Quantitative Aptitude

Problems on Trains

989 Questions
All Passing a moving person or another train 430 Crossing a platform or bridge 379 Crossing a pole or stationary person 104 Meeting point and post-meeting times 52 Journey time, reduced speed, and schedule conditions 24

Problems on Trains Questions

Multiple choice

What is the speed of a train? I. The train crosses a telephone pole in 30 sec. II. The train crosses a bridge of 200 m. length in 40 sec.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement I gives length/time but not actual length or speed. Statement II gives bridge length and time but not train length. Neither alone is sufficient. Together: length = speed×30, and length+200 = speed×40. Solving gives speed = 20 m/s. Both needed, so E is correct.

Multiple choice

If a train of length 650 m long is running at the speed of 72 km/h, crosses a bridge in 1 minute 15 second, then what is the length of the bridge? यदि एक 650 मी. लम्बी ट्रेन 72 किमी/घंटे की चाल से चलते हुए, एक पुल को 1 मिनट 15 सेकंड में पार करती है, तो पुल की लम्बाई कितनी है?

  1. 750 m/मी.

  2. 550 m/मी.

  3. 850 m/मी.

  4. 1250 m/मी.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed = 72 km/h = 72 × 5/18 = 20 m/s. Time = 1 min 15 sec = 75 seconds. Distance covered = speed × time = 20 × 75 = 1500 m. This distance = train length + bridge length. So bridge length = 1500 - 650 = 850 m.

Multiple choice

What is the speed of the train? I. Ratio of length of the train and length of platform is 2:3. II. The train crosses a pole in 24 seconds. III. The train crosses a platform in 60 seconds.

  1. Any two

  2. I and II

  3. II and III

  4. All three together are sufficient

  5. None of these
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement II gives length of train if we know speed. Statement III gives (train length + platform length) if we know speed. Statement I relates train and platform lengths. With all three: let train length = 2x, platform = 3x. From II: train crosses pole in 24s, so speed = 2x/24. From III: crosses platform in 60s, so (2x + 3x) = speed × 60, giving 5x = (2x/24) × 60, which solves. None of the partial combinations work.

Multiple choice

Two trains are running 60 km/h and 45 km/h respectively, in the same direction. The faster train completely passes a man sitting in the slower train in 30 sec. then find the length of the faster train? दो ट्रेन क्रमशः 60 किमी/घंटा और 45 किमी/घंटा की गति से एक ही दिशा में चल रही हैं। तेज गति से चलने वाली ट्रेन, धीमी चलने वाली ट्रेन में बैठे एक व्यक्ति से पूरी तरह से 30 सेकेंड में पार कर जाती है। तेज गति से चलने वाली ट्रेन की लंबाई क्या है?

  1. 225 m/ मीटर

  2. 125 m/ मीटर

  3. 1225 m/ मीटर

  4. 250 m/ मीटर
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed of faster train with respect to man in slower train = 60 - 45 = 15 km/h = 15 × 5/18 = 25/6 m/s. Time taken to pass = 30 seconds. Length of faster train = Relative speed × Time = (25/6) × 30 = 125 m. The man in the slower train is stationary relative to that train, so only the relative speed matters. Option B matches this result.

Multiple choice

A man standing on a platform find that a train takes 4 sec. to pass and another train take 5 sec. to cross the man. If the ratio of length of train is 2 : 3 then find the ratio of speed of both train ? एक ट्रेन प्लेटफार्म पर खड़े व्यक्ति को 4 से. में पार करती है तथा दूसरी ट्रेन व्यक्ति को 5 से. में पार करती है। यदि दोनों ट्रेनों की लम्बाई का अनुपात 2 : 3 है। तो उनकी चालों का अनुपात ज्ञात कीजिए।

  1. 4 : 5

  2. 2 : 3

  3. 5 : 6

  4. Can't be determined/तय नहीं कर सकते
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let lengths be 2x and 3x. Speeds are 2x/4 and 3x/5. Ratio = (2x/4):(3x/5) = (1/2):(3/5) = 5:6. Option C is correct assuming the question means the trains cross the man (not platform).

Multiple choice

A train travelling with uniform speed crosses two bridges of lengths 600 m and 900 m in 45 seconds and 60 seconds respectively. What is the speed of the train? एक ट्रेन एकसमान चाल से चलते हुए 600 मी. और 900 मी. लम्बे पुल को क्रमश: 45 सेकेण्ड और 60 सेकेण्ड में पार करती है। ट्रेन की चाल कितनी है ?

  1. 36 km/hr / किमी./ घंटा

  2. 54 km/hr / किमी./ घंटा

  3. 72 km/hr / किमी./ घंटा

  4. 48 km/hr / किमी./ घंटा
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The train's speed can be found by noting that in the additional 15 seconds (60-45), it travels the extra 300 meters of bridge length (900-600). This gives speed = 300/15 = 20 m/s. Converting to km/hr: 20 × 18/5 = 72 km/hr. Alternatively, total distance = 1500m in 105 seconds, giving the same result.

Multiple choice

Two trains are running at 60 km/hr and 90 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 18 seconds. What is the length of the slower train?

  1. 150 m.

  2. 200 m.

  3. 300 m

  4. Can't be determine.

  5. None of these.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relative speed of fast train with respect to slow train = 90-60 = 30 km/hr = 30×5/18 = 25/3 m/s. In 18 seconds, distance covered = (25/3)×18 = 150 m. This is the length of the FAST train. The question asks for the length of the SLOWER train, which is not provided in the problem.

Multiple choice

Find the value of Q1, Q2 and state the correct relationship-\newline Find speed of train-\newline Q1-Train 115 meter long crosses a pole in 19 second.\newline Q2-Another train 152 meter long crosses a platform 100 meter long in 42 seconds.
  1. $Q1 > Q2$
  2. $Q1 \ge Q2$
  3. $Q1 < Q2$
  4. $Q1 \le Q2$
  5. $Q1 = Q2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For Q1: Speed = Distance/Time = 115/19 ≈ 6.05 m/s. For Q2: Total distance = Train length + Platform length = 152 + 100 = 252 m. Speed = 252/42 = 6 m/s. Therefore Q1 ≈ 6.05 m/s > Q2 = 6 m/s. The relationship Q1 > Q2 is correct.

Multiple choice

Two trains having lengths in the ratio 3 : 4 and the speeds of both trains are in the ratio of 5 : 6 respectively. Find the ratio of the time taken by them to cross a pole? दो रेलगाड़ियों के लंबाई का अनुपात 3: 4 और उनकी चाल का अनुपात 5: 6 है । एक खम्भे को पार करने के लिए उनके द्वारा लिये गये समय का अनुपात क्या है?

  1. 5 : 8

  2. 8 : 5

  3. 9 : 10

  4. 5 : 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Time to cross a pole = Length/Speed. If lengths are 3x, 4x and speeds are 5y, 6y, then times are (3x/5y) and (4x/6y) = (2x/3y). Ratio of times = (3x/5y) : (2x/3y) = 9:10.

Multiple choice

If a train of length 550 m long is running at the speed of 72 km/h, crosses a bridge in 1 minute 25 second, then what is the length of the bridge? यदि एक 550 मी. लम्बी ट्रेन 72 किमी/घंटे की चाल से चलते हुए, एक पुल को 1 मिनट 25 सेकंड में पार करती है, तो पुल की लम्बाई कितनी है?

  1. 950 m

  2. 1150 m

  3. 1250 m

  4. 1050 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Speed = 72 km/h = 72 × (5/18) = 20 m/s. Time = 1 minute 25 seconds = 85 seconds. Total distance covered = speed × time = 20 × 85 = 1700 m. This distance equals train length + bridge length. So bridge length = 1700 - 550 = 1150 m. Standard train-distance problem.

Multiple choice

The speed of two train in the ratio of 7 : 3. They are running in the same direction along the parallel tracks. If each crosses a pole in 12 second. Find the time in which fast train will cross the slower train completely? दो रेलगाड़ियों की चाल का अनुपात 7 रू 3 है। दोनों रेलगाड़ियाँ समान दिशा में चल रही है। प्रत्येक रेलगाड़ी एक खम्भे को 12 सेकेण्ड में पार करती है तो वह समय ज्ञात कीजिए जिसमें तेज रेलगाड़ी धीमी रेलगाड़ी को पूर्णतया पार करेगी।

  1. 45 sec/सेकेण्ड

  2. 21 sec/सेकेण्ड

  3. 20 sec/सेकेण्ड

  4. 30 sec/सेकेण्ड
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Speeds are 7v and 3v. Lengths are both 12v from pole-crossing. Fast train crosses slow train: distance = sum of lengths = 24v, relative speed = 7v - 3v = 4v. Time = 24v/4v = 30 seconds. This uses the relative speed concept for objects moving in same direction.

Multiple choice

By running at 87.5% of its usual speed a train crosses a pole in 36 seconds. By running its usual speed it crosses a 500 meter long platform in 54 seconds. Find the length of train. अपनी वास्तविक चाल के 87.5% पर चलते हुये एक रेलगाड़ी एक खम्भे को 36 सेकेण्ड में पार करती है। अपनी वास्तविक चाल से चलते हुये रेलगाड़ी 500 मीटर लम्बे प्लेटफार्म को 54 सेकेण्ड में पार करती है। रेलगाड़ी की लम्बाई ज्ञात कीजिये।

  1. 500 m/मी.

  2. 700 m/मी.

  3. 300 m/मी.

  4. 400 m/मी.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let usual speed be v m/s and train length be L. At 87.5% speed (7v/8): L = (7v/8)×36 = 31.5v. At usual speed crossing 500m platform: L+500 = v×54 = 54v. Substituting: 31.5v + 500 = 54v, so 500 = 22.5v, v = 500/22.5 = 200/9 m/s. Then L = 31.5×(200/9) = 31.5×22.22 = 700m. The train length is 700 meters.