- 51. In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr?

**Answer: Option 'D'**

**Given
Length of the train = 100 m
Speed of the train = 144 km / hr
---> To convertkm/hr to m/sec multiply speed with (5 / 18)
= 144 x (5 / 18) m/sec
= 40 m/sec
Therefore Speed of the train =40 m/sec
Now, Time taken by the train tocross an electric pole =Length of the train/Speed of the train
T = 100 / 40
= 2.5 sec
The time taken is 2.5 sec.**

- 52. Two trains 100 metres and 120 metres long are running in the same direction with the speeds of 72 km/hr and 54 km/hr .In how much time will the first train cross the second?

**Answer: Option 'C'**

**44 second**

- 53. A train is moving at a speed of 132 km/hr .If the length of the train is 110 metres ,how long will it take to cross a railway platform 165 metres long?

**Answer: Option 'B'**

**7 1/2 sec**

- 54. A train 100 m long is running at the speed of 30 km/hr.Find the time taken by it to pass a man standing near the railway line:

**Answer: Option 'A'**

**12 sec**

- 55. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

**Answer: Option 'B'**

**Relative speed = (45 + 30) km/hr = ( 75 x 5/18 ) m/sec = (125/6 ) m/sec .
We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.
So, distance covered = Length of the slower train.
Therefore, Distance covered = 500 m.
Therefore Required time = ( 500 x 6/125 ) = 24 sec .**

- 56. How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

**Answer: Option 'B'**

**Given, Length of the train = 500 m
Speed of the man = 3 km/hr
Speed of the train = 63 km/hr
**

- 57. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

**Answer: Option 'C'**

**Let the length of the train be x metres and its speed by y m/sec.
Time = Length / Speed of the train
Given,A train moves past a telegraph post in 8 seconds.
Then, x/y = 8
=> x = 8y
Now, the same train moves past a bridge of 264 m long in 20 seconds.
=> (x + 264) / y = 20
Subs x = 8y in the above eqn, we get
=> (8y + 264) = 20y
=> 20y - 8y = 264
=> 12y = 264
=> y = 22.
Therefore Speed = 22 m/sec = ( 22 x 18 /5) km/hr = 79.2 km/hr.**

- 58. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

**Answer: Option 'B'**

**Given time taken by train to pass the pole =15 seconds
=> W.K.T: Time = Distance / speed
=> Time = Length of train / speed of train
=> 15 = Length of train/ speed of train
=>speed of train =Length of train /15 ---> eqn(1)
Given, time taken by train to pass the platform of 100 m long =25 seconds
=>Time = (Length of train + Length of the platform) / speed of train
=> 25 = (Length of train + 100) /speed of train
Substituting eqn (1) in the above eqn, we get
=> 25 =(Length of train + 100) / (Length of train /15)
=> 25 × (Length of train /15) =(Length of train + 100)
=> (5 / 3) × Length of train =(Length of train + 100)
=> 5 × Length of train = 3 (Length of train + 100)
=> 5 × Length of train =3 × Length of train + 300
=> 2 × Length of train = 300
=> Length of train = 150 meter.**

- 59. A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is :

**Answer: Option 'A'**

**Given, Length of the train = 800 m
Speed ofthe train = 78 km/hr
= 78 × (5 / 18) m/s
= 390 / 18 m/s
Time to cross the tunnel = 1 min = 60 sec
**

- 60. A train travelling at a speed of 75 mph enters a tunnel 3 (1/2) miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

**Answer: Option 'B'**

**Total distance covered = ( 7/2 + 1/4 ) miles
= 15/4 miles.
Therefore, Time taken
= ( 15 / 4 x 75 ) hrs
= 1 / 20 hrs
= ( 1/20 x 60 ) min.
= 3 min.**

- 61. A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

**Answer: Option 'B'**

**Speed of train relative to man = (60 + 6) km/hr = 66 km/hr. = ( 66 x 5 /18 m/sec = (55 / 3 ) m/sec
Therefore, Time taken to pass the man = ( 110 x 3/55 ) sec = 6 sec.**

- 62. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

**Answer: Option 'C'**

**Given, Length of each train = 100 m
=> Sum of length of two trains = 100 + 100 = 200 m
Time taken by the trains to cross each other = 8 sec.
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
(Since, two trains are moving in opposite direction, Speed can be added)
Relative speed = speed of the slower train +speed of the faster train
= (x + 2x) m/sec
= 3x m/sec.
W.K.T: Relative speed =Sum of length of two trains /Time taken by the trains to cross each other
=> 3x = (100 + 100) / 8
=> 3x = 200 / 8
=> x = 200/ (8*3) m/sec
=> x = (200 / 24) m/sec
=> x = 8.33m/sec
Speed of faster train = 2x
= 2 × 8.33
= 16.66 m/sec
---> Converting into km/hr
= 16.66 × (18 /5) km/hr
= 299.88/5 km/hr
= 59.976 km/hr
= 60 km/hr
Therefore,Speed of faster train =60 km/hr**

- 63. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

**Answer: Option 'A'**

**Given the length of the first train = 270 metres.
Let the length of the second train be x metres
Relative speed = Speed of first train + Speed of Second Train
= (120 + 80) kmph
= ( 200 x 5/18 ) m/sec
= 1000/ 18 m/sec.
Therefore,**

- 64. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

**Answer: Option 'B'**

**36 sec**

- 65. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

**Answer: Option 'C'**

**Relative speed = (60+ 90) km/hr
= ( 150 x 5/18 ) m/sec
= (125/3 ) m/sec
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time =( 2000 x 3/125) sec = 48 sec.**

- 66. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

**Answer: Option 'A'**

**Formula for converting from km/hr to m/s:
X km/hr = ( X x 5/18 ) m/s.
Therefore, Speed = (45 x 5/18 ) m/sec = 25/2 m/sec
Total distance to be covered = (360 + 140) m = 500 m.
**

- 67. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

**Answer: Option 'A'**

**Let the length of each train be x metres.
Then, distance covered = sum of Length of two trains
= x + x
= 2x metres
Since two trains are moving in the same direction,
Relative speed = faster train speed -slower train speed
=(46 - 36) km/hr
= 10 x (5/18) m/sec
= (25/9) m/sec
Given, Time to passslower train = 36 sec
Therefore, RelativeSpeed = Distance / Time
=> 2x/36 = 25/9
=> 2x = 100
=> x = 50
Hence,length of each train = 50 metres**

- 68. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

**Answer: Option 'B'**

**Given, length of the train = 240 m
Time taken by the train to pass the pole = 24 sec
Length of the Platform = 650 m
To find theTime taken by the train to pass the platform:-
Speed of the train = length of the train /Time taken by the train to pass the pole
= (240/ 24 )
= 10 m/sec.
Therefore, **

- 69. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

**Answer: Option 'B'**

**Given,speed of the train = 54 km/hr
---> converting this speed into meter/ sec
=> **

- 70. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

**Answer: Option 'C'**

**Speed = (45x 5/18 ) m/sec = (25/2) m/sec Time = 30 sec.
Let the length of bridge be x metres.
Then, 130 + x /30 = 25/2 => 2(130 + x) = 750 => x = 245 m.**

- 71. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

**Answer: Option 'B'**

**Given, Length of the train = 125 meter
Time taken by the train to pass the man = 10 sec
Speed of man =5 km/hr
Speed of the train relative to man = (125/10) m/sec
= (25/2)m/sec
=(25/2) x (18/5) km/hr
= 45 km/hr
Let the speed of the train be x km/hr.
Since Man and Train are moving in same direction, speeds must be subtracted
Then, relative speed = Speed of train -Speed of man
=> x - 5 = 45
=> **

- 72. A boat is rowed down a river 40 km in 5 hr and up a river 21 km in 7 hr. Find the speed of the boat and the river.

**Answer: Option 'D'**

**Speed of the boat downstream = 40/5 = 8 kmph
Speed of the boat upstream = 21/7 = 3 kmph
Speed of the boat = 1/2 ( 8+3) = 11/2 = 5.5 kmph**

- 73. A train travels from City X to City Y at a speed of 60 kmph, while on its return journey the train was travelling at speed of 120 kmph. Find the average speed of the train.

**Answer: Option 'C'**

**Given, Onward journey speed (x) = 60 kmph;
Return journeyspeed (y) = 120 kmph.
**

- 74. A train travels from City X to City Y at a speed of 32 kmph, while on its return journey the train was travelling at speed of 96 kmph. Find the average speed of the train.

**Answer: Option 'C'**

**Let x be the speed of the train while going from City X to Y.
Let y be the speed of the train while going from City Y to X.
Average speed of the train is given by = 2xy/(x+y)
Average speed = (2 x 32 x 96) / (32 + 96 ) Average speed = 48**

- 75. A train travels from City X to City Y at a speed of 44 kmph, while on its return journey the train was travelling at speed of 77 kmph. Find the average speed of the train.

**Answer: Option 'A'**

**Let x be the speed of the train while going from City X to Y.
Let y be the speed of the train while going from City Y to X.
**

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