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:

Time to cross a point = 27/2 sec

Speed of the train = 30 km/h

Formula used:

Length of the train = Speed × Time

Calculation:

Speed = 30 × (5/18) = 25/3 m/s

⇒ Length of Train = Speed × Time

⇒ Length = (25/3) × (27/2)

⇒ Length = 112.5 meters

∴ The correct answer is option (1).

Calculation

Trains: 180 m and 270 m

Speeds: 72 km/hr and 90 km/hr ⇒ 20 m/s and 25 m/s

Opposite direction ⇒ Relative speed = 45 m/s

Time to cross each other in n sec

Distance=180 + 270 = 450m

⇒n = 450 / 45 = 10 sec

Smaller train (180 m) crosses bridge in 25n = 25 × 10 = 250 sec

Speed = 72 km/hr = 20 m/s

Distance = 20 × 250 = 5000 m

⇒Bridge length = 5000 − 180 = 4820 

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 each carriage = 40 m.

Total number of carriages = 45.

Length of engine = 120 m.

Speed of train = 54 km/hr.

Length of bridge = 1200 m.

Formula Used:

Time = Total Distance / Speed

Calculation:

Total length of train = Length of engine + (Number of carriages × Length of each carriage)

⇒ Total length = 120 + (45 × 40)

⇒ Total length = 120 + 1800

⇒ Total length = 1920 m

Total distance to pass the bridge = Length of train + Length of bridge

⇒ Total distance = 1920 + 1200

⇒ Total distance = 3120 m

Speed of train in m/s = (54 × 1000) / 3600

⇒ Speed = 15 m/s

Time = Total Distance / Speed

⇒ Time = 3120 / 15

⇒ Time = 208 s

The time taken by the train to pass the bridge is 208 seconds.

Given:

Length of train (L) = 150 m

Speed of train (S) = 54 km/hr

Formula used:

Time (T) = Distance ÷ Speed

Note: Speed needs to be converted from km/hr to m/s.

Calculation:

Speed in m/s = 54 × (1000 ÷ 3600)

⇒ Speed = 15 m/s

Time = 150 ÷ 15

⇒ Time = 10 seconds

∴ The correct answer is option (2).

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

Given:

Length of first train = 150 m

Speed of first train = 54 km/hr

Length of second train = 200 m

Speed of second train = 72 km/hr

Concept used:

Suppose two bodies are moving with speeds x km/h and y km/h respectively, then

If bodies moving in opposite direction = (x + y) km/h

If bodies moving in same direction = (x - y) km/h

Formula used:

Speed = Distance/Time

1 km/h = 5/18 m/s

Calculation:

Since both trains are running opposite to each other,

So, their relative speed = 54 + 72 = 126 km/h

Speed (in m/s) = 126 km/h = 126 × 5/18 = 7 × 5 = 35 m/s

Total distance = length of trains = 150 + 200 = 350 m

So, time required to cross each other = 350 / 35 = 10 sec

∴ The time taken to cross each other is 10 seconds.

∵ 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