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

Two trains are running on parallel track in opposite direction at the speed of 54 km./hr. and 72 km./hr. respectively. The first train crosses a pole in 8 seconds and second train crosses the pole in 15 seconds. In what time will they cross each other ? दो ट्रेन समान्तर पटरियों पर विपरीत दिशा में क्रमशः 54 किमी./घं. और 72 किमी./घं. की चाल से चल रही है। पहली ट्रेन एक पोल को 8 सेकेण्ड में और दूसरी ट्रेन पोल को 15 सेकेण्ड में पार करती है। वे एक दूसरे को कितने समय में पार करेंगी?

  1. 17 sec/सेकेण्ड

  2. 13 sec/सेकेण्ड

  3. 15 sec/सेकेण्ड

  4. 12 sec/सेकेण्ड

  5. 19 sec/सेकेण्ड
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First train length = 54 × (5/18) × 8 = 120 m. Second train length = 72 × (5/18) × 15 = 300 m. Total length = 420 m. Relative speed (opposite direction) = 54 + 72 = 126 km/hr = 126 × (5/18) = 35 m/s. Time to cross each other = 420/35 = 12 seconds. Option D is correct.

Multiple choice

Two trains A and B start simultaneously towards each other from two cities stations. After crossing each other, trains take 16 and 9 hours more respectively to reach their destinations. If the speed of first train is 90 km/hr, find the speed of second train.

  1. 100 km/hr

  2. 120 km/hr

  3. 90 km/hr

  4. cannot be determined

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

After crossing, if trains take t1 and t2 hours to reach destinations, speed ratio is √t2 : √t1. Here t1 = 16, t2 = 9. So v1 : v2 = √9 : √16 = 3 : 4. Given v1 = 90 km/hr, then v2 = (4/3) × 90 = 120 km/hr.

Multiple choice

A train travelling at 72 km/hr. crosses a platform of 160 m in 18 second and another train travelling at 90 km/hr crosses the same platform in 15 second. Find the length of another train? 72 किमी / घंटा की यात्रा करने वाली ट्रेन 18 सेकंड में 160 मीटर का एक प्लेटफॉर्म को और 90 किमी / घंटा की यात्रा करने वाली एक अन्य ट्रेन 15 सेकंड में समान प्लेटफार्म को पार करती है। दूसरी ट्रेन की लंबाई ज्ञात कीजिये?

  1. 160 m

  2. 180 m

  3. 140 m

  4. 200 m

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

Train 1: 72 km/hr = 20 m/s. In 18 seconds, distance = 360 m. Length of train 1 = 360 - 160 = 200 m. Train 2: 90 km/hr = 25 m/s. In 15 seconds, distance = 375 m. Length of train 2 = 375 - 160 = 215 m. The question asks for the length of the other train (215 m), which is not listed in options A-D. Hence, option E is correct.

Multiple choice

Two trains 137m and 163m in lengths are running towards each other on parallel lines, one at the rate of 42 km/h and another at 48 km/h. In what time will they be clear of each other from the moment they meet? दो ट्रैन जिनकी लम्बाई 137 मीटर और 163 मीटर है,समान्तर रेखा में विपरीत दिशा में चल रही है। यदि इनकी चाल 42किमी/घंटा और 48किमी/प्रति घंटा हो तब वह एक दूसरे को कितनी देर में पार करेंगी ?

  1. 10 sec

  2. 12 sec

  3. 14 sec

  4. 15 sec

  5. 16 sec
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance to be covered = sum of train lengths = 137 + 163 = 300 m. Relative speed when moving towards each other = 42 + 48 = 90 km/hr = 90 × 5/18 = 25 m/s. Time = Distance/Speed = 300/25 = 12 seconds. The trains will be clear of each other in 12 seconds from the moment they meet.

Multiple choice

The ratio of the speed of two trains is 5:8. Sum of their length is 660. The ratio of time taken to cross an Electric Pole by train A and B is 4:3. What is the difference between the lengths of two trains? दो ट्रेनों की गति का अनुपात 5: 8 है। उनकी लंबाई का योग 660 है। ट्रेन A और B द्वारा इलेक्ट्रिक पोल को पार करने में लगने वाले समय का अनुपात 4: 3 है। दो ट्रेनों की लंबाई में क्या अंतर है?

  1. 58

  2. 60

  3. 62

  4. 68

  5. 72
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Speed ratio 5:8, time ratio 4:3 for crossing a pole (distance = length). Length = speed × time. Length ratio = (5×4):(8×3) = 20:24 = 5:6. Parts sum to 11, total length 660, so parts are 60 each. Lengths are 300 and 360. Difference = 60.

Multiple choice

A train can cross a platform of equal length in 5 minutes. It can cross a man running in the direction of the train with the speed of 2m/s in 7 minutes. Find the speed of the train (in km/h) ? एक ट्रेन 5 मिनट में बराबर लंबाई के प्लेटफॉर्म को पार कर सकती है। यह ट्रेन की दिशा में चलने वाले एक आदमी को 7 मिनट में 2 मी / सेकेंड की गति से पार कर सकता है। ट्रेन की गति ज्ञात कीजिये (किमी / घंटा में)?

  1. 10.8

  2. 25

  3. 7

  4. 11.2

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

Let train length = L, speed = v. For platform: 2L = v × 300 sec (5 min). For man: L = (v-2) × 420 sec (7 min). From first: L = 150v. Substitute: 150v = (v-2) × 420, so 150v = 420v - 840, giving 270v = 840, v = 28/9 m/s. In km/h: (28/9) × 3.6 = 11.2 km/h. Answer D is correct.

Multiple choice

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 8 and 9 seconds respectively. The speed of the train is:

  1. 35 km/hr

  2. 45 km/hr

  3. 20 km/hr

  4. data inadequate

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

Let train length = L meters, speed = v kmph. Speed in m/s = v × 5/18. Overtaking person at 2kmph: relative speed = (v-2) × 5/18 m/s. Time = 8s, so L = 8(v-2)(5/18). Overtaking person at 4kmph: relative speed = (v-4) × 5/18 m/s. Time = 9s, so L = 9(v-4)(5/18). Equating: 8(v-2) = 9(v-4), giving 8v - 16 = 9v - 36, so v = 20 kmph.

Multiple choice

Two trains (137\text{m}) and (163\text{m}) in lengths are running towards each other on parallel lines, one at the rate of (42\text{ km/h}) and another at (48\text{ km/h}). In what time will they be cross each other from the moment they meet?

  1. 10 sec

  2. 12 sec

  3. 14 sec

  4. 15 sec

  5. 16 sec
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance to cross = 137 + 163 = 300 m. Relative speed = 42 + 48 = 90 km/hr = 90 × 5/18 = 25 m/s. Time = 300/25 = 12 seconds. This matches option B exactly.

Multiple choice

Train A crosses a tower with a speed of 86.4 km/h in ‘t’ seconds while another train B crosses a platform of 80 m length in ‘2t’ seconds with a speed of 108 km/h. If train B is 100% more in length than that of train A then find the length of train B?

  1. 300 m

  2. 400 m

  3. 360 m

  4. 280 m

  5. 320 m
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Train A: speed = 86.4 km/h = 24 m/s. Length = LA, crosses tower in t seconds, so LA = 24t. Train B: speed = 108 km/h = 30 m/s, length LB = 2LA (100% more), crosses 80m platform in 2t seconds. So LB + 80 = 30 × 2t = 60t. Substituting LB = 2LA = 2 × 24t = 48t: 48t + 80 = 60t, giving 12t = 80, so t = 20/3. Then LB = 48 × (20/3) = 320m. Option E is correct.

Multiple choice

Study the following information carefully and give the answer of the following questions. Train M of length 150 meters moving at 54 kmph and train U of length 250 metres moving at 90 kmph running on parallel track enter a 300-metre long tunnel at the same instant from opposite direction. Which train exist the tunnel first and at the moments it exists, what length of the other train is still in the tunnel?

  1. M, 120

  2. U, 130

  3. U, 120

  4. M, 130

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

Train M: 150m at 54 kmph = 15 m/s. Train U: 250m at 90 kmph = 25 m/s. Tunnel length: 300m. Time for M to exit tunnel = (150+300)/15 = 450/15 = 30s. Time for U to exit tunnel = (250+300)/25 = 550/25 = 22s. So U exits first. At 22s, M has traveled: 22 × 15 = 330m. M's tail (end) has entered the tunnel at: 330 - 150 = 180m from tunnel entrance. Tunnel length remaining for M: 300 - 180 = 120m. Therefore, when U exits, 120m of M is still in the tunnel. Answer C (U, 120) is correct.

Multiple choice

Study the following information carefully and give the answer of the following questions. Train M of length 150 meters moving at 54 kmph and train U of length 250 metres moving at 90 kmph running on parallel track enter a 300-metre long tunnel at the same instant from opposite direction. How much percent speed of the faster train will be decreased so that they crossed the tunnel same time?

  1. 26(2/3)%

  2. 16(2/3)%

  3. 20(2/3)%

  4. 26%

  5. 18%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For trains to exit simultaneously, their effective crossing times must equalize. With original speeds 54 and 90 kmph, times are 8.33s and 4.44s. Setting 300/(v+54) = 300/90 and solving gives new speed v = 66 kmph, requiring reduction of 24 kmph, which is 26(2/3)% of 90.