Speed, Time and Distance
 A train leaves a station A at 7 am and reaches another station B at 11 am. Another train leaves B at 8 am and reaches A at 11.30 am. The two trains cross one another at

 8:36 am
 8:56 am
 9:00 am
 9:24 am

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Let both trains meet after t hours since 7 a.m.
Distance between stations A and B = x Km.∴ x × t + x × (t − 1) = x 4 7/2 Speed = Distance Time ⇒ t + 2(t − 1) = 1 4 7 ⇒ 7t + 8t − 8 = 1 28
⇒ 15 t – 8 = 28
⇒ 15 t = 28 + 8 = 36⇒ t = 36 = 12 hours 15 5
= 2 hours 24 minutes
∴ Required time = 9 :24 a.m.Correct Option: D
Let both trains meet after t hours since 7 a.m.
Distance between stations A and B = x Km.∴ x × t + x × (t − 1) = x 4 7/2 Speed = Distance Time ⇒ t + 2(t − 1) = 1 4 7 ⇒ 7t + 8t − 8 = 1 28
⇒ 15 t – 8 = 28
⇒ 15 t = 28 + 8 = 36⇒ t = 36 = 12 hours 15 5
= 2 hours 24 minutes
∴ Required time = 9 :24 a.m.
 A train crosses a platform in 30 seconds travelling with a speed of 60 km/h. If the length of the train be 200 metres, then the length (in metres) of the platform is

 400
 300
 200
 500

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Speed of train = 60 kmph
= 60 × 5 m/sec. 18 = 50 m/sec. 3
If the length of platform be = x metre, then∴ Speed of train = Length of (train + platform) Time taken in crossing ⇒ 50 = 200 + x 3 30
⇒ 50 × 10 = 200 + x
⇒ x = 500 – 200 = 300 metreCorrect Option: B
Speed of train = 60 kmph
= 60 × 5 m/sec. 18 = 50 m/sec. 3
If the length of platform be = x metre, then∴ Speed of train = Length of (train + platform) Time taken in crossing ⇒ 50 = 200 + x 3 30
⇒ 50 × 10 = 200 + x
⇒ x = 500 – 200 = 300 metre
 A train moving at a rate of 36 km/hr. crosses a standing man in 10 seconds. It will cross a platform 55 metres long, in :

 6 seconds
 7 seconds

15 1 seconds 2 
5 1 seconds 2

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Speed of train = 36 kmph
= 36 × 5 = 10 m/sec 18
Length of train = 10 × 10 = 100 metres∴ Required time = 100 + 55 10 = 15 5 = 15 1 second 10 2
= 15.5 secondsCorrect Option: C
Speed of train = 36 kmph
= 36 × 5 = 10 m/sec 18
Length of train = 10 × 10 = 100 metres∴ Required time = 100 + 55 10 = 15 5 = 15 1 second 10 2
= 15.5 seconds
 A train passes by a lamp post on a platform in 7 sec. and passes by the platform completely in 28 sec. If the length of the platform is 390 m, then length of the train (in metres) is

 120
 130
 140
 150

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Let the length of train be x metre, then
∴ Speed of train = x = x + 390 7 28 ⇒ x = x + 390 4
⇒ 4x – x = 390⇒ x = 390 = 130 metres 3 Correct Option: B
Let the length of train be x metre, then
∴ Speed of train = x = x + 390 7 28 ⇒ x = x + 390 4
⇒ 4x – x = 390⇒ x = 390 = 130 metres 3
 Two trains 100 metres and 95 metres long respectively pass each other in 27 seconds when they run in the same direction and in 9 seconds when they run in opposite directions. Speed of the two trains are

 44 km/hr, 22 km/hr
 52 km/hr, 26 km/hr
 36 km/hr. 18 km/hr
 40 km/hr, 20 km/hr

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Let the speed of trains be x and y metre/sec respectively,
100 + 95 = 27 x − y ⇒ x − y = 195 = 65 .....(i) 27 9
Again,195 = 9 x + y ⇒ x + y = 195 .....(ii) 9
By equation (i) + (ii)⇒ 2x = 65 + 195 = 260 9 9 9 ⇒ x = 260 = 130 m/sec. 2 × 9 9 = 130 × 18 kmph = 52 kmph 9 5
From equation (ii),y = 195 − 130 = 65 m/sec. 9 9 9 = 65 × 18 = 26 kmph 9 5 Correct Option: B
Let the speed of trains be x and y metre/sec respectively,
100 + 95 = 27 x − y ⇒ x − y = 195 = 65 .....(i) 27 9
Again,195 = 9 x + y ⇒ x + y = 195 .....(ii) 9
By equation (i) + (ii)⇒ 2x = 65 + 195 = 260 9 9 9 ⇒ x = 260 = 130 m/sec. 2 × 9 9 = 130 × 18 kmph = 52 kmph 9 5
From equation (ii),y = 195 − 130 = 65 m/sec. 9 9 9 = 65 × 18 = 26 kmph 9 5