Aptitude Problems On TrainsPage 3
17. | | Two goods train each 700 m long, are running in opposite directions on parallel tracks. Their speeds are 40 kmph and 30 kmph respectively. Find the time taken by the slower train to pass the driver of the faster one. | | (a)62 seconds | | (b)72 seconds | | (c)48 seconds | | (d)60 seconds |
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Answer is: BRelative speed = (40 + 30) kmph = 70 x (5/18) m/s = 175/9 m/s.
Distance covered = (700 + 700) = 1400 m.
∴ Required time = 1400 x (9/175)
⇒ time = 72 seconds.
18. | | Two trains of equal length are running on parallel lines in the same direction at 66 kmph and 56 kmph. The faster train passes the slower train in 36 seconds. The length of each train is: | | (a)60 m | | (b)74 m | | (c)68 m | | (d)50 m |
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Answer is: DLet the length of each train be X meters.
Then, distance covered = 2X meters.
Relative speed = (66 – 56) kmph = 10 x (5/18) m/s = 25/9 m/s.
∴ (2X/36) = 25/9
⇒ 2X = 100
⇒X = 50.
19. | | A 260 meters long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train? | | (a)250 m | | (b)240 m | | (c)260 m | | (d)255 m |
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Answer is: BRelative speed = (120 + 80) kmph = 200 x (5/18) m/s = 500/9 m/s.
Let the length of the train be X meters.
Then, (X + 260)/9 = 500/9
⇒ X + 260 = 500
⇒ X = 500 – 260
⇒ X = 240.
20. | | A train of length 700 m starts overtaking another train of length 800 m running on a parallel track. What is the distance that should be gained by the first train over the second train to overtake the second train completely? | | (a)1000 m | | (b)1400 m | | (c)1500 m | | (d)1600 m |
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Answer is: CThe first train would have to gain a total distance of 700 + 800 = 1500 m to cross the second train completely.
21. | | Two trains of lengths 700 m and 800 m are running on parallel tracks towards each other. What is the distance travelled by the two trains together from the time they start to cross each other to the time they completely cross each other? | | (a)100 m | | (b)1400 m | | (c)1600 m | | (d)1500 m |
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Answer is: DTo cross each other completely two trains together have to cover a distance equal to the sum of the lengths of the trains.
∴ 700 + 800 = 1500 m.
22. | | A train of length 300 m travels at a speed of 36 kmph. In how many seconds does it cross a bridge of length 700 m? | | (a)100 seconds | | (b)300 seconds | | (c)70 seconds | | (d)200 seconds |
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Answer is: ATo completely cross the bridge the train has to travel a distance of 300 m + 700 m = 1000 m.
The speed = 36 kmph = 36 x 1000/3600 = 10 m/s.
∴ Required time = 1000/10 = 100 seconds.
23. | | Two trains of length 150 m and 250 m run on parallel lines. When they run in the same direction it will take 20 seconds to cross each other and when they run in opposite direction it will take 5 seconds. Find the speed of the two trains? | | (a)180 kmph , 108 kmph | | (b)108 kmph , 180 kmph | | (c)110 kmph , 108 kmph | | (d)108 kmph , 110 kmph |
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Answer is: ALet the speeds of the two trains be p & q m/s.
Total distance covered = sum of length of two trains = 150 + 250 = 400 m.
When they run in the same direction, relative speed (p – q) is given by,
⇒ p – q = 400/20 = 20 →(i)
When they running in opposite directions, relative speed (p + q) is given by,
⇒ p + q = 400/5 = 80 →(ii)
Solving (i) and →(ii), we get,
⇒ p = 50 m/s and q = 30 m/s
∴ speeds of two trains are 180 kmph and 108 kmph.
24. | | Two trains running at 45 kmph and 54 kmph cross each other in 12 seconds when they run in opposite directions. When they run in the same direction, a person in the faster train observe that he crossed the other train in 32 seconds. Find the lengths of the two trains? | | (a)250 m , 90 m | | (b)260 m , 70 m | | (c)240 m , 90 m | | (d)250 m , 80 m |
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Answer is: DLet p, q be the lengths of the slow and faster trains respectively.
When trains are travelling in the opposite directions,
Relative speed = 45 + 54 = 99 kmph = 27.5 m/s
Distance covered = sum of length of two trains = p + q
Then we have,
⇒ p + q = 12 x 27.5
p + q = 330 m →(i)
When trains are travelling in the same direction,
since we are given the time noted by a person in the faster train as 32 seconds the distance covered is equal to the length of the slower train,
∴ distance covered = q
Relative speed = 54 – 45 =9 kmph = 2.5 m/s
∴ q = 2.5 x 32 = 80 m →(ii)
From (i) and (ii) we get,
⇒ p = 250 m.
than, q = 330 - 250 = 80 m.
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