Train Crossing a Running Man or Object MCQ Quiz - Objective Question with Answer for Train Crossing a Running Man or Object - Download Free PDF

Given:

Length of train = 450 m

Speed of train = 65 km/hr

Time taken to cross man = 27 sec

Formula used:

Relative Speed = \(\frac{\text{Distance}}{\text{Time}}\)

If moving in same direction: Relative speed = Train speed − Man speed

If opposite direction: Relative speed = Train speed + Man speed

Calculations:

Relative speed = \(\frac{450}{27} \times \frac{18}{5} = 60\) kmph

Let man's speed be x kmph

If same direction: \(65 - x = 60\)

⇒ \(x = 65 - 60 = 5\) kmph

If the opposite direction: \(65 + x = 60\)

⇒ \(x = 60 - 65 = -5\) kmph

Negative speed is not possible. So, the man is moving in the same direction as the train at 5 km/hr.

∴ The correct answer is Option (3).

Given:

Length of train 1 = 240 m

Speed of train 1 = 200 km/hr

Length of train 2 = 180 m

Speed of train 2 = 160 km/hr

Formula used:

Time taken to cross each other = \(\dfrac{\text{Sum of lengths of trains}}{\text{Relative speed}}\)

Relative speed (opposite direction) = Speed₁ + Speed₂

Calculations:

Relative speed = 200 km/hr + 160 km/hr

⇒ Relative speed = 360 km/hr

⇒ Relative speed = 360 × \(\dfrac{5}{18}\) m/s

⇒ Relative speed = 100 m/s

Sum of lengths of trains = 240 m + 180 m

⇒ Sum of lengths = 420 m

Time taken = 420/100

⇒ Time taken = 4.2 seconds

∴ The correct answer is option (4).

Given:

Length of truck = 1600 m

Length of train = 1500 m

Speed of truck = 112 km/hr

Speed of train = 82 km/hr

Formula used:

Relative speed (same direction) = Difference of speeds

Time = Total distance / Relative speed

1 km/hr = 5/18 m/s

Calculation:

Relative speed = (112 - 82) km/hr = 30 km/hr

= 30 × 5/18 = 25/3 m/s

Total distance = 1600 + 1500 = 3100 m

Time = 3100 ÷ (25/3)

= 3100 × 3 / 25 = 372 seconds

∴ The truck will take 372 seconds to cross the train.

Given:

Speed of Train 1 = 136 km/h

Speed of Train 2 = 44 km/h

Time taken to cross Train 2 = 6 s

Time taken to cross the platform = 45 s

Length of Train 1 = L₁

Length of Train 2 = L₂ = L₁/2

Find the length of the platform.

Formula Used:

Relative Speed (in m/s) = (Speed of Train 1 + Speed of Train 2) × (5/18)

Distance = Speed × Time

Calculation:

Relative Speed of trains = (136 + 44) × (5/18)

⇒ Relative Speed = 180 × (5/18)

⇒ Relative Speed = 50 m/s

Distance covered to cross Train 2 = Relative Speed × Time

⇒ L₁ + L₂ = 50 × 6

⇒ L₁ + L₁/2 = 300

⇒ (3L₁/2) = 300

⇒ L₁ = (300 × 2)/3

⇒ L₁ = 200 m

Speed of Train 1 (in m/s) = 136 × (5/18)

⇒ Speed = 37.78 m/s

Distance covered to cross the platform = Speed × Time

⇒ L₁ + Platform Length = 37.78 × 45

⇒ 200 + Platform Length = 1700

⇒ Platform Length = 1700 - 200

⇒ Platform Length = 1500 m

The length of the platform is 1500 m.

Given:

Length of Train 1 (L1) = 280 m

Speed of Man (S_man) = 5 km/h

Time taken to overtake man (T1) = 42 seconds

Length of Train 2 (L2) = 500 m

Speed of Train 2 (S2) = 43 km/h (opposite direction)

Calculation:

When a train overtakes a man, the distance covered is the length of the train. The relative speed is (Speed of train - Speed of man).

Let the speed of Train 1 be S1 km/h.

Relative speed (S_rel1) = (S1 - 5) km/h = (S1 - 5) × (5/18) m/s

Distance (L1) = 280 m

Time (T1) = 42 seconds

Using Distance = Speed × Time:

280 = (S1 - 5) × (5/18) × 42

280 = (S1 - 5) × (210/18)

280 = (S1 - 5) × (35/3)

(280 × 3) / 35 = S1 - 5

840 / 35 = S1 - 5

24 = S1 - 5

S1 = 24 + 5 = 29 km/h

Total distance to cross (D) = L1 + L2 = 280 + 500 = 780 m

Speed of Train 1 (S1) = 29 km/h

Speed of Train 2 (S2) = 43 km/h

Relative speed (S_rel2) = S1 + S2 (since they are moving in opposite directions)

S_rel2 = 29 km/h + 43 km/h = 72 km/h = 72 × (5/18) = 4 × 5 = 20 m/s

Time taken (T2) = Total distance / Relative speed

T2 = 780 m / 20 m/s

T2 = 39 seconds

∴ It will take 39 seconds for the first train to completely cross the second train.

Given:-

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

Given:

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.

Detailed solution:

Let the speed of train A be x km/h.

Speed of train B = (x – 16) km/h

According to the question

\(\Rightarrow \frac{{96}}{{x - 16}} - \frac{{96}}{x}{\rm{}} = {\rm{}}1\)

\(\Rightarrow \frac{{96{\rm{\;}} \times {\rm{\;}}16}}{{x\left( {x - 16} \right)}}{\rm{}} = {\rm{}}1\)

⇒ x² – 16x = 96 × 16

⇒ x² – 16x – 1536 = 0

⇒ (x – 48) (x + 32) = 0

⇒ x = 48 and x = -32 (not possible)

∴ Speed of train A = 48 km/h

Shortcut Trick Go through the options

Let the speed of train be 48 km/h.

And speed of train B = 48 – 16 = 32

⇒ (96/32) – (96/48) = 1

⇒ 3 – 2 = 1

⇒ 1 = 1 (Satisfied)

Given Data:

Length of the train = 300 m.

Time to cross a tree = 20 sec.

Time to cross another train = 25 sec.

Formula:

Speed = Distance/Time

Solution:

⇒ Speed of first train = Length of train/Time = 300/20 = 15 m/s.

⇒ Relative speed while crossing the second train = Total length/Time

= (300 + 300) / 25 = 24 m/s.

⇒ Speed of the second train = Relative speed - Speed of the first train

= 24 - 15 = 9 m/s 

Hence, the speed of the second train is 9 m/s.

Given data:

Speed of first train: 54 km/h

Speed of second train: 90 km/h

Time taken to cross each other: 12 seconds

Concept: The combined length of two trains equals the relative speed multiplied by the time taken to cross each other.

⇒ Convert speeds from km/h to m/s (multiply by 5/18): 15 m/s and 25 m/s

⇒ Relative speed = 15 + 25 = 40 m/s

⇒ Combined length of trains = 40 m/s x 12 seconds = 480 metres

⇒ Length of each train = 480 metres / 2 = 240 metres

Therefore, the length of each train is 240 metres.

Given:

Length of race is 117m

Speed of A is 30% more than speed of B

Concept Used:

To end the race in a dead heat, both players should reach the finish point at the same time.

Formula Used:

Time = Distance/Speed

Calculation:

Let the speed of B be 10 m/s

⇒ Speed of A = 13 m/s

Time required by A to complete the race

⇒ 117/13 = 9 seconds

Distance covered by B in 9 seconds

⇒ 9 × 10 = 90 m

Required head start = 117 - 90 = 27 m

∴ A should give B a head start of 27 m to end the race in a dead heat.

Given:

Length of train 1 (l₁) = 230m.

Length of train 2 (l₂) = 325m.

Distance between the trains (d) = 145m.

Speed of train 1 (v₁) = 122 km/h

Speed of train 2 (v₂) = 130 km/h

Concept used:

To convert the speed in km/h to m/s, we use

speed in km/hr × (5 / 18) = speed in m/s.

Time taken to cross each other can be found as:

v₁ + v₂ = (l₁ + l₂ + d) / t

where

v₁ = speed of train 1

v₂ = speed of train 2

l₁ = length of train 1

l₂ = length of train 2

d = distance between the trains

t = time taken to cross each other.

Solution:

Using the above formula we get:

v₁ + v₂ = (l₁ + l₂ + d) / t

(122 + 130) × 5 / 18 = (230 + 325 + 145) / t

252 × 5 / 18 = 700 / t

t = (700 × 18) / (252 × 5)

t = 140 × 1 / 14

t = 10 seconds.

∴ The trains will cross each other in 10 seconds.

∵ The ratio of speeds of two trains is 4 : 7;

Suppose the speed of the trains are 4x & 7x respectively;

∵ Both the trains can cross a pole in 12 seconds;

∴ Length of 1^st train = 4x × 12 = 48x

Length of 2^nd train = 7x × 12 = 84x

∵ The train and cyclist are moving in the same direction,

Relative speed = 84 – 12 = 72 km/hr. = 72 × 5/18 = 20 m/sec.

Now, time taken to cross cyclist = Length of train/relative speed

⇒ 13.5 = Length of train/20

Speed of the train = 63 kmph

Length of train = 340 m

Time taken by train to pass the man = 18 s

Relative speed \(= \frac{{{\rm{Length\;of\;train\;}}}}{{{\rm{Time\;taken\;by\;train\;to\;pass\;the\;man}}}} = \frac{{340}}{{18}} = \frac{{170}}{9}\) m/s

Relative speed \(= \frac{{170}}{9} \times \frac{{18}}{5} = 68\) kmph

Since, they travel in the opposite direction

Relative speed = Speed of train + Speed of man