21. A train 120 m long crosses a platform of length 100 m in 10 seconds. What is its speed?
      120 मीटर लंबी एक ट्रेन 10 सेकंड में 100 मीटर की लंबाई के एक प्लेटफॉर्म को पार करती है। उसकी गति क्या है?

Option “B” is correct.

Length of the train and platform are 120 m and 100 m respectively.

As we know,

Speed = Distance/time

Speed = (120 + 100)/10

Speed = 220/10

Speed = 22 m/sec

As we know,

22 m/sec = 22 × (18/5) = 79.2 km/hr

22. A bus passes two bridges of length 500 m and 325 m in 90 seconds and 60 seconds respectively. The length (in m) of the bus is

एक बस क्रमशः 90 सेकंड और 60 सेकंड में 500 मीटर और 325 मीटर लंबाई के दो पुलों को पार करती है। बस की लंबाई (मीटर में) है:

Option “D” is correct.

As we know,

Speed = distance/time

Let the length of the train be x m, As we know, speed is same, then

(500 + x)/90 = (325 + x)/60

⇒ 2 (500 + x) = 3 (325 + x)

⇒ 1000 + 2x = 975 + 3x

⇒ x = 25

∴ Length of the train is 25 m.

23. A train crosses a platform 180 m long in 60 sec at a speed of 72 km/h. the time taken by the train to cross an electric pole is:

180 मीटर लम्बे एक प्लेटफॉर्म को एक ट्रेन 72 किमी/घंटा की गति से 60 सेकंड में पार करती है। बिजली के खम्बे को पार करने में ट्रेन द्वारा लिया गया समय है:

Option “B” is correct.

Let the length of the train be x meter. And length of the platform is 180.

Speed of train = 72 × 5/18 = 20 m/sec

As we know,

Speed = Distance/Time

20 = (180 + x)/60

⇒ 1200 = 180 + x

⇒ x = 1200 – 180 = 1020

∴ Required time to cross poll by train = 1020/20 = 51 sec

24. A train travelling at constant speed crosses two persons walking in the same direction in 8 seconds and 8.4 second respectively. The first person was walking at the speed of 4.5 km/hr while the second was walking at the speed of 6 km/hr. What was the speed of the train in km/hr?

स्थिर गति से चल रही एक ट्रेन समान दिशा में चल रहे दो व्यक्तियों को क्रमशः 8 सेकंड और 8.4 सेकंड में पार करती है। पहला व्यक्ति 4.5 किमी/घंटा की गति से चल रहा था, जबकि दूसरा 6 किमी/घंटा की गति से चल रहा था। ट्रेन की गति किमी/घंटा में क्या थी?


Option “C” is correct.

Let speed of train be x km/hr and length of the train be y m

As we know,

Speed = Distance/Time

(x – 4.5) × 5/18 = y/8

⇒ (x – 4.5) × 5/18 × 8 = y     —-(i)

(x – 6) × 5/18 = y/8.4

⇒ (x – 6) × 5/18 × 8.4 = y    —-(ii)

From equation (i) and equation (ii), we get

(x – 4.5) × 8 = (x – 6) × 8.4

⇒ 8x – 36 = 8.4x – 50.4

⇒ 8.4x – 8x = 50.4 – 36

⇒ 0.4x = 14.4

⇒ x = 14.4/0.4

∴ x = 36 km/hr.

25. A train running at a speed of 60 km/hr takes 24 sec to pass a tunnel. Also,it takes 15 sec to pass a man walking at 6 km/hr in the same direction in which the train is going. Find the length of the train and the length of the tunnel.

एक ट्रेन 60 किमी/घण्टा की गति से एक सुरंग को पार करने में 24 सेकंड का समय लेती है। साथ ही, ट्रेन जिस दिशा में जा रही है उसी दिशा में 6 किमी/घंटा की गति से चलने वाले एक व्यक्ति को पार करने में 15 सेकंड का समय लगता है। ट्रेन की लंबाई और सुरंग की लंबाई ज्ञात कीजिए।

Option “B” is correct.

Given:

A train running at a speed of 60 km/hr takes 24 sec to pass a tunnel

It takes 15 sec to pass a man walking at 6 km/hr in the same direction in which the train is going

Concept:

Consider the two cases seperately, and find train length first. Relative speed in same direction will be the difference of individual speeds

Formula used:

Speed = Distance/Time

Calculation:

Let the length of the train be x

The train takes 15 sec to pass a man walking at 6 km/hr in the same direction in which the train is going

Relative speed = 60 – 6 = 54 km/hr

⇒ 54 km/hr = 54 × (5/18) = 15 m/s

Speed = Distance/Time

15 = x/15

⇒ x = 15 × 15 = 225 m

∴ Length of the Train = 225 m

Now, train running at a speed of 60 km/hr takes 24 sec to pass a tunnel

Let the length of the tunnel be y 

Speed = 60 km/hr = 60 × (5/18) = 50/3 m/s

50/3 = (y + 225)/24

⇒ y + 225 = 24 × (50/3) = 400

∴ y = 400 – 225 = 175 m

Length of the Tunnel = 175 m

The length of the train and the length of the tunnel are 225 m and 175 m respectively

26. A train of length (x + 50) meters is moving with a speed of 72 km/hr. It will take 19 seconds to cross a platform of length (x – 70) meters. Then, find the value of x?

(x + 50) मीटर लंबाई की एक ट्रेन 72 किमी/घंटा की गति से चल रही है। लंबाई (x – 70) मीटर के एक प्लेटफॉर्म को पार करने में 19 सेकंड का समय लगेगा। फिर, x का मान ज्ञात कीजिए?

Option “B” is correct.

Given:

Length of train = (x + 50) meters

Length of platform = (x – 70) meters

Time taken to cross platform = 19 sec

Concept used:

Time taken = (Length of train + Length of platform) / (Speed of train)

Calculation:

Total length = (x + 50) + (x – 70) = (2x – 20) m

Speed = 72 km / hr = 72 × (5 / 18) m / s = 20 m / s

Time taken = Total length / Speed

⇒ 19 = (2x – 20) / 20

⇒ 380 = 2x – 20

⇒ 2x = 380 + 20

⇒ 2x = 400

⇒ x = 400 / 2

⇒ x = 200

∴ The value of x is 200.

27.A train 180 m long passes a wagon 90 m long moving at speed of 36 m/s in 30 seconds. Calculate the speed of the train if the wagon is moving in the same direction as that of the train.

180 मीटर लंबी एक ट्रेन 36 मी/से. की गति से चलने वाली 90 मीटर लंबी माल के डिब्बे को 30 सेकंड में पार करती है, यदि माल डिब्बा, ट्रेन की दिशा में चल रहा है तो ट्रेन की गति की गणना कीजिये।

Option “D” is correct.

Given:

Length of train = 180 m

Length of wagon = 90 m

Speed of wagon = 36 m/s

Time taken to cross the wagon = 30 Seconds

Formula used:

Speed = Distance/ Time

Concept:

When two objects run in the same direction, their relative speed is a difference of their individual speeds

When two objects run in the opposite direction, their relative speed is an addition of their individual speeds.

When a train crosses a vertical object, Distance traveled by train = Length of train

When a train crosses a horizontal object, Distance traveled by train = Length of train + Length of the object

Calculation:

Let speed of train be s

∴ Relative speed = s – 36

Now,

speed = distance/time

⇒ (s – 36) = (180 + 90)/30

⇒ (s – 36) = 270/30

⇒ (s – 36) = 9

⇒ s = 36 + 9

⇒ s = 45 m/s

Now,

1 km/hr = (5/18) m/s —(∵ 18 km/hr = 5 m/s)

∴ 45 m/s = 162 km/hr

28. A train travelling at 38 kmph crosses a bus having 1/4th its length and travelling in the same direction at 20 kmph, in 60 seconds. It also crosses a railway platform in 72 seconds then the length of the platform is –

38 किमी/घंटा की गति से चलती हुई एक ट्रेन इसकी एक-चौथाई लंबाई वाली और समान दिशा में 20 किमी/घंटा की गति से चलती हुई एक बस को 60 सेकंड में पार करती है। यह एक प्लेटफार्म को भी यह 72 सेकंड में पार करती है, तब प्लेटफार्म की लंबाई क्या है?

Option “A” is correct.

Let the length of the train be A meters.

Length of the bus = A/4 meters

Relative speed = 38 – 20 = 18 kmph

⇒ 18 × 5/18 = 5 m/sec

Given,

⇒ (A + A/4)/5 = 60

⇒ A = 240 m

Let the length of the platform be B meter.

Speed of the train = 38 × 5/18 = 95/9 m/sec

Then,

⇒ (240 + B) × 9/95 = 72

⇒ 240 + B = 760

⇒ B = 760 – 240

⇒ B = 520 m

∴ Length of platform is 520 m.

29. A man in a train notices that he can count 16 electric posts in one minute. If they are known to be 60 m apart, then what is the speed of the train?

एक रेलगाड़ी में एक आदमी अवलोकन करता है कि वह एक मिनट में 16 बिजली के खंबे गिन सकता है। यदि उनके बीच की दूरी 60 मीटर है, तो रेलगाड़ी की गति क्या है?

Option “D” is correct.

Man counts 16 electric posts 60 m apart in 1 minute

⇒ Distance travelled by train in 1 min = 15 × 60 = 900 m

⇒ Train travels 900 m in 60 seconds

∴ Speed = 900/60 = 15 m/s = 15 × 18/5 km/h = 54 km/h

30. A train takes 1 minute to cross a stationary pole. How much time (in seconds) will it take to cross a bridge whose length is twice that of the train?

यदि किसी ट्रेन को एक स्थिर स्तंभ को पार करने में 1 मिनट का समय लगता है। तब  उस ट्रेन को एक पुल को पार करने में कितना समय (सेकंड में) लगेगा जिसकी लंबाई ट्रेन से दोगुनी है?

Option “A” is correct.

Let the length of train be x

Speed of train = length of train/time

Speed of train = x/60

Length of the bridge = 2x

Speed of train = (length of train + length of bridge) /time

x/60 = (x + 2x) /time

time = 60 × 3 = 180 seconds

∴ Train will take 180 seconds to cross the bridge.

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