Practice Questions on Aptitude section- Train Sums

1). If a train 280 metre long runs at the speed of 7.4 m/second, how much time will it take to cross a platform 460 metre long ?

a)   95 sec.

b)   96 sec.

c)   98 sec.

d)   99 sec.

e)   100 sec.

2). A train running at the speed of 108 kmph, crosses a 365 metre long platform in 21 seconds. What is the length of the train ?

a)   260 metres

b)   275 metres

c)   265 metres

d)   285 metres

e)   None of these

3). A 380 metre long train crosses a platform in 23 seconds. What is the speed of train ?

a)   146 kmph

b)   46 kmph

c)   49 kmph

d)   Cannot be determined

e)   None of these

4). A 500 m long goods train crosses a platform in 36 seconds. If the length of the platform is 220 m then what is the speed of the goods train in km/hr ?

a)   60

b)   72

c)   80

d)   85

e)   None of these

5). Two trains of equal length are running on parallel lines in the same direction at 46 km/h and 36 km/hr . The faster train passes, the slower train in 36 sec. the length of each train is :

a)   50m

b)   80m

c)   72m

d)   82m

e)   None f these

6). The length of a train and a platform is equal. The train at the speed of 90km/hr crosses the platform in 1 minute. What is the length of platform ?

a)   750m

b)   690m

c)   760m

d)   810m

e)   None of these

7). Train A crosses a pole and platform in 18 seconds and 39 seconds respectively. The length of platform is 157.5 metre. What will be the length of train B if it is equal to the sum of half of the length of train A and twice the length of the platform ?

a)   382.5 metre

b)   328.5 metre

c)   238.5 metre

d)   315 metre

e)   None of these

8). A 222 metre long train crosses a pole in 6 seconds. The same train crosses a man running in the same direction in 10 seconds. What will be the speed of man ?

a)   15 m/ sec

b)   17 m / sec

c)   18 m / sec

d)   14 m / sec

e)   None of these

9). Trains leave a station A for another station B after a gap of every one hour. While trains leave station B for the station A also after a gap of every one hour. Each train takes 4 hours to complete the journey. Trains leave the stations A and B simultaneously after an interval of every one hour. If a person starts from the station A for the station B, how many trains will he cross before arriving at the station B ?

a)   4

b)   5

c)   7

d)   8

e)   None of these

10). A train can travel 50% faster than a car. Both start from point A at the same time and reach point B. 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

a)   100 km / h

b)   110 km / h

c)   120 km / h

d)   130 km / h

e)   None of these

1).Total distance to be covered = 280 + 460 = 740 metre

:. Time taken = 740 / 7.4 = 100 second

2). Speed of train = 108 kmph = [108 × (5/18)] m/ second

= 30 m/ second

If the length of train be x metre, then

Speed of train = length of train and platform / time taken à 30 = (x+365) / 21

30 × 21 = x+365 à 630 = x+365

x = 630 – 365 = 265 metre

3). Speed of train = length of train and platform / time taken in crossing

Here, the length of platform is not given. Hence cannot be determined.

4). Speed f goods train

= length of (platform + goods train) / time taken in crossing = (220 + 500) / 36 m/sec

= 20 m/ sec = (20 × 18) / 5 kmph

= 72 kmph

5). Let the length of each train be x metre. Relative speed = (46 – 36) kmph = 10 kmph

=( (10 × 5)/18) m /sec = (25/9) m /sec

Now (x + x) / (25 / 9) = 36 à (25/9) × 36 = 2x

2x = 100 à x = 50 metre

6). Let the length f platform be x metre. Speed = 90 kmph

= [(90 × 5)/18 ] m/ sec = 25 m / sec

Time = 1 minute = 60 seconds

:. 2x / 25 = 60 à 2x = 25 × 60

x = (25 × 60) / 2 = 750metre.

7). Length of train A = x metre

Speed of the train

:. x/18 = (x + 157.5) / 39 à 13x = 6x + 157.5 × 6

7x = 945 à x = 945 / 7 = 135 metre

:. Length of train B =[ (135/2) + 2 × 157.5] metre

= (67.5 + 315) metre = 382.5 metre

8). Speed of train = 222 / 6 = 37 m /sec

If the speed of man be x m / sec, then 220 / (37 -x) = 10

220 = 370 – 10x à 10x = 370 – 220 = 150

X = 15 m /sec

9). If the person starts at 7am from A, he will cross the trains starting from B at 4am, 5am, 6am, 7am, 8am, 9am, 10am.

10). Speed of car = x kmph

Speed of train = 3x / 2 kmph

:. ( 75 / x) – [75 / (3x/2)] = 12.5/60

75 [(1/x) – (2/3x)] = 5/24 à 75 [(3-2) / 3x] = 5/24

75 / 3x = 5/24 à 15 × 8 = x

:. x = 120 kmph