Speed, Time and Distance
 Two trains of equal length, running in opposite directions, pass a pole in 18 and 12 seconds. The trains will cross each other in

 14.4 seconds
 15.5 seconds
 18.8 seconds
 20.2 seconds

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Let the length of each train be x metre.
Speed of first train = x m/sec 18 Speed of second train = x m/sec 12
When both trains cross each other, time taken= 2x x + x 18 12 = 2x 2x + 3x 36 = 2x × 36 5x = 72 = 14.4 seconds 5 Correct Option: A
Let the length of each train be x metre.
Speed of first train = x m/sec 18 Speed of second train = x m/sec 12
When both trains cross each other, time taken= 2x x + x 18 12 = 2x 2x + 3x 36 = 2x × 36 5x = 72 = 14.4 seconds 5
 Two trains 105 metres and 90 metres long, runs at the speed of 45 km/hr and 72 km/hr respectively, in opposite directions on parallel tracks. The time which they take to cross each other, is

 8 seconds
 6 seconds
 7 seconds
 5 seconds

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Length of both trains
= 105 + 90 = 195 m.
Relative speed = (45 + 72) = 117 kmph= 117 × 5 or 65 m/sec. 18 2 ∴ Time taken = 195 65 2 = 195 × 2 = 6 seconds 65 Correct Option: B
Length of both trains
= 105 + 90 = 195 m.
Relative speed = (45 + 72) = 117 kmph= 117 × 5 or 65 m/sec. 18 2 ∴ Time taken = 195 65 2 = 195 × 2 = 6 seconds 65
 Two trains are moving on two parallel tracks but in opposite directions. A person sitting in the train moving at the speed of 80 km/hr passes the second train in 18 seconds. If the length of the second train is 1000 m, its speed is

 100 km/hr
 120 km/hr
 140 km/hr
 150 km/hr

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Let the speed of second train be x m/s.
80 km/h = 80 × 5 m/s 18
According to the question1000 = 18 x + 80 × 5 18
⇒ 1000 = 18x + 400∴ x = 600 m/s 18 = 600 × 18 km/h = 120 km/h 18 5 Correct Option: B
Let the speed of second train be x m/s.
80 km/h = 80 × 5 m/s 18
According to the question1000 = 18 x + 80 × 5 18
⇒ 1000 = 18x + 400∴ x = 600 m/s 18 = 600 × 18 km/h = 120 km/h 18 5
 Two trains start from stations A and B and travel towards each other at speed of 50 km/hour and 60 km/hour respectively. At the time of their meeting, the second train has travelled 120 km more than the first. The distance between A and B is :

 990 km
 1200 km
 1320 km
 1440 km

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Let train A start from station A and B from station B.
Let the trains A and B meet after t hours.
∴ Distance covered by train A in t hours = 50t
Distance covered by train B in t hours = 60t km
According to the question,
60t – 50t = 120⇒ t = 120 = 12 hours. 10
∴ Distance AB = 50 × 12 + 60 ×
12 = 600 + 720 = 1320 km
Second Method :
Here, a = 60, b = 50, d = 120Distance between A and B = a + b × d a − b = 60 + 50 × 120 60 − 50 = 110 × 120 = 1320 km 10 Correct Option: C
Let train A start from station A and B from station B.
Let the trains A and B meet after t hours.
∴ Distance covered by train A in t hours = 50t
Distance covered by train B in t hours = 60t km
According to the question,
60t – 50t = 120⇒ t = 120 = 12 hours. 10
∴ Distance AB = 50 × 12 + 60 ×
12 = 600 + 720 = 1320 km
Second Method :
Here, a = 60, b = 50, d = 120Distance between A and B = a + b × d a − b = 60 + 50 × 120 60 − 50 = 110 × 120 = 1320 km 10
 Two trains 140 m and 160 m long run at the speed of 60 km/ hour and 40 km/hour respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is :

 10 sec.
 10.8 sec.
 9 sec.
 9.6 sec.

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Total length of trains
= 140 + 160 = 300 m.
Relative speed = 60 + 40 = 100 kmph= 100 × 5 m/sec. 18 or 250 m/sec. 9
∴ Time taken to cross each other= 300 250 9 = 300 × 9 = 10.8 sec. 250 Correct Option: B
Total length of trains
= 140 + 160 = 300 m.
Relative speed = 60 + 40 = 100 kmph= 100 × 5 m/sec. 18 or 250 m/sec. 9
∴ Time taken to cross each other= 300 250 9 = 300 × 9 = 10.8 sec. 250