Speed, Time and Distance
 Points ‘A’ and ‘B’ are 70 km apart on a highway. A car starts from ‘A’ and another from ‘B’ at the same time. If they travel in the same direction, they meet in 7 hours, but if they travel towards eachother, they meet in one hour. Find the speed of the two cars (in km/hr).

 20, 30
 40, 30
 30, 50
 20, 40

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Let speed of car starting from A be x kmph
and speed of car starting from B be y kmph
Case I
When cars meet at P,
7x = AP = AB + BP = 70 + 7y
⇒ 7x – 7y = 70
⇒ x – y = 10 ...(i)
Case II
When cars meet at Q,
x + y = 70 ...(ii)
On adding these equations,
x = 40 kmph
Putting the value of x in equation (i),
y = 40 – 10 = 30 kmphCorrect Option: B
Let speed of car starting from A be x kmph
and speed of car starting from B be y kmph
Case I
When cars meet at P,
7x = AP = AB + BP = 70 + 7y
⇒ 7x – 7y = 70
⇒ x – y = 10 ...(i)
Case II
When cars meet at Q,
x + y = 70 ...(ii)
On adding these equations,
x = 40 kmph
Putting the value of x in equation (i),
y = 40 – 10 = 30 kmph
 A train crosses a pole in 15 seconds and a platform 100 metres long in 25 seconds. Its length (in metres) is

 50
 100
 150
 200

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Let the length of train be x metre.
∴ x = x + 100 15 25 ⇒ x = x + 100 3 5
⇒ 5x = 3x + 300
⇒ 2x = 300⇒ x = 300 = 150 metres 2 Correct Option: C
Let the length of train be x metre.
∴ x = x + 100 15 25 ⇒ x = x + 100 3 5
⇒ 5x = 3x + 300
⇒ 2x = 300⇒ x = 300 = 150 metres 2
 A train passes a platform 110 m long in 40 seconds and a boy standing on the platform in 30 seconds . The length of the train is

 100 m
 110 m
 220 m
 330 m

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Let the length of the train be x metres.
Speed of train in crossing boy = x 30 Speed of train in crossing platform = x + 110 40
According to the question,x + 110 = x 40 30 ⇒ x + 110 = x 4 3
⇒ 4x = 3x + 330
⇒ x = 330 metresCorrect Option: D
Let the length of the train be x metres.
Speed of train in crossing boy = x 30 Speed of train in crossing platform = x + 110 40
According to the question,x + 110 = x 40 30 ⇒ x + 110 = x 4 3
⇒ 4x = 3x + 330
⇒ x = 330 metres
 A moving train crosses a man standing on a platform and a bridge 300 metres long in 10 seconds and 25 seconds respectively. What will be the time taken by the train to cross a platform 200 metres long ?


16 2 seconds 3  18 seconds
 20 seconds
 22 seconds


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Let the length of the train be x metre
Speed of train when it crosses man = x 10 Speed of train when it crosses platform = x + 300 25
According to the question,Speed of train = x = x + 300 10 25
⇒ 25x = 10x + 3000
⇒ 15x = 3000⇒ x = 3000 = 200 metres 15
∴ Length of train = 200 metreSpeed of train = x = 200 10 10 ∴ Time taken in crossing a 200 m long platform = 200 + 200 20
= 20 secondsCorrect Option: C
Let the length of the train be x metre
Speed of train when it crosses man = x 10 Speed of train when it crosses platform = x + 300 25
According to the question,Speed of train = x = x + 300 10 25
⇒ 25x = 10x + 3000
⇒ 15x = 3000⇒ x = 3000 = 200 metres 15
∴ Length of train = 200 metreSpeed of train = x = 200 10 10 ∴ Time taken in crossing a 200 m long platform = 200 + 200 20
= 20 seconds
 A train passes a platform 90 metre long in 30 seconds and a man standing on the platform in 15 seconds. The speed of the train is :

 12.4 kmph
 14.6 kmph
 18.4 kmph
 21.6 kmph

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Let the length of the train be x
According to the question,Speed of the train = x + 90 = x 30 15
⇒ x + 90 = 2x
⇒ x = 90 m∴ Speed of train = 90 15 = 6 m/s = 6 × 18 kmph 5
= 21.6 kmphCorrect Option: D
Let the length of the train be x
According to the question,Speed of the train = x + 90 = x 30 15
⇒ x + 90 = 2x
⇒ x = 90 m∴ Speed of train = 90 15 = 6 m/s = 6 × 18 kmph 5
= 21.6 kmph