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

The following questions are accompanied by three statements (A), (B), and (C). You have to determine which statement(s) is/are sufficient/necessary to answer the questions. A train crosses another train in 10 sec. Find out the lengths of the trains. A. Ratio between the lengths of the second and first train is 4: 5. B. Ratio between the speed of first and second trains is 1: 2. C. The speed of first train is 36 km/hr निम्नलिखित प्रश्न तीन कथन (A), (B), और (C) के साथ हैं। आपको यह निर्धारित करना होगा कि प्रश्नों का उत्तर देने के लिए कौन सा कथन पर्याप्त / आवश्यक है। एक ट्रेन 10 सेकंड में एक अन्य ट्रेन पार करती है। ट्रेनों की लंबाई ज्ञात कीजिये । A. दूसरी और पहली ट्रेन की लंबाई के बीच अनुपात 4: 5 है । B. पहली और दूसरी ट्रेनों की गति के बीच अनुपात 1: 2 है । C. पहली ट्रेन की गति 36 किमी / घंटा है ।

  1. Only A and B together केवल A और B एक साथ

  2. Only B and C together केवल B और C एक साथ

  3. Only A and C together केवल A और C एक साथ

  4. Questions can’t be answered even after using all the information सभी जानकारी का उपयोग करने के बाद भी सवालों का जवाब नहीं दिया जा सकता है

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

For two trains crossing in 10 seconds, we need (L1 + L2)/(relative speed) = 10. Statement A gives L2:L1 = 4:5, so L2 = 4k, L1 = 5k, and total = 9k. Statement B gives speed ratio S1:S2 = 1:2. Statement C gives S1 = 36 km/hr = 10 m/s, so S2 = 20 m/s. But we don't know if they're moving in same or opposite direction, affecting relative speed. Even with all info, we have two unknowns (direction and the value of k) with insufficient constraints.

Multiple choice

The question given below contains two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Mark answer- नीचे दिए गए प्रश्नों में दो कथनों के माध्यम से कुछ जानकारियां दी गई हैं आपको यह निर्णय करना है कि क्या कथनो में दी गई जानकारी उत्तर देने के लिए पर्याप्त है। उत्तर दीजिए- Find the time taken by Rakesh to cross a platform- एक प्लेटफॉर्म पार करने में राकेश द्वारा लिया गया समय ज्ञात कीजिये- I- A train moving with 48 Km/h cross a platform in 60 seconds. II-Rakesh running at 8 Km/h opposite in the direction of train crosses it in 24 seconds. I-एक ट्रेन 48 किमी / घंटा के साथ चलती हुई एक प्लेटफॉर्म को 60 सेकंड में पार करती है । II-राकेश ट्रेन की विपरीत दिशा में 8 किमी / घंटा की चाल से दौड़ते हुए इसे 24 सेकंड में पार करता है।

  1. Only I केवल I

  2. Only II केवल II

  3. Either I or II या तो I अथवा II

  4. Both together are sufficient दोनों एक साथ पर्याप्त हैं

  5. Both together are not sufficient दोनों एक साथ पर्याप्त नहीं है
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives: Train speed = 48 km/h = 48 × (5/18) = 40/3 m/s. Time to cross platform = 60 sec. So train length + platform length = (40/3) × 60 = 800 m. But we can't separate platform length from train length. INSUFFICIENT alone. Statement II gives: Rakesh's speed = 8 km/h = 20/9 m/s. He runs opposite to train, crosses it in 24 sec. Relative speed = train speed + Rakesh's speed = 40/3 + 20/9 = 140/9 m/s. Train length = (140/9) × 24 = 373.33... m. This gives train length but NOT platform length. INSUFFICIENT alone. COMBINING: From II, train ≈ 373.33 m. From I, train + platform = 800 m. So platform = 800 - 373.33 = 426.67 m. Now we can find time to cross platform: distance = platform + train = 800 m, Rakesh's speed = 20/9 m/s, time = 800 / (20/9) = 360 sec. Both statements TOGETHER are sufficient. Answer D is correct.

Multiple choice

The following questions are accompanied by three statement I, II and III. You have to determine which statement (s) is/are necessary/sufficient to answer the question. निम्नलिखित प्रत्येक प्रश्न में तीन कथन I, II और III दिये गये हैं। आपको यह पता लगाना है कि कौन सा/से कथन प्रश्न का उत्तर देने के लिए पर्याप्त है। At what time will the train reach point X from point Y? ट्रेन किस समय बिंदु Y से बिंदु X पर पहुंच जाएगी? I. The train crosses another train of equal distance of 250 m in 25 sec. running opposite direction. II. The train of 250 m crosses a signal pole in 10 sec. III. The distance between point X and point Y is 360 km. I. ट्रेन विपरीत दिशा में चल रही 250 मीटर की समान लम्बाई की एक और ट्रेन को 25 सेकंड में पार करती है। II. 250 मीटर की ट्रेन 10 सेकंड में एक सिग्नल के खम्भे को पार करती है। III. बिंदु X और बिंदु Y के बीच की दूरी 360 किमी है।

  1. None of these इनमें से कोई नहीं

  2. II and III together are sufficient II तथा III पर्याप्त हैं

  3. III and (I or II are sufficient) III तथा (I या II) पर्याप्त हैं

  4. All three together are sufficient तीनो एक साथ पर्याप्त हैं

  5. All three together are not sufficient तीनो एक साथ भी पर्याप्त नहीं हैं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II gives the train's length (250m) and time to cross a pole (10s), so speed = 250/10 = 25 m/s. Statement III gives the distance (360 km = 360000 m). With speed and distance, time = 360000/25 = 14400 seconds = 4 hours. However, the question asks 'at what time' will the train reach, which requires knowing the departure time - none of the statements give this. II and III give travel duration but not arrival time.

Multiple choice

The following questions are accompanied by three statement I, II and III. You have to determine which statement (s) is/are necessary/sufficient to answer the question. निम्नलिखित प्रत्येक प्रश्न में तीन कथन I, II और III दिये गये हैं। आपको यह पता लगाना है कि कौन सा/से कथन प्रश्न का उत्तर देने के लिए पर्याप्त है। A train crosses another train coming from the opposite direction in 9 sec.If the length of both the train is 100m then what is the speed of other train? एक रेलगाड़ी एक दूसरी रेलगाड़ी को जो विपरीत दिशा से आ रही है, को 9 सेकण्ड में पार करती है। यदि प्रत्येक रेलगाड़ी की लम्बाई 100 मी. हो तो दूसरी रेलगाड़ी की चाल ज्ञात कीजिये। (I) The train passes a platform in 14 sec. (II) The speed of the first train is 90km/hour. (III) The other train passes a pole in 6 sec. (I) रेलगाड़ी प्लेटफार्म को 14 सेकण्ड में पार करती है। (II) पहली रेलगाड़ी की चाल 90 किमी/घं.है। (III) दूसरी रेलगाड़ी एक खम्भे को 6 सेकण्ड में पार करती है।

  1. Only II केवल II

  2. Only III केवल III

  3. Only I केवल I

  4. Either II or III या तो II या III

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

Relative speed = 200m/9s = 80 km/hr (opposite direction). With III alone: Other train passes pole in 6s, so its speed = 100m/6s = 60 km/hr. Since they're opposite direction, first train's speed = 80 - 60 = 20 km/hr. With III alone, we find the other train's speed is 60 km/hr. Option II seems to give inconsistent data.

Multiple choice

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. निम्नलिखित प्रश्नों में, दो समीकरणों के मात्रा I और मात्रा II दिए गए हैं। आपको दोनों समीकरणों को हल करना है और प्रश्न का उत्तर देना है। I-A man can row a distance of 4km upstream in 30 min and returns the same distance in 20 min. How much time will he take to row the same distance in downstream if due to a wind the speed of the current gets doubled? II-A 200 meter long train crosses a 600 meter long bridge in 20 seconds. What time will it take to cross a platform 480 meter long?\ I- एक आदमी 30 मिनट में 4 किमी तक की दूरी बहाव के विपरीत तय कर सकता है और उसी दूरी को 20 मिनट में बहाव के साथ तय कर सकता है। यदि एक हवा के कारण धारा की गति दोगुनी हो जाती है, तो उसे बहाव के साथ समान दूरी तय करने में कितना समय लगेगा? II- 200 मीटर लंबी ट्रेन 600 मीटर लंबे पुल को 20 सेकंड में पार करती है। 480 मीटर लंबे एक प्लेटफॉर्म को पार करने में कितना समय लगेगा?

  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity II > Quantity I मात्रा II > मात्रा I

  4. Quantity II ≥ Quantity I मात्रा II ≥ मात्रा I

  5. Quantity I = Quantity II or Relation cannot be established मात्रा I = मात्रा II या सम्बन्ध स्थापित नहीं किया जा सकता है
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: From upstream (8 km/hr) and downstream (12 km/hr), boat speed = 10 km/hr, current = 2 km/hr. Doubled current = 4 km/hr, new downstream speed = 14 km/hr. Time for 4 km = 4/14 hr ≈ 17.14 min. Quantity II: Train speed = (200+600)m/20s = 40 m/s. Crossing 480m platform = (200+480)m/40m/s = 17s. Quantity I (≈17.14 min) > Quantity II (17s).

Multiple choice

Each of these questions consists of a question followed by informations in three statements. You have to study the question and the statements and decide that information in which of the statement(s) is/are necessary to answer the question. What is the speed of the train? Statement I: The train crosses 150 meters long platform in 45 seconds. Statement II: The train crosses another stationary train of same length in 60 seconds. Statement III: The train crosses a signal pole in 30 seconds. नीचे प्रत्येक प्रश्न में, एक प्रश्न और उसके बाद तीन कथनों में जानकारी दी गई है। आप प्रश्नो और कथनों का अध्ययन कीजिए और यह तय कीजिये कि कौनसा/से कथनों में दी गई जानकारी प्रश्न का उत्तर देने के लिए आवश्यक है/हैं। ट्रेन की गति क्या है? कथन I: यह ट्रेन 45 सेकंड में 150 मीटर लम्बे प्लेटफार्म को पार करती है। कथन II: ट्रेन 60 सेकंड में अपनी लम्बाई के बराबर दूसरी स्थिर ट्रेन को पार करती है। कथन III: ट्रेन एक सिग्नल को 30 सेकंड में पार करती है।

  1. I and III I तथा III

  2. I and either II or III I तथा II या III

  3. Any two कोई भी दो

  4. All three together तीनो एक साथ

  5. All three together are not sufficient तीनो एक साथ भी पर्याप्त नहीं हैं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find train speed, we need train length. Statement I gives platform crossing (train length + 150m in 45s). Statement II gives crossing another train of same length (2 × train length in 60s), so train length = 30m and speed = 1m/s. Statement III gives crossing a signal pole (train length in 30s), so train length = 30m. Statement I alone is insufficient (two variables). II or III alone give train length, but I+II or I+III both give complete solution. Therefore I + (II or III) is correct.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. निम्नलिखित प्रत्येक प्रश्न में दिए गए कथन को पढ़िए और उसके आधार पर मात्रा I और मात्रा II की तुलना कीजिए। A train travelling at 54 kmph crosses a platform in 20 seconds and a man standing on the same platform in 12 seconds Quantity I : length of train Quantity II : : length of platform एक ट्रेन 54 किमी/घंटा की गति से एक प्लेटफॉर्म को 20 सेकंड में पार करती है और उसी प्लेटफॉर्म पर खड़े एक व्यक्ति को 12 सेकंड में पार करती है मात्रा I : ट्रेन की लंबाई। मात्रा II : प्लेटफार्म की लंबाई

  1. Quantity : I > Quantity : II मात्रा : I > मात्रा : II

  2. Quantity : I ≥ Quantity : II मात्रा : I ≥ मात्रा : II

  3. Quantity : I < Quantity : II मात्रा : I < मात्रा : II

  4. Quantity : II ≥ Quantity : I मात्रा : II ≥ मात्रा : I

  5. Quantity I = Quantity II or relation can't be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Speed = 54 km/hr = 54 × 5/18 = 15 m/s. Time to cross man = 12 sec (train length only). Train length = 15 × 12 = 180 m. Time to cross platform = 20 sec. Total distance (train + platform) = 15 × 20 = 300 m. Platform length = 300 - 180 = 120 m. Since 180 > 120, Quantity I > Quantity II.

Multiple choice

A 125 m long train take 25 s to cross a person who is going in the same direction with the speed of 4 km/h. After crossing that person, the train can reach next station in 30 min. How long that person takes to reach that station after being crossed by them? एक 125 मीटर लंबी ट्रेन एक व्यक्ति को पार करने में 25 सेकंड का समय लेती है जो समान दिशा में 4 किमी / घंटा की गति से जा रहा है। उस व्यक्ति को पार करने के बाद, ट्रेन अगले स्टेशन पर 30 मिनट में पहुंच सकती है। वह व्यक्ति उनके द्वारा पार किए जाने के बाद उस स्टेशन तक पहुँचने में कितना समय लेता है?

  1. 2 hr 40 min 2 घंटा 40 मिनट

  2. 2 hr 45 min 2 घंटा 45 मिनट

  3. 1 hr 15 min 1 घंटा 15 मिनट

  4. 1 hr 40 min 1 घंटा 40 मिनट

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

Train length = 125m, time to cross person = 25s. Relative speed (train - person) = 125/25 = 5 m/s = 18 km/h. Person's speed = 4 km/h, so train speed = 22 km/h. Train reaches station in 30 min, so distance = 22 × 0.5 = 11 km. Person travels this at 4 km/h, taking 11/4 = 2.75 hours = 2h 45min. B is correct.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. Speed of train A is 72 km/hr whose length is half of length of a platform & crosses the platform in 12 sec. Quantity I: 50% of sum of length of train A and length of platform. Quantity II: Length of train B which travel with 50% of speed of train A and crosses the train A in 10 sec when coming from opposite direction.

  1. Quantity : I > Quantity : II

  2. Quantity : I ≥ Quantity : II

  3. Quantity : I < Quantity : II

  4. Quantity : II ≥ Quantity : I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed of train A = 72 km/hr = 20 m/s. Let platform length = P, then train length = P/2. Total distance to cross platform = P + P/2 = 3P/2 = 20 * 12 = 240 m. So platform = 160 m, train = 80 m. Quantity I = 50% of (160 + 80) = 120 m. Train B speed = 50% of 72 = 36 km/hr = 10 m/s. Relative speed when opposite = 20 + 10 = 30 m/s. Time = 10 sec, so train B length = 30 * 10 - 80 = 220 m (distance = sum of both train lengths). Therefore Quantity I (120 m) < Quantity II (220 m).

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. निम्नलिखित प्रत्येक प्रश्न में दिए गए कथन को पढ़िए और उसके आधार पर मात्रा I और मात्रा II की तुलना कीजिए। A train of length 360 m is travelling at a speed of 54 km/hr 360 मीटर लंबी एक ट्रेन 54 किमी/घंटा की गति से यात्रा कर रही है Quantity I : Find the time take by train to cross a pole Quantity II : If its speed is increased by 20% then find the time in which it can cross a platform of length 130 m मात्रा I : ट्रेन द्वारा एक खम्भे को पार करने में लगने वाला समय ज्ञात कीजिए मात्रा II : यदि इसकी गति में 20% की वृद्धि की जाती है, तो 130 m लम्बाई के एक प्लेटफार्म को पार करने में लगने वाला समय ज्ञात कीजिए

  1. Quantity : I > Quantity : II मात्रा : I > मात्रा : II

  2. Quantity : I ≥ Quantity : II मात्रा : I ≥ मात्रा : II

  3. Quantity : I < Quantity : II मात्रा : I < मात्रा : II

  4. Quantity : II ≥ Quantity : I मात्रा: II ≥ मात्रा: I

  5. Quantity I = Quantity II or relation can't be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Train length 360m, speed 54 km/hr = 15 m/s. Time to cross pole = 360/15 = 24 seconds. Quantity II: Speed increased by 20% = 54 × 1.2 = 64.8 km/hr = 18 m/s. Total distance = 360 + 130 = 490m. Time = 490/18 = 27.2 seconds. Since 24 < 27.2, Quantity I < Quantity II, so option C is correct.

Multiple choice

The following questions are accompanied by three statements. You have to determine which statement(s) is/are/sufficient/necessary to answer the question? In what time two trains will cross a 400m long platform? A Trains are running in opposite directions and their speeds are 72km/h and 81km/h respectively. B The length of trains are 180 m. and 210 m. and they reach at the ends of platform simultaneously. C The trains will cross each other in 9 seconds.

  1. All A, B & C are required

  2. A, B & C even together is not sufficient.

  3. Either A or B or C sufficient

  4. Either A and B together or B and C together or C and A together are sufficient.

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

We need relative motion information and platform length. A gives speeds in opposite direction (relative speed = 72+81 = 153 km/h = 42.5 m/s). B gives train lengths. C says trains cross each other in 9 seconds, which gives relative speed = (180+210)/9 ≈ 43.33 m/s - inconsistent with A! With A+B: relative speed from A, combined length from B, we can find time to cross platform if we know platform length. But we don't! With B+C: we can verify relative speed, but still need platform length. None of the combinations give us platform length or which train reaches first. So E (None of these) is correct.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? Mark answer - What is the speed of the train ? I. It takes 25 seconds to pass a bridge 1000 m long. II. It takes 10 seconds to pass a pole.

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

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

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

  4. statement I and II together are not sufficient.

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

Speed of train = length of train / time to pass pole. Statement I: 25 seconds for 1000m bridge gives (train length + 1000)/25 = speed, but we need train length. Statement II: 10 seconds to pass pole means train length / 10 = speed, so we can find length from speed, or speed from length. Neither alone gives both. Together: Let length = L. From II: speed = L/10. From I: speed = (L+1000)/25. Equating: L/10 = (L+1000)/25, solving gives L = 666.67m, speed = 66.67 m/s. Both needed.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? Mark answer - What is the length of the tunnel (in metres) ? I. A train 700 m. long is running at the speed of 72 km/hr. II. It crosses a tunnel in 1 minute.

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

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

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

  4. statement I and II together are not sufficient.

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

Tunnel length + train length = speed × time to cross. Statement I: Train length = 700m, speed = 72 km/hr = 20 m/s. Need time to find tunnel length. Statement II: Time = 1 minute = 60 seconds. Need train length and speed. Neither alone sufficient. Together: distance = speed × time = 20 × 60 = 1200m. This is train + tunnel, so tunnel = 1200 - 700 = 500m. Both statements needed.

Multiple choice

A train crosses a man travelling in another train in the opposite direction in 8 seconds, however the train requires 25 seconds to cross the same man travelling in same direction. If the length of first train is 200 meters and that of the length of another train in which the man is sitting is 160 meters then find the speed of the first train ?/ एक रेलगाड़ी विपरीत दिशा से आ रही रेलगाड़ी में यात्रा कर रहे व्यक्ति को 8 सेकेण्ड में पार करती है जबकि समान दिशा में गतिमान रेलगाड़ी में यात्रा कर रहे व्यक्ति को पार करने में 25 सेकेण्ड लेती है । यदि पहली रेलगाड़ी की लम्बाई 200 मी. एवं अन्य रेलगाड़ी की लम्बाई 160 मी. जिसमें व्यक्ति बैठा है तो पहली ट्रेन की चाल ज्ञात कीजिए ।

  1. 59.8

  2. 59.4

  3. 59.6

  4. 59.2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speed of first train = v1, speed of second train = v2. Opposite direction: (v1 + v2) = 200/8 = 25 m/s. Same direction: (v1 - v2) = 200/25 = 8 m/s. Adding: 2v1 = 33, v1 = 16.5 m/s = 59.4 km/hr. Options A, C, and D are incorrect.

Multiple choice

A train 100 m long travelling at 40 m/s starts overtaking another train 200 m long travelling at 30 m/s. The time taken by the first train to pass the second train completely is:

  1. 30 s

  2. 40 s

  3. 50 s

  4. 60 s
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The relative speed of the first train with respect to the second is 40 - 30 = 10 m/s. The total distance to cover is the sum of the lengths of both trains, 100 + 200 = 300 m. Time = distance / relative speed = 300 / 10 = 30 s.