opposite)vrel = 60 + 6 = 66 km/hr = 66 × (5/18) = 18.3333 m/s Step 2: Time to cross the mant = distance ÷ speed = 110 ÷ 18.3333 = 6 s Final AnswerThe train passes the man in 6 s.

Question 6

Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

Accepted Answer

Given Data Speeds = 60 km/hr and 90 km/hr (opposite directions) Lengths = 1.10 km and 0.90 km Step 1: Relative speed & distancevrel = 60 + 90 = 150 km/hrDistance to cross = 1.10 + 0.90 = 2.00 km Step 2: Timet (hours) = 2.00 ÷ 150 = 1/75 ht (seconds) = (1/75) × 3600 = 48 s Final AnswerTime taken = 48 s.

Question 7

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

Given Data Train speed = 72 km/hr Platform length = 250 m Time to cross platform = 26 s Step 1: Convert speed72 × (5/18) = 20 m/s Step 2: Total distance while crossingDistance = 20 × 26 = 520 mTrain length = 520 − 250 = 270 m Final AnswerLength of goods train = 270 m.

Question 8

Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

Accepted Answer

Given Data Equal train lengths = 120 m each Times to pass a post: 10 s and 15 s Step 1: Find individual speedsv1 = 120/10 = 12 m/sv2 = 120/15 = 8 m/s Step 2: Cross each other in opposite directionsRelative speed = 12 + 8 = 20 m/sDistance = 120 + 120 = 240 mt = 240 ÷ 20 = 12 s Final AnswerThey will cross in 12 s.

Question 9

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

Accepted Answer

Given Data Distance AB = 110 km A→B train: 20 km/hr starting 7 a.m. B→A train: 25 km/hr starting 8 a.m. Step 1: Staggered startBy 8 a.m., A→B train covers 20 × 1 = 20 km.Remaining distance at 8 a.m. = 110 − 20 = 90 km. Step 2: Relative speed towards each othervrel = 20 + 25 = 45 km/hrTime after 8 a.m. = 90 ÷ 45 = 2 h Final AnswerMeet at 10:00 a.m.

Question 10

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

Accepted Answer

Given Train A speed = 48 km/h Train B speed = 42 km/h (opposite direction) Train B length = half of Train A Two trains completely cross in 12 s Train A crosses a platform in 45 s Step 1: Find Train A's lengthRelative speed (opposite) = (48 + 42) km/h = 90 km/h = 90 × (5/18) = 25 m/sTotal distance when two trains cross = L + L/2 = 1.5L1.5L = 25 × 12 = 300 ⇒ L = 300/1.5 = 200 m Step 2: Find platform lengthSpeed of Train A = 48 × (5/18) = 13.333… m/sDistance in 45 s while crossing platform = 13.333… × 45 = 600 mL + Platform = 600 ⇒ Platform = 600 − 200 = 400 m Notes When crossing a platform, add train and platform lengths. Always convert km/h to m/s by × 5/18.

Question 11

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

Accepted Answer

Given Speed = 60 km/h Time to cross a pole = 9 s Compute lengthConvert speed: 60 × (5/18) = 16.6667 m/sLength = speed × time = 16.6667 × 9 = 150 m Tip: Crossing a pole means distance equals train length only.

Question 12

A train travelling at a speed of 75 mph enters a tunnel 3½ miles long. The train is ¼ 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

Given Speed = 75 mph Tunnel length = 3.5 miles Train length = 0.25 mile Total distance to clear tunnelDistance = 3.5 + 0.25 = 3.75 milesTime (hours) = 3.75 / 75 = 0.05 hTime (minutes) = 0.05 × 60 = 3 minutes Note: Add train length to tunnel length for full clearance.

Question 13

Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

Accepted Answer

Given Equal lengths = L (each) Speeds = 46 km/h and 36 km/h (same direction) Overtake time = 36 s ComputeRelative speed = (46 − 36) km/h = 10 km/h = 10 × (5/18) = 2.7778 m/sDistance to overtake = L + L = 2L2L = 2.7778 × 36 = 100 ⇒ L = 50 m

Question 14

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

Given Lengths = 140 m & 160 m Speeds = 60 km/h & 40 km/h (opposite) ComputeRelative speed = (60 + 40) km/h = 100 km/h = 100 × (5/18) = 27.7778 m/sTotal distance = 140 + 160 = 300 mTime = 300 / 27.7778 = 10.8 s

Question 15

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

Accepted Answer

Given Train length = 130 m Speed = 45 km/h Total crossing time = 30 s ComputeSpeed = 45 × (5/18) = 12.5 m/sTotal distance = 12.5 × 30 = 375 m = train + bridgeBridge = 375 − 130 = 245 m

Question 16

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Accepted Answer

Given Speed = 54 km/h Time past a man = 20 s Time past a platform = 36 s Step 1: Train lengthSpeed = 54 × (5/18) = 15 m/sTrain length L = 15 × 20 = 300 m Step 2: Platform lengthTotal distance in 36 s = 15 × 36 = 540 mPlatform = 540 − 300 = 240 m

Question 17

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

Accepted Answer

Given Train 1 passes a man in 27 s Train 2 passes a man in 17 s They cross each other in 23 s (opposite) Let speeds be v1, v2 (m/s)Lengths: l1 = v1 × 27, l2 = v2 × 17Crossing: (l1 + l2)/(v1 + v2) = 23⇒ 27v1 + 17v2 = 23v1 + 23v2⇒ 4v1 = 6v2 ⇒ v1/v2 = 3:2

Question 18

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

Accepted Answer

Given Train length = 360 m Bridge length = 140 m Speed = 45 km/h ComputeSpeed = 45 × (5/18) = 12.5 m/sTotal distance = 360 + 140 = 500 mTime = 500 / 12.5 = 40 s

Question 19

A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

Accepted Answer

Given Train length = 240 m Time to pass a pole = 24 s ⇒ speed Platform length = 650 m Step 1: Find speedSpeed = distance/time = 240 / 24 = 10 m/s Step 2: Time to pass platformTotal distance = 240 + 650 = 890 mTime = 890 / 10 = 89 s Tip: For platforms, add train and platform lengths.

Question 20

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

Given Two pedestrians walk in the same direction at 2 km/h and 4 km/h. The train completely overtakes them in 9 s and 10 s respectively. Let the train's speed be v km/h and its length be L metres. Relative-speed methodWhen overtaking the 2 km/h walker: L = (v − 2) × (5/18) × 9 = (5/2)(v − 2)When overtaking the 4 km/h walker: L = (v − 4) × (5/18) × 10 = (25/9)(v − 4)Equate: (5/2)(v − 2) = (25/9)(v − 4)⇒ 9(v − 2) = 10(v − 4) ⇒ v = 22 km/hNow L = (5/2)(22 − 2) = 50 m Final Answer:The train's length is 50 m.

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