Speed, Time and Distance
 A train passes two persons walking in the same direction at a speed of 3 km/hour and 5km/hour respectively in 10 seconds and 11 seconds respectively. The speed of the train is

 28 km/hour
 27 km/hour
 25 km/hour
 24 km/hour

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Let the speed of train be x kmph and its length be y km.
When the train crosses a man, it covers its own length
According to he question,= y = 10 (x − 3) × 5 3
⇒ 18 y = 10 × 5(x –3)
⇒ 18y = 50x –150 ..... (i)and, y = 11 (x − 5) × 5 18
⇒ 18y = 55(x–5)
⇒ 18y = 55x –275 .... (ii)
From equations (i) and (ii),
55x –275 = 50x–150
⇒ 55x –50x = 275 – 150
⇒ 5x = 125⇒ x = 125 = 25 5
∴ Speed of the train = 25 kmph
Second Method :
Here, S_{1} = 3, S_{2} = 5t_{1} = 10 , t_{2} = 11 3600 3600 Speed of train = t_{1}S_{1} − t_{2}S_{2} t_{1} − t_{2} = 3 × 10 − 5 × 11 3600 3600 10 − 11 3600 3600 = − 25 × 3600 3600 − 1
= 25 m/secCorrect Option: C
Let the speed of train be x kmph and its length be y km.
When the train crosses a man, it covers its own length
According to he question,= y = 10 (x − 3) × 5 3
⇒ 18 y = 10 × 5(x –3)
⇒ 18y = 50x –150 ..... (i)and, y = 11 (x − 5) × 5 18
⇒ 18y = 55(x–5)
⇒ 18y = 55x –275 .... (ii)
From equations (i) and (ii),
55x –275 = 50x–150
⇒ 55x –50x = 275 – 150
⇒ 5x = 125⇒ x = 125 = 25 5
∴ Speed of the train = 25 kmph
Second Method :
Here, S_{1} = 3, S_{2} = 5t_{1} = 10 , t_{2} = 11 3600 3600 Speed of train = t_{1}S_{1} − t_{2}S_{2} t_{1} − t_{2} = 3 × 10 − 5 × 11 3600 3600 10 − 11 3600 3600 = − 25 × 3600 3600 − 1
= 25 m/sec
 If a train, with a speed of 60 km/ hr, crosses a pole in 30 seconds, the length of the train (in metres) is :

 1000
 900
 750
 500

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Speed of train = 60 kmph
= 60 × 5 × 50 m/sec 18 3
&there4: Length of train
= Speed × Time= 50 × 30 = 500 m 3 Correct Option: D
Speed of train = 60 kmph
= 60 × 5 × 50 m/sec 18 3
&there4: Length of train
= Speed × Time= 50 × 30 = 500 m 3
 A man observed that a train 120 m long crossed him in 9 seconds. The speed (in km/hr) of the train was

 42
 45
 48
 55

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Speed of train
= 120 × 18 = 48 kmph 9 5 Correct Option: C
Speed of train
= 120 × 18 = 48 kmph 9 5
 In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hour ?

 2.5 seconds
 5 seconds
 12.5 seconds

3 5 seconds 4

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Speed of the train
= 144 kmph = 144 × 5 = 40 m/s 18
When a train crosses a pole, it covers a distance equal to its own length.The required time = 100 40 = 5 = 2 5. seconds. 2 Correct Option: A
Speed of the train
= 144 kmph = 144 × 5 = 40 m/s 18
When a train crosses a pole, it covers a distance equal to its own length.The required time = 100 40 = 5 = 2 5. seconds. 2
 A 75 metre long train is moving at 20 kmph. It will cross a man standing on the platform in

 12 seconds
 14 seconds
 13.5 seconds
 15.5 seconds

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Speed of train (in m/s) = 20 × 5 = 50 m/sec 18 9 Required time = 75 × 9 50
= 13.5 secondsCorrect Option: C
Speed of train (in m/s) = 20 × 5 = 50 m/sec 18 9 Required time = 75 × 9 50
= 13.5 seconds