Speed, Time and Distance
- 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
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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 ?
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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 :
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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
- In a 200 metre race, A beats B by 20 metres; while in a 100 metres race, B beats C by 5
metres. Assuming that the speed of A, B and C remain the same in various races, by how many metres will A beat C in one kilometre race ?
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According to the question,
when A covers the distance of 200 metres, B covers only 200– 20 = 180 metres
Again, in 100 metre race, B beats C by 5 metres.
Hence, if B runs 100 metres, C runs 100–5 = 95 metres
∵ If B runs 100 m, C runs = 95 m
∴ If B runs 180 m, C runs= 95 × 180 = 171 m 100
∴ A : B : C = 200 : 180 : 171
Hence, A will beat C by
= 200–171 = 29 m in 200 m race.
i.e., 29 × 5 = 145 m in 1 km race.Correct Option: C
According to the question,
when A covers the distance of 200 metres, B covers only 200– 20 = 180 metres
Again, in 100 metre race, B beats C by 5 metres.
Hence, if B runs 100 metres, C runs 100–5 = 95 metres
∵ If B runs 100 m, C runs = 95 m
∴ If B runs 180 m, C runs= 95 × 180 = 171 m 100
∴ A : B : C = 200 : 180 : 171
Hence, A will beat C by
= 200–171 = 29 m in 200 m race.
i.e., 29 × 5 = 145 m in 1 km race.
- A man standing on a 170 metre long platform watches that a train takes
the platform. Find the speed of train.7 1 seconds to pass him and 21 seconds to cross 2
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Let the length of the train be x m and its speed y m/sec.
Distance covered in crossing the platform = 170 + x metres
and time taken = 21 seconds∴ Speed y = 170 + x ...(i) 21
Distance covered to cross the man = x metresand time taken = 7 and time taken = 7 1 = 15 seconds 2 2 ∴ Speed y = x = 2x ...(ii) 15/2 15
From equations (i) and (ii),170 + x = 2x 21 15
⇒ 2550 + 15x = 42x
⇒ 42x – 15x = 2550
⇒ 27x = 2550⇒ x = 2550 = 94 4 metres 27 9
From equation (ii),y = 2 × 2550 15 × 27 = 340 = 12 16 m per sec. 27 27 Hence, speed = 12 16 m per sec. 27 Correct Option: A
Let the length of the train be x m and its speed y m/sec.
Distance covered in crossing the platform = 170 + x metres
and time taken = 21 seconds∴ Speed y = 170 + x ...(i) 21
Distance covered to cross the man = x metresand time taken = 7 and time taken = 7 1 = 15 seconds 2 2 ∴ Speed y = x = 2x ...(ii) 15/2 15
From equations (i) and (ii),170 + x = 2x 21 15
⇒ 2550 + 15x = 42x
⇒ 42x – 15x = 2550
⇒ 27x = 2550⇒ x = 2550 = 94 4 metres 27 9
From equation (ii),y = 2 × 2550 15 × 27 = 340 = 12 16 m per sec. 27 27 Hence, speed = 12 16 m per sec. 27
