Problem on Trains MCQ Quiz - Objective Question with Answer for Problem on Trains - Download Free PDF
Last updated on May 14, 2025
Latest Problem on Trains MCQ Objective Questions
Problem on Trains Question 1:
The ratio of the speed of train A and train B is 1 : 2 respectively. Train B crosses a pole in 10 sec. Average of the length of train A and train B is 1500 meter. Ratio of the length of train A and train B is 2 : 1. Find the time taken by train A to cross a pole.
Answer (Detailed Solution Below)
Problem on Trains Question 1 Detailed Solution
Calculation
Let length of train A and train B is 2x and x respectively.
So, [2x +x]/2 = 1500
Or, 3x = 3000
Or, x = 1000
So, Length of train A is 2000 and length of train B 1000.
Speed of train B is 1000/10 = 100 m/sec
Speed of train A is 100/2 = 50 m/sec
So, required time = [2000/50] = 40 sec
Problem on Trains Question 2:
Train A of length 80m while moving crosses a pole in 16 seconds. lf it is known that the lengths of train B and train A is in the ratio of 3:1, then how long would it take train B to cross a platform which is half the length of train A if the speed of train B is same as that of train A?
Answer (Detailed Solution Below)
Problem on Trains Question 2 Detailed Solution
Calculations:
Speed of Train A = Distance / Time = 80 m / 16 s = 5 m/s.
Since the speed of Train B is the same as Train A, the speed of Train B = 5 m/s.
Length of Train B = 3 × Length of Train A
⇒ 3 × 80 = 240 m.
Length of the platform = (1/2) × Length of Train A
⇒ (1/2) × 80 = 40 m.
To cross the platform, Train B needs to cover its own length plus the length of the platform, i.e., 240 m + 40 m = 280 m.
Time taken by Train B to cross the platform = Distance / Speed
⇒ 280 m / 5 m/s = 56 seconds.
∴ It would take Train B 56 seconds to cross the platform.
Problem on Trains Question 3:
A train travels from Delhi to Jamnagar at a speed of 80 km/hr and returns at a speed of 82 km/hr. If it takes 162 hours for the total travel, then find the distance between Delhi and Jamnagar. (In km)
Answer (Detailed Solution Below)
Problem on Trains Question 3 Detailed Solution
Given:
Speed from Delhi to Jamnagar (S1) = 80 km/hr
Speed from Jamnagar to Delhi (S2) = 82 km/hr
Total time taken (T) = 162 hours
Formula Used:
Time = Distance / Speed
Let the distance between Delhi and Jamnagar be D km.
Time taken to travel from Delhi to Jamnagar (T1) = D / S1
Time taken to travel from Jamnagar to Delhi (T2) = D / S2
Total time (T) = T1 + T2
Calculation:
T = T1 + T2
162 = (D / 80) + (D / 82)
⇒ 162 = D × (1/80 + 1/82)
⇒ 162 = D × ((82 + 80) / (80 × 82))
⇒ 162 = D × (162 / 6560)
⇒ D = 162 × (6560 / 162)
⇒ D = 6560
∴ The distance between Delhi and Jamnagar is 6560 km.
Problem on Trains Question 4:
A train started from station A and proceeded towards station B at a speed of 208 kmph. 45 minutes later, another train started from station B and proceeded towards station A at 25 kmph. If the distance between the two stations is 855 kms, at what distance from station A will the trains meet? (In km)
Answer (Detailed Solution Below)
Problem on Trains Question 4 Detailed Solution
Given:
Speed of train from A (SA) = 208 kmph
Speed of train from B (SB) = 25 kmph
Time after which train B started = 45 minutes = 45/60 hours = 0.75 hours
Distance between station A and station B (D) = 855 km
Formula Used:
Distance = Speed × Time
Relative speed when trains move towards each other = Sum of their speeds
Calculation:
Distance covered by train A in the first 0.75 hours = SA × Time = 208 × 0.75 = 156 km
Remaining distance between the trains when train B starts = Total distance - Distance covered by train A
Remaining distance = 855 - 156 = 699 km
Relative speed of the two trains = SA + SB = 208 + 25 = 233 kmph
Time taken for the trains to meet after train B starts = Remaining distance / Relative speed
Time = 699 / 233 = 3 hours
Distance from station A where the trains meet = Distance covered by train A in the first 0.75 hours + Distance covered by train A in the next 3 hours
Distance from A = 156 + (208 × 3)
Distance from A = 156 + 624
Distance from A = 780 km
The trains will meet at a distance of 780 km from station A.
Problem on Trains Question 5:
A train started from station A and proceeded towards station B at a speed of 204 kmph. 45 minutes later, another train started from station B and proceeded towards station A at 30 kmph. If the distance between the two stations is 855 kms, at what distance from station A will the trains meet? (In km)
Answer (Detailed Solution Below)
Problem on Trains Question 5 Detailed Solution
Given:
Speed of train from A = 204 kmph
Speed of train from B = 30 kmph
Calculation:
Let the distance the trains meet be 'x'
Distance covered by train A in x hours + Distance covered by train B in \({(x - {3\over 4} )}\) hours = 855 kms
⇒ 204x + 30\({(x - {3\over 4} )}\) = 855
⇒ 204x + 30x - \(90 \over 4\) = 855
⇒ 234x = 855 + \(90 \over 4\)
⇒ 234x = 877.5
⇒ x = \(877.5 \over 234\)
⇒ x = 3.75
Distance the train meet,
⇒ 204 × 3.75
⇒ 765
∴ The distance the trains meet from station A is 765 km.
Top Problem on Trains MCQ Objective Questions
Running at a speed of 60 km per hour, a train passed through a 1.5 km long tunnel in two minutes, What is the length of the train ?
Answer (Detailed Solution Below)
Problem on Trains Question 6 Detailed Solution
Download Solution PDFGiven:
Speed is 60 km per hour,
Train passed through a 1.5 km long tunnel in two minutes
Formula used:
Distance = Speed × Time
Calculation:
Let the length of the train be L
According to the question,
Total distance = 1500 m + L
Speed = 60(5/18)
⇒ 50/3 m/sec
Time = 2 × 60 = 120 sec
⇒ 1500 + L = (50/3)× 120
⇒ L = 2000 - 1500
⇒ L = 500 m
∴ The length of the train is 500 m.
Two trains, one 152.5 m long and the other 157.5 m long, coming from opposite directions crossed each other in 9.3 seconds. The combined speed of the two trains every hour would then be:
Answer (Detailed Solution Below)
Problem on Trains Question 7 Detailed Solution
Download Solution PDFGiven:-
Train1= 152.5m
Train2= 157.5m
Time = 9.3 sec
Calculation:-
⇒ Total distance to be covered = total length of both the trains
= 152. 5 + 157.5
= 310 m
Total time taken = 9.3 sec
Speed = distance/time
= (310/9.3) m/sec
= (310/9.3) × (18/5)
= 120 km/hr
∴ The combined speed of the two trains every hour would then be 120 km/hr.
Alternate Method When two trains are moving in opposite direction-
Let the speed of ine is 'v' and the second is 'u'
∴ Combined speed = v + u
Total distance = 152.5 + 157.5
= 310 m
∴ Combined speed = Total distance/total time
⇒ (v + u) = 310/9.3
⇒ (v + u) = 33.33 m/s
⇒ (v + u) = 33.33 × (18/5)
⇒ (v + u) = 120 km/hr
Two trains of equal lengths take 13 seconds and 26 seconds, respectively, to cross a pole. If these trains are moving in the same direction, then how long will they take to cross each other?
Answer (Detailed Solution Below)
Problem on Trains Question 8 Detailed Solution
Download Solution PDFGiven:
Train A takes 13 seconds to cross a pole.
Train B takes 26 seconds to cross a pole.
Concept:
Speed = Distance / Time
When two trains are moving in the same direction, their relative speed is the difference of their speeds.
Solution:
Let the length of each train be L.
⇒ Speed of train A = L/13, speed of train B = L/26.
When the two trains cross each other, the total distance covered is 2L (length of train A + length of train B).
Relative speed of the two trains = speed of train A - speed of train B = L/13 - L/26 = L/26.
Time taken to cross each other = total distance / relative speed = 2L / (L/26) = 52 seconds.
Hence, the two trains take 52 seconds to cross each other.
Two trains are running on opposite tracks between stations A and B. After crossing each other they take 4 hr and 9 hr respectively to reach their destination. If speed of first train is 54 kmph, find the speed of second train.
Answer (Detailed Solution Below)
Problem on Trains Question 9 Detailed Solution
Download Solution PDFGiven:
Two trains are running on opposite tracks between stations A and B.
After crossing each other they take 4 hr and 9 hr respectively to reach their destination.
Speed of first train is 54 kmph.
Formula used:
After crossing each other, if time taken by 2 trains is T1 and T2 resp. then, S1/S2 = √T2/√T1
where, S1 and S2 are speeds of first and second train respectively
Calculation:
We have, T1 = 4hr, T2 = 9hr, S1 = 54 kmph
⇒ 54/ S2 = √[9/4] = 3/2
⇒ S2 = 54 × 2 × 1/3 = 36 kmph
⇒ Speed of second train = 36 kmph
Alternate Method
Let the speed of the second train be 'x' kmph
Also, time taken to cross each other = √(T1 × T2) = √(9 × 4) = 6 hrs
Total distance = 54 × 6 + x × 6 = x × 9 + 54 × 4
⇒ 9x - 3x = 54 × (6 - 2)
⇒ 6x = 216
⇒ x = 36 kmph = Speed of second train
A train crossed a 110 m long platform in 13.5 seconds and a 205 m long platform in 18.25 seconds. What was the speed of the train?
Answer (Detailed Solution Below)
Problem on Trains Question 10 Detailed Solution
Download Solution PDFLet the length of train be x m.
⇒ Speed of train = (length of platform + length of train)/time
According to question,
⇒ (110 + x)/ 13.5 = (205 + x)/18.25
⇒ (110 + x)/2.7 = (205 + x)/3.65
⇒ 401.5 + 3.65x = 553.5 + 2.7x
⇒ 0.95x = 152
⇒ x = 160
⇒ Speed of train = (110 + 160)/13.5 = 20 m/sec = 20 × (18/5) = 72 km/hrA 1200 m long train crosses a tree in 120 sec, how much time will it take to pass a platform 700 m long?
Answer (Detailed Solution Below)
Problem on Trains Question 11 Detailed Solution
Download Solution PDFGiven:
Length of a train is 1200m
Train took 120 sec to cross a tree
Length of a platform is 700m
Formula USed:
Speed = Distance/Time
Calculation:
Speed = 1200/120 = 10 m/sec
Total distance = 1200 + 700 = 1900 m
Time = distance/speed = 1900/10 = 190 sec
∴ Time required to cross a platform is 190 sec.
A train having a length of 500 m passes through a tunnel of 1000 m in 1 minute. What is the speed of the train in Km/hr?
Answer (Detailed Solution Below)
Problem on Trains Question 12 Detailed Solution
Download Solution PDFLet the speed of the train be x m/s.
Given length of the train = 500 m
Length of the tunnel = 1000 m
Time taken to pass the tunnel = 1 minute = 60 seconds
∴ x = (500 + 1000) ÷ 60
x = 25 m/s
Speed of the train in km/hr =\(\;25 \times \frac{{18}}{5}\frac{{km}}{{hr}}\)
Speed of the train = 90 km/hr.Two train running towards each-other at the speed of 50 km/hr and 60 km/hr from station A and B. When two trains meet each other, the second train covered 120 km more distance than first train. What is the distance between both stations?
Answer (Detailed Solution Below)
Problem on Trains Question 13 Detailed Solution
Download Solution PDFGiven:
Two train running towards each-other at the speed of 50 km/hr and 60 km/hr.
Two trains meet each other, the second train covered 120 km more distance than first train.
Formula used:
Speed × time = distance
Calculations:
Let the two trains meet after x hours.
Then, 60x − 50x = 120
⇒10x = 120
⇒x = 12hrs
Distance = (Distance covered by slower train) + (Distance covered by faster train) = [(50 × 12) + (60 × 12)] km
= 600km + 720km = 1320 km
∴ The answer is 1320 km
Two trains are running in opposite directions. They cross a man standing on a platform in 28 seconds and 10 seconds. respectively. They cross each other in 24 seconds. What is the ratio of their speeds?
Answer (Detailed Solution Below)
Problem on Trains Question 14 Detailed Solution
Download Solution PDFShortcut Trick
We can solve this question by applying the allegation method.
Thus,
Ratio of their speed = 14 : 4 = 7 : 2
∴ The correct answer is option (1).
Alternate Method
Given:
Train one crosses a man in 28 seconds
Train two crosses the man in 10 seconds
They both cross each other in 24 seconds
Formula used:
Time = Distance/ speed
As the trains travel in opposite directions, the speed of the trains added
Calculation:
Let the speed of the first train & second train be x m/s and y m/s respectively.
Length of the first train is 28x metres
Length of the second train is 10y meters
According to the question,
⇒ 24 = (28x + 10y) / (x + y)
⇒ 24x + 24y = 28x + 10y
⇒ 14y = 4x
⇒ x/y = 7/2
∴ The ratio of the speed of the train is 7 : 2.
Find the average speed of train if it covers first half of the distance at 3 kmph and second half of the distance at 6 kmph.
Answer (Detailed Solution Below)
Problem on Trains Question 15 Detailed Solution
Download Solution PDFGiven:
Train covers first half of the distance at 3 kmph and second half of the distance at 6 kmph.
Formula used:
When distance is equal, Average speed = [2 × S1 × S2] / [S1 + S2]
Calculation:
Average speed = (2 × 3 × 6)/(3 + 6)
⇒ 36 / 9
⇒ 4 kmph
∴ The average speed is 4 kmph
Alternate Method
Let total distance be 36 km.
Time taken to cover 1st half distance = 18/3 = 6 hr
Time taken to cover 2nd half distance = 18/6 = 3 hr
∴ Average speed = Total distance/Total time = 36/(6 + 3) = 36/9 = 4 km/h