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

Passage

Directions : In this problem, a question is given followed by two statements numbered I and II. Read the statements and determine which of them is/are sufficient/necessary to answer the question. Choose the correct option accordingly. Mark your answer as (a) if the question can be answered by using statement I alone, but cannot be answered by using statement II alone (b) if the question can be answered by using statement II alone, but cannot be answered by using statement I alone (c) if both statements I and II together are necessary to answer the question (d) if the question can be answered by using either of the two statements alone (e) if both the statements together are not sufficient to answer the question

A train is moving at a speed of 72 km/hr. Find the length of the train. I. The train crosses a man in 8 seconds. II. The train crosses an 80-m long platform in 12 seconds.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Speed = 72 km/hr = 20 m/s. I: L = 20 * 8 = 160m. II: L + 80 = 20 * 12 = 240m => L = 160m. Both statements alone are sufficient.

Multiple choice

Passage

Directions : The question given below is followed by two statements I and II. You are to determine whether the data given in the statement is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer according to the following codes: (a) If the question can be answered by using statement I alone but cannot be answered by using statement II alone. (b) If the question can be answered by using statement II alone but cannot be answered by using statement I alone. (c) If both statements I and II together are required to answer the question. (d) If the answer can be found by using any of the two statements alone. (e) If both the statements together are not sufficient to answer the question.

Two trains moving in opposite directions are crossing each other. If train1 crosses train2 moving at the speed of 162 km/hr, find the length of train1. I. Train1 crosses train2 of length 160 m in 4 seconds. II. Train1 moving at the speed of 144 km/hr crosses train2 of length 160 m in 4 seconds.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find the length of train 1, we need its speed and the relative speed. Statement I gives time and length of train 2 but not speed of train 1. Statement II gives the speed of train 1 (144 km/hr) and the length of train 2 (160 m) and the time (4 seconds). Using relative speed (144 + 162 = 306 km/hr = 85 m/s), we can find the total length (160 + L1 = 85 * 4 = 340), so L1 = 180 m. Thus, II alone is sufficient.

Multiple choice

Passage

Directions: Read the passage below and answer the questions that follow. The Ludhiana-New Delhi superfast express departs Ludhiana Railway station for New Delhi railway station at 7:00 a.m. in the morning travelling at an average speed of 60 km/hr. The New Delhi-Ludhiana express departs New Delhi railway station for Ludhiana exactly an hour later travelling at an average speed of 100 km/hr. The distance between the two railway stations is 300 km.

At what time do the two trains cross each other?

  1. 9:30 a.m.

  2. 9:52 a.m.

  3. 11:00 a.m.

  4. 12:00 p.m.

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

Train 1 (7:00 AM) travels 60km in 1 hour. At 8:00 AM, distance between trains is 300-60 = 240km. Relative speed = 60+100 = 160 km/hr. Time to meet = 240/160 = 1.5 hours. 8:00 AM + 1.5 hours = 9:30 AM.

Multiple choice

Passage

Directions: Read the passage below and answer the questions that follow. The Ludhiana-New Delhi superfast express departs Ludhiana Railway station for New Delhi railway station at 7:00 a.m. in the morning travelling at an average speed of 60 km/hr. The New Delhi-Ludhiana express departs New Delhi railway station for Ludhiana exactly an hour later travelling at an average speed of 100 km/hr. The distance between the two railway stations is 300 km.

Train from Ludhiana starts 1 hour late and train from New Delhi starts on time. Let the two trains run at their normal speed for the 1st hour after which their speeds get interchanged. How far from the Ludhiana railway station do they now cross each other?

  1. 140 km

  2. 147.5 km

  3. 160 km

  4. 167.5 km

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

Passage

Directions: The following question is accompanied by statements (A), (B) and (C). Determine the statements(s) sufficient/necessary to answer the question.

A man is passed by a passenger train running at 41 km/h. Assuming man's length as negligible, in how many seconds will the train cross the man? Statements: A. Another 50 m long goods train, coming from opposite direction, running at 40 km/h, crosses the passenger train. B. The passenger train is 100 m long. C. The man is running at 5 km/h in the same direction in which the passenger train is going.

  1. A and C together

  2. A and B together

  3. B and C together

  4. A and either B or C

  5. All statements are necessary
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the time taken to cross the man, we need the relative speed and the length of the train. Statement B provides the length (100m). Statement C provides the man's speed, allowing calculation of relative speed (41 - 5 = 36 km/h). Statement A is irrelevant as it introduces a different train.

Multiple choice

Passage

Directions: The question is followed by two statements I and II. You have to determine whether the data given in the statements is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.

Train Y, which has a length of 450 m and is running at 72 kmph, will take how much time to cross train Z, which is 550 m long and is running at a certain speed in the opposite direction? I. Train Z is faster than Train Y. It takes 100 seconds for both the trains to get apart from each other moving in the same direction. II. Train Z can cover 288 km in 2 hours and 40 minutes.

  1. The question can be answered by using statement I alone but cannot be answered by using the other statement alone.

  2. The question can be answered by using statement II alone but cannot be answered by using the other statement alone.

  3. The question can be answered by using either of the statements alone.

  4. The question can be answered by using both of the statements together, but cannot be answered by using either of the statements alone.

  5. The question cannot be answered even by using both the statements together.
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

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 length of platform? I. Train crosses a platform in 24 seconds. II. Train crosses a man moving at the speed of 5 km/h in opposite direction in 12 seconds. III. Train crosses a pole in 14.4 seconds.

  1. I and II together

  2. II and III together

  3. All three together

  4. All together are not sufficient

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

Statement I: L = 24 × (train speed) - train length (insufficient alone). Statement II: (train speed + 5 km/h) × 12 = train length (insufficient alone). Statement III: L = 14.4 × train speed (gives L in terms of speed). Combining all three: From III, train length L = 14.4v. Substituting in I and II gives two equations to solve for both v and L. Thus all three together are sufficient (Option C).

Multiple choice

Passage

Find the value of Q1 and Q2 and state the correct relationship.

Quantity I: Time taken by A to complete 1/5th of work if B takes 6 days to complete 3/5th of work and together they take 5 days to complete 3/4th of work Quantity II: Time taken by a train to cross a platform of length 60 km given that it crosses a pole in two and a half hours running at 60 km/hr

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: B does 3/5 work in 6 days, so B's rate = 1/10 per day. Together A+B do 3/4 work in 5 days, so combined rate = 3/20 per day. A's rate = 3/20 - 1/10 = 1/20. A does 1/5 work in 4 days. Quantity II: Train speed 60 km/hr, crosses pole in 2.5 hrs, so length = 60×2.5 = 150 km. To cross 60 km platform, time = (150+60)/60 = 3.5 hrs. 4 hours > 3.5 hours, so Quantity I is greater.

Multiple choice

Passage

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।

Speed of train A is 72 km/hr whose length is half of length of a platform & crosses the platform in 12 sec. ट्रेन A की गति 72 किमी/घंटा है जिसकी लंबाई एक प्लेटफॉर्म की लंबाई से आधी है और 12 सेकंड में प्लेटफॉर्म को पार करती है। Quantity I: 30% 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. मात्रा I: ट्रेन A की लंबाई और प्लेटफॉर्म की लंबाई के योग का 30% मात्रा II: ट्रेन B की लंबाई जो ट्रेन A की 50% गति से यात्रा करती है और विपरीत दिशा से आने पर ट्रेन A को 10 सेकंड में पार करती है।

  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

Train A: Speed = 72 kmph = 20 m/s. Let length = L, platform length = 2L. Total distance = 3L covered in 12 seconds: 3L = 20 × 12, so L = 80 m, platform = 160 m. Quantity I = 0.3 × (80 + 160) = 72 m. Train B: Speed = 10 m/s, relative speed when opposite = 30 m/s. In 10 seconds, distance = 300 m = Length A + Length B, so Length B = 220 m. Quantity I (72) < Quantity II (220). Don't confuse train length with platform length.

Multiple choice

Passage

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 500 meters length can cross completely a platform of 800 meters length in 130 second. 500 मीटर लंबी एक ट्रेन 130 सेकंड में 800 मीटर लंबे प्लेटफॉर्म को पूरी तरह से पार कर सकती है। Quantity I : What is the speed of the train in meters per second? Quantity II : A man running in the same direction of the train can pass the train completely in 4 minutes 10 seconds then what was the speed of the man in meters per sec? मात्रा I : ट्रेन की गति मीटर प्रति सेकंड में क्या है? मात्रा II : एक व्यक्ति ट्रेन की समान दिशा में दौड़ रहा है और 4 मिनट 10 सेकंड में ट्रेन को पूरी तरह से पार कर सकता है तो मीटर प्रति सेकंड में आदमी की गति क्या थी?

  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: Distance = 500 + 800 = 1300 m. Speed = 1300/130 = 10 m/s. Quantity II: Relative speed = 500 m / 250 s = 2 m/s. Since man runs in same direction, train speed - man speed = 2, so man speed = 10 - 2 = 8 m/s. Clearly 10 m/s > 8 m/s, so Quantity I > Quantity II. Option C correctly states I < II.

Multiple choice

Passage

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।

Quantity I: A train can cross a pole in 12 sec with a speed of 75 km/h. Length of train? Quantity II: A train can cross a pole in 12sec and a tunnel in 50 sec. If length of tunnel is 3800 m. length of train. मात्रा I: एक ट्रेन 75 किमी/घंटा की गति से एक खम्भे को 12 सेकंड में पार कर सकती है। ट्रेन की लंबाई ? मात्रा II: एक ट्रेन एक खम्भे को 12 सेकंड में और एक सुरंग को 50 सेकंड में पार कर सकती है। यदि सुरंग की लंबाई 3800 मी. ट्रेन 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
C Correct answer
Explanation

Quantity I: Speed = 75 km/h = 75×5/18 = 20.83 m/s. Time = 12 sec. Length = 20.83 × 12 = 250 m. Quantity II: Train crosses pole in 12 sec (so length = speed × 12). Train crosses tunnel (3800 m) in 50 sec. So L + 3800 = speed × 50. From pole: L = speed × 12. Substituting: 12s + 3800 = 50s, so 38s = 3800, s = 100 m/s. Then L = 100 × 12 = 1200 m. Comparing: 250 m < 1200 m, so Quantity I < Quantity II.

Multiple choice

Passage

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।

Quantity I: The ratio between the speeds of two trains is 7:8. If the second train runs 400 km in 4 hours, then the speed of the first train. Quantity II: Find the speed (km/hr) of a train which passes a tree in 12 seconds. The length of the train is 264m. मात्रा I: दो ट्रेनों की गति के बीच का अनुपात 7:8 है। यदि दूसरी ट्रेन 4 घंटे में 400 किमी चलती है, तो पहली ट्रेन की गति। मात्रा II: एक ट्रेन की गति (किमी/घंटा) ज्ञात कीजिए जो एक पेड़ को 12 सेकंड में पार करती है। ट्रेन की लंबाई 264 मीटर है।

  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

Quantity I: Speed of second train = 400/4 = 100 km/h. Ratio of speeds is 7:8, so speed of first train = (7/8) × 100 = 87.5 km/h. Quantity II: Train length = 264 m = 0.264 km. Time to pass tree = 12 sec = 12/3600 hr = 1/300 hr. Speed = Distance/Time = 0.264/(1/300) = 0.264 × 300 = 79.2 km/h. Therefore Quantity I (87.5) > Quantity II (79.2).

Multiple choice

Passage

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis.

Train ‘A’ can cross a pole in 20 seconds and a platform which is 60 m long in 25 seconds. Train ‘A’ can cross train ‘B’ coming from opposite direction in 15 seconds. Ratio between speed of train ‘A’ to train ‘B’ is 2 : 3. Quantity I: Length of train ‘B’ Quantity II: Length of train ‘A’

  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

Let train A's length = L and speed = S. L/20 = S (pole crossing time). (L+60)/25 = S (platform crossing). Equating: L/20 = (L+60)/25, giving L = 240 m and S = 12 m/s. Speed ratio A:B = 2:3, so B's speed = 18 m/s. When crossing opposite: (12+18) × 15 = 240 + Length_B, giving 450 = 240 + Length_B, so Length_B = 210 m. Comparing: 210 m < 240 m, so Quantity I < Quantity II.

Multiple choice

Passage

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis.

A train of length 360 m is travelling at a speed of 54 km/hr. 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 120 m.

  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

Quantity I: Train length = 360 m, speed = 54 km/hr = 54 × 5/18 = 15 m/s. Time to cross pole = 360/15 = 24 seconds. Quantity II: New speed = 54 × 1.2 = 64.8 km/hr = 64.8 × 5/18 = 18 m/s. Total distance = 360 + 120 = 480 m. Time = 480/18 = 26.67 seconds. Comparing: 24 seconds < 26.67 seconds, so Quantity I < Quantity II.

Multiple choice

Passage

Each of these questions consists of a question followed by information 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. 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 कौन सा/से कथनों में दी गई जानकारी प्रश्न का उत्तर देने के लिए आवश्यक है/हैं।

What is the speed of the train? ट्रेन की गति क्या है? Statement I: The train crosses 100 meters long platform in 30 seconds. Statement II: The train crosses another stationary train of 1.5 times of its length in 60 seconds. Statement III: The train crosses a signal pole in 24 seconds. कथन I: यह ट्रेन 30 सेकंड में 100 मीटर लम्बे प्लेटफार्म को पार करती है। कथन II: ट्रेन 60 सेकंड में अपनी लम्बाई के 1.5 गुनी लम्बी दूसरी स्थिर ट्रेन को पार करती है। कथन III: ट्रेन एक सिग्नल को 24 सेकंड में पार करती है।

  1. All three together are sufficient सभी तीनों एक साथ पर्याप्त हैं

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

  3. II and III alone are sufficient II तथा III अकेले पर्याप्त हैं

  4. Any two are sufficient कोई भी दो पर्याप्त हैं

  5. II and (I or III) are sufficient II तथा (I या III) पर्याप्त हैं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

From statement III, speed v = L/24 where L is train length. Combining with statement I (v = (L+100)/30) gives v = 50/3 m/s uniquely. Statement II gives v = L/24 which is equivalent to III. So I combined with either II or III is sufficient.