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 crosses 100 m and 60 m long tunnels in 12 seconds and 8 seconds, respectively. Find the length and speed of the train.

  1. 20 m, 36 km/h

  2. 35 m, 54 km/h

  3. 40 m, 72 km/h

  4. 50 m, 90 km/h

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

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

Length of the train be L m.

Length of the first tunnel = T m 

Length of the second tunnel = t m

The train crosses the first tunnel in 12 seconds, so

t = (L + T)/V

12 = (L + 100)/V

12V - L = 100 --------------------(1) 

Similarly, 8 = (L + 60)/V 

8V - L = 60 -----------------------(2) 

From (1) and (2),

V = 10 m/s = 36 km/h 

Now, putting the value of V in equation (1),

12V - L = 100

12(10) - L = 100

L = 20 m

So, length of the train is 20 m and speed is 36 km/h.

Multiple choice

A train, running at a speed of 96 km/h, crosses a man running at a speed of 6 km/h in the opposite direction in 3 seconds. Find the length of the train.

  1. 170 m

  2. 255 m

  3. 340 m

  4. 85 m

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

Let the length of the train be L m.

Speed of the train (V) = 96 km/h = 96 * 5/18 = 80/3 m/s

Speed of the man (v) = 6 km/h = 6 * 5/18 = 5/3 m/s

Now, by using this shortcut formula,

t = L/(V + v) 

3 = L/(80/3 + 5/3)

L = 85 m, so length of the train is 85 m.

Multiple choice

Two trains, 140 m and 110 m long, are going in the same direction. The faster train takes 50 seconds to pass the other train completely. If they are moving in opposite directions, they pass each other completely in 5 seconds. Find the speed of both the trains.

  1. 99 km/h, 81 km/h

  2. 55 km/h, 45 km/h

  3. 90 km/h, 80 km/h

  4. 72 km/h, 54 km/h

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

Length of the faster train (L) = 140 m

Length of the slower train (l) = 110 m

Speed of the faster train = V km/h 

Speed of the slower train = v km/h 

Now, by using the formula,

t = (L +l)/(V - v) 

50 = (140 + 110)/(V - v) 

V - v = 5 ----------------(1) 

Similarly,

t = (L + l)/(V + v) 

5 = (140 + 110)/(V + v) 

V + v = 50 -----------------(2) 

From (1) and (2),

V = 55/2 = (55/2) * (18/5) = 99 km/h

v = (45/2) * (18/5) = 81 km/h So, the speed of the faster train is 99 km/h and the speed of the slower train is 81 km/h.

Multiple choice

A train 110 m in length travels at 60 km/h. How much time does the train take in passing a man walking at 6 km/h in the opposite direction of the train?

  1. 5.67 s

  2. 7.34 s

  3. 1.67 s

  4. 6 sec

  5. 5.82 sec
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relative speed of the train and the man=(60+6) =66km/h =66 *5/18 m/s Distance=110m Therefore, Time taken in passing the man =Distance/Speed                                                                                                     =(110*18)/(66*5)
=6 s It is the correct answer.

Multiple choice

A 280 metre long train moving with an average speed of 108 km/h crosses a platform in 12 seconds. A man crosses the same platform in 10 seconds. What is the speed of the man?

  1. 5 m/s

  2. 8 m/s

  3. 12 m/s

  4. Cannot be determined

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

Speed of train = 108 km/hr = (108*5/18) = 30 m/sec Let the length of the platform be x meters Then, x + 280 m = 360 m x = (360-280) m = 80 m Then, the speed of man = (80 m)/ (10 s) = 8 m/s

Multiple choice

Two trains of equal lengths take 10 seconds and 15 seconds to pass a telegraph post. If the length of each train is 120 metres, then in what time (in seconds) will they pass each other travelling in opposite directions?

  1. 10 seconds

  2. 15 seconds

  3. 12 seconds

  4. 20 seconds

  5. 25 seconds
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed of the first train = 120/10 = 12 m/sec Speed of the second train =120/15 = 8 m/sec Relative speed = (12 + 8) = 20 m/sec Therefore, the required time = (120 + 120)/20 = 12 sec

Multiple choice

Two trains of equal lengths are running on parallel tracks in the same direction at the speeds of 58 km/h and 48 km/h, respectively. The faster train passes the slower train in 54 sec. The length of each train is

  1. 100 m

  2. 435 m

  3. 150 m

  4. 75 m

  5. 360 m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the length of each train be x metres.

Then, the total distance covered by the faster train in 54 sec = (x + x) = 2x m

Relative speed = (58 - 48) km/h

                      = 10 km/h                                           = (10 * 5)/18 m/s (since both trains are moving in the same direction)

Hence, time = distance/speed

54 = 2x/(50/18)

54 = (2x * 18)/50

x = (54 * 50)/(18 * 2)

x = 3 * 25 x = 75 m

It is the correct answer.

Multiple choice

Two trains move in the same direction at 50 Kmph and 32 Kmph respectively. A man in the slower train observes the 15 seconds elapse before the faster train completely passes by him. What is the length of faster train?

  1. 100m

  2. 75m

  3. 120m

  4. 50m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When two objects move in the same direction, their relative speed is the difference of their speeds. Here, relative speed = 50 - 32 = 18 kmph = 5 m/s. In 15 seconds, the faster train covers length = relative speed × time = 5 × 15 = 75m. This is the length needed for the faster train to completely pass the observer.