A train is moving and crossing a man who is runnin | Problems on Trains Questions & Answers

Q:

Agra and Delhi are 160 km apart. A train leaves Agra for Delhi and at the same time another train leaves Delhi for Agra. Both the trains meet 5 hrs after they start moving. If the train travelling from Agra to Delhi travels 6 km/hr faster than the other train, find the speed of the faster train?

A) 19 kmph	B) 13 kmph
C) 7 kmph	D) 9 kmph

Answer & Explanation Answer: A) 19 kmph

Explanation:

Let the speed of the slower train = p kmph

ATQ,

Speed of the faster train = (p + 6) kmph

Then,

(p + p + 6) x 5 = 160

10p + 30 = 160

10p = 130

p = 13 kmph

Then, speed of the faster train = p + 6 = 13 + 6 = 19 kmph.

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Q:

A 150 m long train crosses another 210 m long train running in the opposite direction in 10.8 seconds. If the shorter train crosses a pole in 12 seconds, what is the speed of longer train ?

A) 75 kmph	B) 80 kmph
C) 54 kmph	D) 45 kmph

Answer & Explanation Answer: A) 75 kmph

Explanation:

Total distance = 150 + 210 = 360 mts

Time taken to cross each other when moving in opposite direction = 10.8 sec

Relative speed of trains = (350/10.8) x 18/5 = 3600/30 = 120 kmph

Speed of shorter train = (150/12) x 18/5 = 45 kmph

Hence, speed of longer train = 120 - 45 = 75 kmph.

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Q:

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train?

A) 42 kmph	B) 43 kmph
C) 40 kmph	D) 45 kmph

Answer & Explanation Answer: C) 40 kmph

Explanation:

We know that, Speed = Distance/time

Let the speed of the train be = x kmph

           NORMAL SPEED                           SPEED 5 KMPH MORE

          Distance = 360 Km                         Distance =360

          speed    = X Kmph                        Speed = (x+5)

            Time =360/X                              Time =360/(x+15)

For the same journey if the speed increased 10 kmph more it will take 1 hour less

Time with original speed - time with increased speed = 1

=> (360/x) - (360/x+10) = 1

=> (360(x+5)-360x)/x(x+5) =1

=> 360X + 1800 -360X = X(X+5)

  => X^2 + 5x - 1800 = 0

X = 40 or -45

X cannot be negetive value

X = 40 kmph.

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Q:

A passenger train covers the distance between station K and L, 40 minutes faster than a goods train. Find this distance between K and L if the average speed of the passenger train is 50 km/h and that of goods train is 30 km/h?

A) 50 kms	B) 48 kms
C) 46 kms	D) 44 kms

Answer & Explanation Answer: A) 50 kms

Explanation:

Let the distance be 'd' kms.

According to the given data,

$\frac{d}{30} - \frac{d}{50} = \frac{40}{60} hrs = > 6 d = 300 = > d = 50 kms .$

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Q:

A train travelling with a speed of 60 km/hr catches another train travelling in the same direction and then leaves it 120m behind in 18 seconds. The speed of the second train is

A) 42 kmph	B) 72 kmph
C) 36 kmph	D) 44 kmph

Answer & Explanation Answer: C) 36 kmph

Explanation:

Given speed of the first train = 60 km/hr = 60 x 5/18 = 50/3 m/s

Let the speed of the second train = x m/s

Then, the difference in the speed is given by

$\frac{50}{3} - x = \frac{120}{18}$

=> x = 10 m/s

=> 10 x 18/5 = 36 km/hr

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Q:

Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

A) 27 7/9 mts	B) 25 8/7 mts
C) 21 1/4 mts	D) 22 mts

Answer & Explanation Answer: A) 27 7/9 mts

Explanation:

Relative speed = (40 - 20) km/hr =		20 x	5		m/sec =		50		m/sec.
			18				9

Length of faster train =		50	x 5		m =	250	m = 27	7	m.
		9				9		9

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Q:

A train travelling at 48 kmph crosses another train, having half its length and travelling in opposite direction at 42 kmph, in 12 sec. It also covers a bridge in 45 sec. Find the length of the bridge ?

A) 250 mts	B) 400 mts
C) 320 mts	D) 390 mts

Answer & Explanation Answer: B) 400 mts

Explanation:

Let the length of the 1st train = L mts

Speed of 1st train = 48 kmph

Now the length of the 2nd train = L/2 mts

Speed of 2nd train = 42 kmph

Let the length of the bridge = D mts

Distance = L + L/2 = 3L/2

Relative speed = 48 + 42 = 90 kmph = 90 x 5/18 = 25 m/s(opposite)

Time = 12 sec

=> 3L/2x25 = 12

=> L = 200 mts

Now it covers the bridge in 45 sec

=> distance = D + 200

Time = 45 sec

Speed = 48 x5/18 = 40/3 m/s

=> D + 200/(40/3) = 45

=> D = 600 - 200 = 400 mts

Hence, the length of the bridge = 400 mts.

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Q:

The difference between the time taken by two trains to travel a distance of 350 km is 2 hours 20 minutes. If the difference between their speeds is 5 km/hr, what is the speed of faster train ?

A) 36 kmph	B) 30 kmph
C) 34 kmph	D) 40 kmph

Answer & Explanation Answer: B) 30 kmph

Explanation:

Let the speed of the faster train be 'S' kmph

Then speed of the slower train will be '(S-5)' kmph

Time taken by faster train = 350/S hrs

Time taken by slower train = 350/(S-5) hrs

$\frac{350}{s - 5} - \frac{350}{s} = 2 h r s 20 m i n = 2 \frac{1}{3} = \frac{7}{3}$

=> S = 30 km/hr.

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A) 202 mts	B) 188 mts
C) 165 mts	D) 156 mts

A train is moving and crossing a man who is running on a platform of 100 m at a speed of 8 kmph in the direction of the train, in 9 sec. If the speed of the train is 74 kmph. Find the length of the train ?

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