1. Two trains are moving in the same direction at a speed of 38 km/hr and 92 km/hr, their lengths are 400 m and 350 m respectively. What is the time taken (in seconds) by the faster train to cross the slower train?

दो ट्रेन 38 किमी. /घंटा और 92 किमी. /घंटा की गति से एक ही दिशा में चल रही हैं, उनकी लंबाई क्रमशः 400 मीटर और 350 मीटर है। धीमी चल रही ट्रेन को पार करने में तेज चल रही ट्रेन को (सेकंड में) कितना समय लगेगा?

Option “B” is correct.

As two trains are running in the same direction,

⇒ Relative speed = 92 – 38 = 54 km/hr

= 54 × (5/18) = 15 m/s

⇒ Time = Distance/Speed

⇒ Time = (400 + 350)/15 = 750/15 = 50 seconds

2. A train 300 m long is running at a speed of 90 km/h. How much time will it take to cross a 200 m long train running in opposite direction at 60 km/h?

एक 300 मी लंबी ट्रेन 90 किमी/घंटा की गति से चल रही है। इसे विपरीत दिशा में 60 किमी/घंटा की गति से चल रही 200 मी लंबी ट्रेन को पार करने में कितना समय लगेगा?

Option “A” is correct.

Length of train = 300 m

Speed of one train = 90 × 5/18 = 25 m/s

Speed of the other train = 60 × 5/18 = 16.67 m/s

Relative speed = 25 + 16.67 = 41.67 m/s

Required time = (300 + 200) / (41.67) = 12 seconds

3. A 360 m long train running at a uniform speed, crosses a platform in 55 seconds and a man standing on the platform in 24 seconds. What is the length (in meter) of the platform?

एकसमान गति पर चलने वाले एक 360 मीटर लंबी ट्रेन 55 सेकेंड में एक प्लेटफार्म को पार करती है और प्लेटफार्म पर खड़े एक व्यक्ति को 24 सेकेंड में पार करती है। तो प्लेटफार्म  की लम्बाई (मीटर में) क्या है?

Option “D” is correct.

Speed pf the train = 360/24 = 15 mps (Speed = distance/time)

Let the length of the platform be x.

Time taken to cover the platform = 55 seconds

⇒ (360 + x)/15 = 55

⇒ x = 465 m

4. A train with 72 km/h speed crosses a stationary pole in 35 seconds. How much time (in minutes) does it take to cross a 1.1 km long bridge?

72 किमी/घंटा की गति वाली एक ट्रेन 35 सेकंड में एक स्थिर स्तम्भ को पार करती है। 1.1 किमी लंबे पुल को पार करने में ट्रेन को कितना समय (मिनटों में) लगेगा?

Option “B” is correct.

Given, speed of train = 72 km/hour = 20 m/second

Let the length of the train be x m

According to question,

⇒ x = 20 × 35

⇒ x = 700m

And again according to question,

⇒ 1100 + 700 = 20 × time

⇒ Time = 1800/20 = 90 seconds = 1.5 minutes

∴ The required time to cross the bridge is 1.5 minutes.

5. A train crosses a pole in 12 sec, and a bridge of length 170 m in 36 sec. Then the speed of the train is:
 
एक ट्रेन 12 सेकंड में एक खंभे को और 36 सेकंड में 170 मीटर की लंबाई के पुल को पार कर सकती है। तो ट्रेन की गति है:

Option “B” is correct.

Shortcut Trick

If train cross its length in 12 seconds and 170 m bridge in (36 – 12 = 24) seconds.

Speed of train = [170/24] × [18/5] = 25.5 km/hr

Alternate Method

Let the length of the train be x m.

As we know,

Speed = Distance/time

Speed = x/12       —(1)

Speed = (x + 170)/36       —(2)

Frome equation (1) and equation (2)

x/12 = (x + 170)/36

⇒ 3x = x + 170

⇒ 2x = 170

⇒ x = 170/2

⇒ x = 85 m

From equation (1)

Speed = 85/12 × (18/5) km/hr

∴ Speed = 25.5 km/hr

6. A goods train leaves a station at a certain time and at a fixed speed. After 10 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph, this train catches up the goods train in 8 hours. Find the speed of the goods train.

एक मालगाड़ी एक विशिष्ट समय पर एक निश्चित गति से एक स्टेशन से निकलती है। 10 घंटों के बाद, एक एक्सप्रेस ट्रेन समान दिशा में 90 किमी/घंटा की एकसमान गति से स्टेशन से निकलती है, यह ट्रेन मालगाड़ी से 8 घंटे में मिलती है। मालगाड़ी की गति ज्ञात कीजिये।

Option “C” is correct.

Let the speed of the goods train be x km/h

According to the question,

⇒ x(10 + 8) = 90 × 8

⇒ 18x = 720

⇒ x = 40

∴ Speed of the goods train = 40 km/h

7.A train ‘B’ speeding with 100 kmph crosses another train C, running in the same direction, in 2 mins. If the length of the train B and C be 150m and 250m respectively, what is the speed of the train C (in kmph)?

100 किमी प्रति घंटे की रफ्तार से चल रही एक ट्रेन ‘B’ दूसरी ट्रेन C को 2 मिनट में पार करती है जो की समान दिशा में चल रही है। यदि ट्रेन B और C की लंबाई क्रमशः 150 मीटर और 250 मीटर है तो ट्रेन C की गति (किमी प्रति घंटे) क्या है?

Option “B” is correct.

Given:

Speed of train B = 100 km/h 

Length of B = 150 m 

Length of C = 250 m 

Time taken by B to cross C in same direction = 2 mins 

Concept used:

Concept used:

1.) Relative speed is defined as the speed of a moving object with

respect to another.

2.) When two objects are moving in the same direction, the relative speed is calculated as their difference.

Relative speed when moving in the same direction = a – b

3.) When two objects are moving in the opposite direction, the relative speed is computed by adding the two speeds.

Relative speed when moving in opposite direction = a + b

4.) Time taken to meet = Distance/Relative speed

Calculations:

Speed of train B = 100 kmph

Let the speed of train C be x km/hr

Length of train B and C are 150 m and 250 m respectively.

As we know,

Speed = Distance/Time

⇒ (100 – x) × 5/18 = (150 + 250)/(2 × 60)

⇒ (100 – x) = 400/120 × 18/5

⇒ 100 – x = 12

⇒ x = 100 – 12

⇒ x = 88

∴ Speed of the train C is 88 km/hr.

8. The distance between two stations, A and B, is 575 km, A train from station ‘A’ at 3.00 p.m and moves towards station ‘B’ at an average speed of 50 km/h. Another train starts from station ‘B’ at 3.30 p.m and moves towards station ‘A’ at an average speed of 60 km/h, how far from station ‘A’ will the trains meet?

दो स्टेशनों, A और B के बीच की दूरी 575 किमी है, स्टेशन ‘A’ से 3.00 बजे एक ट्रेन स्टेशन ‘B’ की ओर 50 किमी/घंटा की औसत गति से चलती है। एक अन्य ट्रेन 3.30 बजे स्टेशन ‘B’ से शुरू होती है और स्टेशन ‘A’ की ओर 60 किमी/घंटा की औसत गति से चलती है, स्टेशन ‘A’ से कितनी दूर ट्रेनें मिलेंगी?

Option “C” is correct.

The distance between two stations, A and B = 575 km,

Speed of first train = 50 km/hr

Speed of second train = 60 km/hr

Distance covered by first train in 30 min (1/2 hr) = 50 × 1/2 = 25 km

Remaining distance = 575 – 25 = 550 km

Relative speed, if opposite direction = 50 + 60 = 110 km/hr

As we know,

Time = Distance/speed

Both train meet each other in = 550/110 = 5 hrs

Distance covered in 5 hrs by first train = 5 × 50 = 250 km

Total distance covered by first train = 25 + 250 = 275 km

Both trains meet each other 275 km far from station A.

9. A 270 m long train running at a speed of 120 km/h crosses another train running in opposite direction at the speed of 80 km/h in 9 seconds. What is the length of the other train?

120 किमी/घंटा की गति से चलने वाली एक 270 मीटर लंबी ट्रेन 80 किमी/घंटा की गति से विपरीत दिशा में चलने वाली दूसरी ट्रेन को 9 सेकेंड में पार करती है। तो दूसरी ट्रेन की लम्बाई क्या है?

Option “D” is correct.

Let length of the train be x m

Length of first train = 270 m

Speed of the two trains is 120 km/hr and 80 km/hr respectively.

Relative speed, if opposite direction = 120 + 80 = 200 × 5/18 = 500/9 m/sec

As we know,

Speed = distance/time

⇒ 500/9 = (270 + x)/9

⇒ x = 500 – 270

⇒ x = 230 m

10. The distance between the two stations is 2000 km. A train after travelling ‘D’ km meets with an accidents then proceeds with 80% of its former speed and arrives at its destination 7.5 hrs late. Had the accident occurred 200 km further, it would have reached the destination 6.5 hr late. Then, find the original speed of the train?

दोनों स्टेशनों के बीच की दूरी 2000 किमी है। ’D’ किमी की यात्रा के बाद एक रेल की दुर्घटना हो जाती है, और फिर अपनी पूर्व गति की 80% गति के साथ वह आगे बढ़ती है और अपने गंतव्य पर 7.5 घंटे देरी से पहुंचती है। यदि दुर्घटना 200 किमी आगे होती, तो यह केवल। 6.5 घंटे देर से पहुंचती। तब, रेल की सामान्य गति क्या है?

Option “B” is correct.

Concept used:

Distance = Speed × Time

Calculation:

The total distance travelled by train = 2000 km

Original speed of the train = 5x km/hr

Then, Reduced speed of the train = 4x km/hr

∴ The difference between time is because of 200 km.

⇒ 200/4x – 200/5x = 7.5 – 6.5

⇒ 200(5 – 4)/20x = 1

⇒ 200/20x = 1

⇒ x = 10

∴ The original speed of the train = 5x km/hr = 50 km/hr

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