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 maths compound measures and motion kinetic graphs time - calcuation of distance travel graphs

Two goods train each 500 m long, are running in opposite direction on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

  1. 12 sec

  2. 24 sec

  3. 48 sec

  4. 60 sec
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Relative speed = (45 + 30) km/hr
$ = \left ( 75 \times \dfrac{5}{18} \right ) m/sec$
$= \left( \dfrac{125}{6} \right) m/sec.$
We have to find the time taken by the slower train to pass the Driver of the faster train and not the complete train.
So, distance covered = Length of the slower train.
Therefore, Distance covered = 500 m.
$\therefore$ Required time $\left( 500 \times \dfrac{6}{125} \right ) = 24 sec.$

Multiple choice maths compound measures and motion kinetic graphs time - calcuation of distance travel graphs

After travelling for 30 minutes a train meets an accident, due to which it has to stop for 45 minutes. Due to the accident its speed is also reduced to 2/3 of its former value and the train reaches its destination 1 hour 30 minutes late. Had the accident occurred 60 km later, the train would have reached 30 minutes earlier. The length of the journey is

  1. 90 km

  2. 120 km

  3. 150 km

  4. 180 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the length of Journey = x km, and
Speed of the train = v km/hr

$\displaystyle\therefore30:min.+45:min.+\frac{\displaystyle\left(x-\frac{v}{2}\right)}{\displaystyle\frac{2}{3}v}$

$\displaystyle=\frac{x}{v}+1:hour:30:min.$

$\displaystyle\implies\frac{1}{2}+\frac{3}{4}+\frac{\displaystyle\frac{2x-v}{2}}{\displaystyle\frac{2v}{3}}=\frac{x}{v}+\frac{3}{2}$

$\displaystyle\implies\frac{3(2\times-v)}{4v}=\frac{x}{v}+\frac{1}{4}$

$\displaystyle=\frac{4x+v}{4v}$

$2x=4v$ ....(i)

Again, it accident occurred 60 kms later,

$\displaystyle\therefore30:min.+\frac{60}{v}+45:min.+\frac{\displaystyle\left(x-60-\frac{v}{2}\right)}{\displaystyle\frac{2}{3}v}$

$\displaystyle=\frac{x}{v}+1:hour:30:min.-30:min.$

$\displaystyle\implies\frac{1}{2}+\frac{60}{v}+\frac{3}{4}+\frac{3(2x-120-v)}{4v}=\frac{x}{v}+1$

$\displaystyle\implies\frac{x}{v}-\frac{60}{v}-\frac{3(2x-120-v)}{4v}=\frac{5}{4}-1$

$\displaystyle\implies\frac{4x-240-6x+360+3v}{4v}=\frac{1}{4}$

$\implies2x=2v+120$ ....(ii)
Solving eq. (i) and eq. (ii), we get
$\therefore x=120:km$

Multiple choice physics along with motion motion around us motion and rest moving things around us

A train of length 200 m traveling at $30 { ms }^{ -1 }$ overtakes another train of length 300 m traveling at $20 { ms }^{ -1 }$. The time taken by the first train to pass the second is 

  1. 10 s

  2. 30 s

  3. 40 s

  4. 50 s
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The relative speed of the first train with respect to the second is 30 - 20 = 10 m/s. The total distance to be covered to overtake is the sum of the lengths of both trains: 200 + 300 = 500 m. Time = Distance / Relative Speed = 500 / 10 = 50 s.

Multiple choice physics accelerated motion calculus methods of motion equations equation of motion the equation of motion and its derivation

Two trains A and B each of length 400m Are moving on two parallel tracks The same direction (while A is ahead of B) With same speed 72 km / h.The driver of B decides to overtake And accelerate by $1m/{ s }^{ 2 }$. If after 50 seconds B Just brushes past A, Calculate the original distance between A and B


  1. $850m$
  2. $1000m$
  3. $1250m$
  4. $2250m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice maths number work indian place value chart place value of digit largest and smallest numbers writing and expanding numbers

A train overtakes two persons who are walking in the same direction in which the train is going at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

  1. 20 m

  2. 30 m

  3. 40 m

  4. 50 m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let the length of the train be x metres and speed  be y $m/s$

Speed of the first person$=2kmph$

                                          $=2\times\dfrac{5}{18}$

                                            $=\dfrac{5}{9}m/s$

Speed of the second train $=4kmph$

                                              $=4\times\dfrac{5}{18}$

                                               $=\dfrac{10}{9}m/s$

$\dfrac{x}{y-\dfrac{5}{9}}=9$

$9y-5=x$   
                                       
$90y-50=10x$...........................................(1)

                                            
$\dfrac{x}{y-\dfrac{10}{9}}=10$

$90y-100=9x$...........................................(2)

Substracting $1$ and $2$

$90y-50-90y+100=10x-9x$

$x=50$

So, the length of the train$=50m$



Multiple choice maths measurement (length) conversion of length using decimals in units of length define weight and units of weight how much does it weigh?

A train $280 m$ long, running with a speed of 63$\mathrm { km } /$ hr will pass a tree in 

  1. $15 sec$
  2. $16 sec$
  3. $18 sec$
  4. $20 sec$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$Speed\>of\>train\>=\>63(\dfrac{Km}{hr})\\=(\dfrac{63\cdot100m}{3600s})\\=17.5(\dfrac{m}{s})\\By\>passing\>a\>tree,\>train\>will\>have\>to\>cross\>its\>own\>length\\\therefore\>Time\>taken\>=\>(\dfrac{280}{17.5})=16sec$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

Choose the correct answer from the alternatives given.
The ratio of length of two trains is 5 : 3 and the ratio of their speed is 6: 5. The ratio of time taken by them to cross a pole is

  1. $5 :6$
  2. $11:8$
  3. $25: 18$
  4. $27: 16$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

It is given that,
$\displaystyle \dfrac{l _1}{l _2} \, = \, \dfrac{5}{3} \, and \, \dfrac{s _1}{s _2} \, = \, \dfrac{6}{5} \, \Rightarrow \, \dfrac{t _1}{t _2} \, = \, \frac{s _1}{l _2} \, = \, \dfrac{l _1}{l _2} \, \times \, \dfrac{s _2}{s _1} \, = \, \dfrac{5}{3} \, \times \, \dfrac{5}{6} \, = \, \dfrac{25}{18}$
Hence, $t _1 : t _2$ = $25 : 18$

Multiple choice business maths linear programming problems structure of linear programming model linear programming problem operations research

A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

  1. $400 m$
  2. $200 m$
  3. $600 m$
  4. $250 m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the length of the first train be $x$ metres


length of the second train$=\dfrac{x}{2}$m


relative speed of the two trains$=48+42$

                                                    $=90kmph$

                                                    $=90\times\dfrac{5}{18}$

                                                    $=25m/s$

$25=\dfrac{x+\dfrac{x}{2}}{12}$

$25=\dfrac{2x+x}{24}$

$3x=25\times24$

$x=25\times8$

$x=200$

So, the length of the train $=200m$

Let the length of the platform be y

Speed of the train $=48 kmph$

                                 $=48\times\dfrac{5}{18}$

                                  $=\dfrac{40}{3}m/s$

$\dfrac{40}{3}=\dfrac{200+y}{45}$

$40\times45=600+3y$

$1800=600+3y$

$3y=1200$

$y=400$

So, the length of the platform$=400m$


Multiple choice maths fractions, decimals and rational numbers representation of rational numbers on number line rational numbers on the number line rational numbers between two rational numbers

A train of length 180 m crosses a man standing on a platform in 12 seconds and cross another train coming from opposite direction in 12 sec. If the second train running at 2/3 rd speed of the firstthen find the length of the second train?

  1. 56

  2. 120

  3. 20

  4. 44
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Length of the first train$=180m$


 Time taken by  the train to cross the man standing on the platform$=12s$


Speed of the first train$=\dfrac{180}{12}$

                                      $=15m/s$

Speed of the second train$=\dfrac{2}{3}\times15$

                                            $=10m/s$

Relative speed$=15+10$

                          $=25m/s$
 
Let the length of the train be $y$ metres.

$Distance =Speed\times time$

$y+180=25\times12$

$y+180=300$

$y=300-180$
$y=120$
So, the length of the second train$=120m$

Multiple choice time speed and distance problems involving speed word problems on speed time and distance time and distance word problems on simultaneous equations applications of simultameous equations unitary method idea of speed distance and time speed math time work and distance ratio and proportions linear equations in two variables maths

A goods train of length 500 m transverse a 2-km-long tunnel at a constant speed of 36 km/hour. The time needed for the train to completely pass through the tunnel is

  1. 3 minutes 20 seconds

  2. 4 minutes 10 seconds

  3. 4 minutes 40 seconds

  4. 6 minutes 10 seconds
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance to cover = 2000 m + 500 m = 2500 m = 2.5 km. Speed = 36 km/hr = 10 m/s. Time = distance / speed = 2500 / 10 = 250 seconds. 250 seconds = 4 minutes and 10 seconds.

Multiple choice

A train passes a telegraph pole in 10 seconds and a platform 200 meters long in 20 seconds. What is the speed of the train in kilometers per hour?

  1. 36 km/h

  2. 48 km/h

  3. 60 km/h

  4. 72 km/h
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The speed of the train can be calculated using the formula speed = distance / time. The distance traveled by the train in 10 seconds is the length of the telegraph pole, which is negligible. Therefore, the distance traveled by the train in 20 seconds is 200 meters. The speed of the train is therefore 200 / 20 = 10 meters per second. Converting this to kilometers per hour, we get 10 * 3600 / 1000 = 72 km/h.

Multiple choice

A train crosses a 100-meter long platform in 10 seconds and a 200-meter long bridge in 30 seconds. What is the speed of the train in km/h?

  1. 72 km/h

  2. 80 km/h

  3. 88 km/h

  4. 96 km/h
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speed = Distance / Time. To find the speed of the train, we need to convert the distances and times to the same units. Converting 100 meters to kilometers: 100 meters = 0.1 kilometers. Converting 200 meters to kilometers: 200 meters = 0.2 kilometers. Converting 10 seconds to hours: 10 seconds = 10/3600 hours = 1/360 hours. Converting 30 seconds to hours: 30 seconds = 30/3600 hours = 1/120 hours. Speed of the train when crossing the platform = 0.1 km / (1/360) h = 36 km/h. Speed of the train when crossing the bridge = 0.2 km / (1/120) h = 24 km/h. Average speed of the train = (36 km/h + 24 km/h) / 2 = 30 km/h. Converting 30 km/h to km/h: 30 km/h = 30 * 18/5 km/h = 88 km/h.

Multiple choice

A train leaves a station at 10:00 AM and travels at a speed of 60 mph. Another train leaves the same station at 11:00 AM and travels in the same direction at a speed of 75 mph. At what time will the second train overtake the first train?

  1. 12:00 PM

  2. 12:30 PM

  3. 1:00 PM

  4. 1:30 PM
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The second train travels 75 mph - 60 mph = 15 mph faster than the first train. Therefore, it takes 1 hour for the second train to cover the distance that the first train travels in 1 hour. Since the second train leaves 1 hour after the first train, it will overtake the first train 1 hour after 11:00 AM, which is 1:00 PM.