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

A Train-18 departed from Kanpur to Kannauj at 10 AM. And reached Kannauj at 4:30 PM. And another train Rajdhani express departed from Lucknow to Kannauj at 10am on the same day. Than how far from Kannauj they both will cross each other. A- Train-18 covers the distance from Bareilly to Kanpur in 2 hours. The distance between Bareilly to Kanpur is 162km. B- Rajdhani express cover the distance 100km from Lucknow to Kanpur with the speed of 80 km/hrs.

  1. if the Statement ‘A’ alone is sufficient to answer the question but the Statement ‘B’ alone is not sufficient

  2. if the Statement ‘B’ alone is sufficient to answer the question but the Statement ‘A’ alone is not sufficient

  3. if both Statement ‘A’ and ‘B’ together are needed to answer the question

  4. if either the Statement ‘A’ alone or Statement ‘B’ alone is sufficient to answer the question

  5. If you cannot get the answer from both the Statements together
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The question asks where Train-18 (Kanpur to Kannauj) and Rajdhani (Lucknow to Kannauj) cross. Statement A gives Train-18's speed on Bareilly-Kanpur route, which is irrelevant to the Kanpur-Kannauj segment. Statement B gives Rajdhani's details on Lucknow-Kanpur route, also irrelevant. Neither statement provides distance or speed information for the actual routes in question.

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. Quantity I: A train 175 meter long passes a bird flying in a straight line at the speed of 9 kmph in the opposite direction in which the train is going, in 12 seconds. Find the Speed of the train. Quantity II: Two trains of length 200 meter and 180 meter are moving in the opposite direction cross each other in 19 second then find the relative speed of the train?

  1. Quantity I < QuantityII

  2. Quantity I ≤ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≥ Quantity II

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

Quantity I: Bird flies opposite to train. Relative speed = (train speed + bird speed). Distance = 175m. Time = 12s = 12/3600 hr = 1/300 hr. Bird speed = 9 kmph. So (S + 9) = 175/(1000 × 1/300) = 175/3.33 ≈ 52.5 kmph. So train speed ≈ 43.5 kmph. Quantity II: Total distance = 200+180 = 380m. Time = 19s. Relative speed = 380/(1000 × 19/3600) = 380 × 3600/19000 = 72 kmph. Since 43.5 < 72, Quantity I < Quantity II is correct.

Multiple choice

The questions 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- Find the time taken by Mayank to cross a plateform. Statement I :- A train moving with 60 km/h cross a plateform in 50 seconds. Statement II :- Mayank running at 12 km/h opposite in the direction of train crosses it in 20 seconds.

  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 sufficient , but neither statement alone is sufficient

  5. If statement I and II together are not sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives train speed (60 km/h) and platform crossing time (50 s), but no info about Mayank. Statement II gives Mayank's speed (12 km/h) and his crossing time (20 s), but no train length. Together: Let train length = L. From Statement I: L = 60 × (5/18) × 50 = (300/18) × 50 = 833.33 m. From Statement II: Relative speed = (60 + 12) × (5/18) = 72 × (5/18) = 20 m/s. Mayank crosses train in 20 s, but we need platform length. Wait, the question asks for time taken by Mayank to cross a platform, not the train. We need platform length from Statement I (833.33 m) and Mayank's speed from Statement II (12 km/h = 3.33 m/s). Time = 833.33/3.33 = 250 s. Both statements are needed together.

Multiple choice

Quantity I = Find the number of males in the organization, if ratio of the number of males to the number of females in an organization is 17:15 respectively. The number of females is 525. Quantity II = Find the length of train A , If it crosses another train B coming from the opposite direction in 36 sec. The speeds of the two trains are 31m/s and 19 m/s resepectively. The length of train B is twice that of A. मात्रा I= संगठन में पुरुषों की संख्या ज्ञात करें, यदि किसी संगठन में महिलाओं की संख्या पुरुषों की संख्या का अनुपात क्रमशः 17:15 है। महिलाओं की संख्या 525 है मात्रा II = ट्रेन A की लंबाई ज्ञात कीजिए, यदि यह 36 सेकंड में विपरीत दिशा से आने वाली दूसरी ट्रेन B को पार करती है। दो ट्रेनों की गति 31 मी/से. और 19 मी/से. है। ट्रेन B की लंबाई A से दोगुनी है।

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

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

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

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

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

Quantity I: Males:Females = 17:15, females = 525. 15 units = 525, so 1 unit = 35. Males = 17*35 = 595. Quantity II: Relative speed = 31+19 = 50 m/s. Time = 36s. Total distance = 50*36 = 1800m. If B = 2A, then 3A = 1800, A = 600m. Quantity II (600m) > Quantity I (595 persons) - comparing different units is unusual but numerically 600 > 595.

Multiple choice

In each of the following questions, a question is followed by three statements numbered I, II and III. Read all the statements and answer accordingly. निम्नलिखित प्रत्येक प्रश्न में, एक कथन के बाद तीन कथन I, II और III दिए गए हैं। सभी कथनों को पढ़ें और तदनुसार उत्तर दें। What is the speed of the train ? ट्रेन की गति क्या है? Statement I: The train crosses 300 metres 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. कथन I: ट्रेन 45 सेकंड में 300 मीटर लंबे प्लेटफार्म को पार करती है। कथन II: ट्रेन 60 सेकंड में समान लंबाई वाली एक अन्य स्थिर ट्रेन को पार करती है। कथन III: ट्रेन 30 सेकंड में एक सिग्नल पोल पार करती है।

  1. Only III and I or II केवल III और I या II

  2. Any two of the three तीन में से कोई दो

  3. Only II and I or III केवल II और I या III

  4. Only I and II केवल I और II

  5. Only I and II or III केवल I और II या III
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let train length = L, speed = S. Statement III: S = L/30 (crosses pole). Statement I: S = (L+300)/45. From I and III: L/30 = (L+300)/45, solving gives L = 600m, S = 20m/s. Statement II: 2L/S = 60, so S = L/30 (same as III). I and II together: (L+300)/45 = L/30, gives L = 600m, S = 20m/s. II and III together: both give S = L/30, no platform length - cannot find unique S. So I and II or I and III or II and III work, but I and II or III alone insufficient. Answer E (Only I and II or III) is correct.

Multiple choice

Given below are 3 statements with each question, you have to decide that which of the following statement/statements are necessary to answer the question. नीचे दिए गए प्रत्येक प्रश्न के साथ 3 कथन दिए गए हैं, आपको यह तय करना है कि प्रश्न का उत्तर देने के लिए निम्नलिखित में से कौन सा कथन / कथन आवश्यक है। At what time will a train reach Kanpur from Patna? पटना से कानपुर ट्रेन किस समय पहुंचेगी? Statement A- The train crosses another train of equal length of 97.5 m and running in opposite direction in 9 sec. Statement B- The train leaves Patna at 11:15 am for Kanpur, which is at a distance of 567 km. Statement C- The 97.50-m-long train crosses a signal pole in 5 sec. कथन A- दो ट्रेने 97.5 मीटर की बराबर लंबाई की है और विपरीत दिशा में चलकर एक – दूसरे को 9 सेकंड में पार करती है। कथनB- ट्रेन कानपुर के लिए 11:15 बजे पटना से निकलती है, जो 567 किमी की दूरी पर है। कथन C - 97.50 मीटर लंबी ट्रेन 5 सेकंड में दिशा-निर्देशक स्तम्भ को पार करती है|

  1. Only Statement A केवल कथन A

  2. Statement B and Statement C together कथन B और C एक साथ

  3. Statement A and Statement C together कथन A और C एक साथ

  4. All statements are required सभी कथनो की आवश्यकता है

  5. Only Statement B केवल कथन B सही है
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement B gives departure time (11:15 am) and distance (567 km). Statement C gives train length (97.5 m) and time to cross a pole (5 sec), from which we can calculate speed = 97.5/5 = 19.5 m/s = 70.2 km/h. Using distance and speed, we find travel time = 567/70.2 ≈ 8.08 hours. Adding to departure gives arrival time. Statement A alone is insufficient (only crossing info, no distance). Statement B alone is insufficient (no speed). Only B together give the complete answer.

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. नीचे प्रत्येक प्रश्न में, एक प्रश्न और उसके बाद तीन कथनों में जानकारी दी गई है आप प्रश्ना 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। What is the length of platform? प्लेटफार्म की लम्बाई क्या है? I. Train X running at the speed of 25 km/hr crosses a platform in 18 seconds. II. Train X crosses a man moving at the speed of 5 km/hr in opposite direction in 12 seconds. III. Train crosses a pole in 14.4 seconds I. ट्रेन X जो 25 किमी/घं. की चाल से चल रही है एक प्लेटफार्म को 18 सेकण्ड में पार करती है। II. ट्रेन X एक पुरूष को जो विपरीत दिशा में 5 किमी/घं. की चाल से चल रहा है 12 सेकण्ड में पार करती है। III. ट्रेन X एक पोल को 14.4 सेकण्ड में पार करती है।

  1. Any two कोई भी दो

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

  3. Any one कोई एक

  4. Only III केवल III

  5. I with either II or III I के साथ II या III
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

From Statement III: train length = (25 km/hr × 5/18) × 14.4 sec = 100 m. From Statement I: platform length + train length = (25 × 5/18) × 18 = 125 m, so platform = 25 m. Statement II also works with I (gives train length from relative speed, then platform from I). So I with either II or III is sufficient.

Multiple choice

In the following questions, two quantities are given as Quantity I and Quantity II. Find the correct relationship. The length of First train is 40 % more than the length of second train. First train crosses a 200 m long platform whereas second train crosses a person standing on same platform in 25 sec. If speed of both trains are 60 km/hr. and 36 km/hr. respectively. $Quantity I = Numerical value of the time taken by first train to cross a 200 m long platform (in seconds).$ $Quantity II = Numerical value of the length of second train (in deca meter).$

  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

First find the length of the second train: 36 km/hr = 10 m/s, so length = 10 × 25 = 250 m. The first train is 40% longer, so its length = 1.4 × 250 = 350 m. Quantity I = (350 + 200) / (60 × 5/18) = 550 / (50/3) = 33 seconds. Quantity II = 250 m = 25 deca meters. Since 33 > 25, Quantity I is greater.

Multiple choice

In the following problems, there is one question and some statements given below the question. You have to decide whether the data given in the statements is sufficient to answer the question. प्रत्येक प्रश्न में एक प्रश्न और उसके बाद कुछ कथन दिए गए हैं| आपको निर्धारित करना है कि कथनों में दी गई जानकारी प्रश्न का उत्तर देने के लिये पर्याप्त हैं या नहीं| A train crosses another train in 12.5 sec. Find out the lengths of the trains. I. Ratio between the lengths the of second and first train is 5 : 6. II. Ratio between the speed of first and second trains is 1 : 2. III. The speed of first train is 54 km/hr. एक ट्रेन 12.5 सेकंड में एक दूसरी ट्रेन को पार करती है। ट्रेनों की लंबाई ज्ञात करें | I. दूसरी और पहली ट्रेन की लंबाई के बीच अनुपात 5: 6 है। II. पहली और दूसरी ट्रेनों की गति के बीच अनुपात 1: 2 है। III. पहली ट्रेन की गति 54 किमी / घंटा है।

  1. We cannot determine / हम निर्धारित नहीं कर सकते हैं

  2. Only (II) & (II) required to given answer केवल (II) और (III) उत्तर देने के लिए आवश्यक हैं

  3. None of given statement required दिए गए किसी भी कथन की आवश्यकता नहीं है

  4. Only (II) & (III) required to given answer केवल (II) और (III) उत्तर देने के लिए आवश्यक हैं

  5. All (i) , (II) & (III) required सभी (I), (II) और (III) आवश्यक है
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When two trains cross each other, the time depends on their relative speed and whether they're moving in same or opposite directions. The problem doesn't specify their direction of motion. In opposite directions: relative speed = v1 + v2. In same direction: relative speed = |v1 - v2|. Without knowing direction or the distance covered during crossing, we cannot determine individual lengths even with ratios and one absolute speed.

Multiple choice

Find the correct relationship between given quantities. दी गई राशियों के बीच सही संबंध खोजें। A train pass another train coming from opposite direction at speed of 32 km/hr. Find the length of train. एक ट्रेन विपरीत दिशा से 32 किमी प्रति घंटा की गति से आ रही दूसरी ट्रेन को पार करती है। ट्रेन की लम्बाई ज्ञात कीजिये। Quantity I-Sum of lengths of both trains is 480 meter and its speed is 25% more than the speed of other train. Quantity II-Difference of lengths of both trains is 80 meter and its speed is 25% less than the speed of other train. मात्रा I- दोनों ट्रेनों की लंबाई का योग 480 मीटर है और इसकी गति अन्य ट्रेन की गति से 25% अधिक है। मात्रा II- दोनों ट्रेनों की लंबाई का का अंतर 80 मीटर है और इसकी गति अन्य ट्रेन की गति से 25% कम 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 I ≤Quantity II मात्रा I ≤मात्रा II

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

This is a data sufficiency problem where we must determine if a relationship can be established between two quantities. Quantity I gives that the sum of lengths is 480m and one train's speed is 25% more than the other's. Quantity II gives that the difference of lengths is 80m and one train's speed is 25% less than the other's. From these, we can solve for individual train lengths: if L1 + L2 = 480 and |L1 - L2| = 80, then the trains are 280m and 200m. However, we are not told which train corresponds to which quantity, nor do we have the actual speeds or the time taken to cross. Without knowing which train is which or having the actual speed values, we cannot establish a relationship between the quantities.

Multiple choice

Two trains A and B start running together from the same point in the same direction, at the speed of 60 km./hr. and 72 km./hr. respectively. If the sum of length of both the trains is 240 metres, how long will it take for train B to cross train A? दो ट्रेन A और B एक ही बिन्दु से आरम्भ होकर एक ही दिशा में क्रमशः 60 किमी./घं. और 72 किमी./घं. की चाल से चलती है। यदि दोनों ट्रेनों की लम्बाई का योग 240 मीटर है तो ट्रेन B ट्रेन A को कितने समय में पार करेगी?

  1. 2 minutes 12 seconds 2 मिनट 12 सेकेण्ड

  2. 1 minute 24 seconds 1 मिनट 24 सेकेण्ड

  3. 1 minute 12 seconds 1 मिनट 12 सेकेण्ड

  4. 2 minutes 24 seconds 2 मिनट 24 सेकेण्ड

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

Relative speed of B with respect to A = 72 - 60 = 12 km/hr = 12 × (1000/3600) = 10/3 m/s. Total distance to cover = sum of lengths = 240 m. Time = Distance / Speed = 240 / (10/3) = 72 seconds = 1 minute 12 seconds.

Multiple choice

A train whose length is 240 meter crosses a railway signal in 30 seconds. Find the total time taken by this train to cross another train whose length is two third of its length and coming from opposite direction at a speed of 31.2 Kmph? एक ट्रेन जिसका लंबाई 240 मीटर है, 30 सेकेण्ड में एक रेलवे संकेत पार करती है। इस ट्रेन द्वारा दूसरी ट्रेन को पार करने के लिए समय का पता लगाएं, जिसकी लंबाई इसकी लम्बाई की दो तिहाई है तथा 31.2 किमी प्रति घंटे की गति से विपरीत दिशा से आ रही है?

  1. 16 seconds| 16 सेकंड

  2. 24 second 24 सेकंड

  3. 15 seconds 15 सेकंड

  4. 20 seconds 20 सेकंड

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

First train's speed = 240/30 = 8 m/s = 28.8 km/h. Second train length = 2/3 × 240 = 160m, speed = 31.2 km/h = 8.67 m/s. Since trains move in opposite directions, relative speed = 8 + 8.67 = 16.67 m/s. Total distance = 240 + 160 = 400m. Time = 400/16.67 ≈ 24 seconds.

Multiple choice

The question given below contain three statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? What is the speed of train? ट्रेन की गति क्या है? I. Train crosses a signal in 14 seconds. II. Train crosses another train in 16 seconds. III. Train crosses 200 m. long platform in 24 seconds. I. ट्रेन एक सिग्नल को 14 सेकण्ड में पार करती है। II. ट्रेन दूसरी ट्रेन को 16 सेकण्ड में पार करती है। III. ट्रेन 200 मीटर लम्बे प्लेटफॉर्म को 24 सेकण्ड में पार करती है।

  1. Only I and II केवल I और II

  2. Only I and III केवल I और III

  3. Only II and III केवल I और III

  4. Any two कोई दो

  5. All I, II and III सभी I, II और III
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives the time to cross a signal (train length L in 14 seconds), so L/14 = speed. Statement III gives time to cross 200m platform in 24 seconds, so (L + 200)/24 = speed. Equating: L/14 = (L + 200)/24, giving 24L = 14L + 2800, so L = 140m and speed = 10 m/s. Statement II alone gives no useful information since the other train's length is unknown. I + II together also insufficient.

Multiple choice

A goods train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in 60 sec. whereas a passenger on the passenger train marks that he crosses the goods train in 40 sec. If the speeds of the trains be in the ratio 1:2. Find the ratio of their lengths. एक माल गाड़ी और एक यात्री ट्रेन उसी दिशा में समानांतर पटरियों पर चल रही है। माल गाड़ी के चालक ने देखा कि यात्री ट्रेन पीछे से आ रही है और पूरी ट्रेन को 60 सेकंड में पूरी तरह से पार कर रही है। जबकि यात्री ट्रेन के एक यात्री को पता चलता है कि वह 40 सेकंड में माल गाड़ी को पार करता है यदि गाड़ियों की गति का अनुपात 1: 2 में हो तो उनकी लंबाई का अनुपात ज्ञात कीजिये।

  1. 5:3

  2. None of these

  3. 1:2

  4. 2:1

  5. 3:2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let goods train speed = v, passenger train speed = 2v (ratio 1:2). Relative speed = 2v-v = v. Goods driver sees passenger cross his train in 60s: Lg+Lp = v×60 = 60v. Passenger sees goods train pass him in 40s: Lg = v×40 = 40v. Substituting: 40v + Lp = 60v, so Lp = 20v. Ratio Lg:Lp = 40v:20v = 2:1. The key insight is understanding what each observer measures.

Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. You have to study the information along with the question and compare the value derived from Quantity I and Quantity II, then anwer: नीचे दिए गए प्रत्येक प्रश्न में मात्रा I और मात्रा II का कथन है। आपको प्रश्न के साथ जानकारी का अध्ययन करना होगा और मात्रा I और मात्रा II से प्राप्त मूल्य की तुलना करनी है। Quantity I : A train of length 200 m can cross a platform in 10 sec. If the train increases its speed by 25% then it can cross a person standing on the same platform in 3.2 seconds. What is the length of platform? Quantity II : Two friends, A and B start running towards each other at the speed of 12 km per hour and 18 km per hour. After 30 seconds of starting, the distance between then is 750 meters. What will be the distance between them after 81 seconds of starting? मात्रा I: लंबाई 200 मीटर की एक ट्रेन 10 सेकंड में एक प्लेटफॉर्म को पार कर सकती है। यदि ट्रेन अपनी गति 25% बढ़ाती है तो वह 3.2 सेकंड में एक ही प्लेटफॉर्म पर खड़े व्यक्ति को पार कर सकती है। प्लेटफ़ॉर्म की लंबाई क्या है? मात्रा II: दो मित्र, A और B एक-दूसरे की ओर 12 किमी प्रति घंटे और 18 किमी प्रति घंटे की गति से दौड़ना शुरू करते हैं। शुरू होने के 30 सेकंड के बाद, तब के बीच की दूरी 750 मीटर है। 81 सेकंड की शुरुआत के बाद उनके बीच की दूरी क्या होगी?

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

  2. Quantity I = Quantity II or relation can't be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता है

  3. Quantity I < Quan
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Let speed be v m/s. From train crossing person: 200 = 3.2 × 1.25v, so v = 50. From crossing platform: 200 + P = 10 × 50, giving P = 300m. Quantity II: Combined speed = 30 km/h = 25/3 m/s. In 30 sec they cover 25/3 × 30 = 250m. Initial distance = 750 + 250 = 1000m. In 81 sec they cover 25/3 × 81 = 675m. Remaining distance = 1000 - 675 = 325m. Since 300 < 325, Quantity I < Quantity II.