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 general knowledge math & puzzles

Two trains A and B which run at constant speed are running on parallel tracks.After crossing eact other they take 36minutes and 144minutes to reach their destinations which is to exchange their positions.What is the ratio of their speeds of A and B.

  1. 0.5

  2. 2

  3. 2.4

  4. 4.8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The ratio of speeds of two objects starting from A and B and meeting at a point, then reaching their destinations in times t1 and t2, is given by SpeedA / SpeedB = sqrt(t2 / t1). Here, sqrt(144 / 36) = sqrt(4) = 2.

Multiple choice general knowledge math & puzzles

A train of 77m length is running at a speed of 60 km/hour. If it crosses a bridge in 30 seconds, then find the length of the bridge.

  1. 403 m

  2. 423 m

  3. 412 m

  4. 396 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First convert speed: 60 km/h = 60 × (1000/3600) = 16.67 m/s. Distance covered in 30 seconds = 16.67 × 30 = 500 m. This distance equals train length + bridge length, so bridge = 500 - 77 = 423 m. The train's length must be added to the bridge length when calculating total crossing distance.

Multiple choice

At 9 a.m, train T left the station and two hours later train S left the same station on a parallel track. If train T averaged 60 kilometers per hour and train S averaged 75 kilometers per hour until S passed T, at what time did S pass T?

  1. 2 p.m

  2. 5 p.m

  3. 6 p.m

  4. 7 p.m

  5. 9 p.m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If the two trains met x hours after the first train left the station, we get the equation 60x = 75(X - 2). So, 15x = 150, or x = 10. So, the two trains would meet 10 hours after 9 a.m, or at 7 p.m.

Multiple choice

A train travelling with a uniform speed crosses a 180 m long platform in 16 seconds and a 125 m long platform in 14 seconds. Find the speed of the train.

  1. 17.5 km/hr

  2. 35.5 km/hr

  3. 63 km/hr

  4. 30 km/hr

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

Let the length of the train be x m.

Then, the speed of the train to cross both the platforms is the same. 

(x + 160)/16 = (x + 125)/14 

After solving, we get

x = 120 m

So, the speed of the train is (120 + 160)/16 = 35/2 m/s = (35/2) * (18/5) = 63 km/hr.

Multiple choice

A train crosses two persons travelling at the rates of 6 km/hr and 8 km/hr in the same direction in 12 sec and 16 sec, respectively. Find the speed of the train.

  1. 14 km/hr

  2. 20 km/hr

  3. 16 km/hr

  4. 24 km/hr

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

Let the speed of the train be x km/hr. So, speed of the train with first person in the same direction = (x - 6) km/hr  And speed of the train with second person in the same direction = (x - 8) km/hr So, the length of the train = (x - 6) * 12/60 = (x - 8) * 16/60 After solving, we get  x = 14 So, speed of the train = 14 km/hr

Multiple choice

A train passes a platform and a man standing on the platform in 24 seconds and 10 seconds, respectively. If the speed of the train is 72 km/h, then find the length of the platform.

  1. 480 m

  2. 380 m

  3. 280 m

  4. 580 m

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

Speed of the train (V) = 72 km/h = 72 * 5/18 = 20 m/s 

Length of the train = L m and length of the platform = l m 

Time taken by the train to cross the man is 10 seconds. 

So, t = L/V 

10 = L/20

L = 200 m 

Now, time taken by the train to cross the platform is 24 seconds. 

So, t = (L + l)/V 

24 = (200 + l)/20 

l = 280 m

So, the length of the train is 280 m.

Multiple choice

A train crosses a man standing on a 140 m long platform in 5 seconds and crosses the platform completely in 15 seconds. Find the length and speed of the train.

  1. 84 m, 50.4 km/h

  2. 70 m, 50.4 km/h

  3. 84 m, 54 km/h

  4. 72 m, 60.4 km/h

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

Let the length of the train be L m and the length of the platform be l m.

Let the speed of the train be V km/h.

The train crosses the platform in 15 seconds. 

So, t = (L + l)/V 

15 = (L + 140)/V -------------------------(1),

Now,the train crosses the man in 5 seconds. 

So, t = L/V

5 = L/V

L = 5V ---------------------------------(2),

From (1) and (2),

V = 14 m/s = 14 * 18/5 = 50.4 km/h

Now, putting the value of "V" in equation (2), we get

L = 5V 

L = 5*14 

L = 70 m 

So, the length and speed of the train are 70 m and 50.4 km/h, respectively.

Multiple choice

A train overtakes two persons who are walking in the same direction in which the train is running, at the rates of 3 kmph and 5 kmph, and passes them completely in 10 and 12 seconds, respectively. Find the length of the train.

  1. 70 m

  2. 50 m

  3. 60 m

  4. 75 m

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

Let the speed of the train be x m/s.

Then, speed of the train in the same direction with respect to first person = x - 3 * 5/18 = (x - 5/6) m/s 

Now, speed of the train in the same direction with respect to second person = x - 5 * 5/18 = (x - 25/18) m/s 

So, length of the train is (x - 5/6) * 10 = (x - 25/18) * 25/18.

After solving, we get

x = 25/3 m/s

So, the speed of the train is 25/3 m/s,

Then, length of the train is (25/3 - 5/6) * 10 = 75 m.

Multiple choice

A train running at 24 km/h takes 12 seconds to pass a platform. Next, it takes 8 seconds to pass a man walking at 8 km/h in the same direction. Find the length of the platform and the length of the train.

  1. 30 m, 40 m

  2. 30 m, 60 m

  3. 44 m, 36 m

  4. 55 m, 30 m

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

Let the length of the train be L m. 

Let the length of the platform be l m.

Speed of the train (V) = 24 km/h = 24 * 5/18 = 20/3 m/s

Speed of the man (v) = 8 km/h = 8 * 5/18 = 20/9 m/s

The train takes 8 seconds to pass the man. 

So, t = L/(V - v) 

8 = L/(20/3 - 20/9) 

L = 320/9

L = 35.55 m = 36 m (approximately) 

So, length of the train = 36 m 

Now, the train takes 12 seconds to cross the platform. 

So, t = (L + l)/V 

12 = (320/9 + l)/(20/3) 

l = 400/9

l = 44.44 m = 44 m (approximately) 

So, the length of the platform is 45 m and that of the train is 36 m.

Multiple choice

Two trains of lengths 360 m and 540 m are running in opposite directions on parallel tracks. If their speeds are 45 km/h and 36 km/h, respectively, then in what time will they cross each other?

  1. 30 seconds

  2. 40 seconds

  3. 20 seconds

  4. 50 seconds

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

Length of the first train (L) be 360 m

Length of the second train (l) = 540 m

Speed of the first train (V) = 45 km/h = 45 * 5/18 = 25/2 m/s

Speed of the second train (v) = 36 km/h = 36 * 5/18 = 10 m/s

So, the required time to cross each other is,

t = (L + l)/(V + v) 

t = (360 + 540)/(25/2 + 10)

t = 40 seconds

Multiple choice

Two trains are running in the same direction at 50 km/h and 30 km/h. The faster train crosses a man in the slower train in 30 seconds. Find the length of the faster train.

  1. 168 m

  2. 180 m

  3. 167 m

  4. 200 m

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

The man is in the slower train, so the speed of the slower train is equal to the speed of the man.

Now, let the speed of the faster train be L m.

So, using the following formula:

t = L/( V - v)

30 = L/((50 - 30) * 5/18)

L = 166.6 

L = 167 m So, the length of the faster train is 167 m.

Multiple choice

A train running with a speed of 108 km/h crosses a bridge in 5 seconds. Another train, 70 m shorter, crosses the same bridge at 72 km/h. Find the time taken by the second train to cross the bridge.

  1. 7 seconds

  2. 3 seconds

  3. 6 seconds

  4. 4 seconds

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

Let the length of the first train be L m.

Length of the second train = (L - 70) m

And length of the bridge = x m 

Speed of first train (V) = 108 km/h = 108 * 5/18 = 30 m/s

Speed of second train (v) = 72 km/h = 72 * 5/18 = 20 m/s

Now,

t = (L + x)/V 

5 = (L + x)/30 

L + x = 150 -------------------------(1)

Similarly,

t = (L - 70 + x)/20 ----------------(2) 

Now, putting the value of (L + x) in (2), we get

t = (150 - 70)/20 

t = 4 seconds

Multiple choice

A train, 60 m long, overtakes a man who is walking at the rate of 9 km/h and crosses him in 4 seconds. Again, the train overtakes another person in 4.8 seconds. At what rate is the second person travelling?

  1. 18 km/h

  2. 12 km/h

  3. 10 km/h

  4. 8 km/h

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

Let the length of the train (L) be 60 m.

Speed of the train = V km/h

Speed of the first man (v1) = 9 km/h = 9 * 5/18 = 5/2 m/s

Let the speed of the second man be v2.

Now, 4 seconds are taken by the train to cross the first person.

t = L/(V - v1) 

4 = 60/(V - 5/2)

V = 35/2

So, the speed of the train is 35/2 m/s. 

Now, time taken by the train to cross the second person is 4.8 seconds.

Then, t = L/(V - v2) 

4.8 = 60/(35/2 - v2) 

v2 = 5 m/s = 5 * 18/5 = 18 km/h, so the speed of the second person is 18 km/h.