Problems on Trains - Quantitative Aptitude (MCQ) questions

1)   Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 60 km more than the other. What is the distance between the two stations?
- Published on 06 May 16

a. 620 km
b. 540 km
c. 460 km
d. 720 km
Answer  Explanation 

ANSWER: 540 km

Explanation:
Let us assume that trains meet after 'x' hours
Distance = speed * Time
Distance traveled by two trains = 20x km and 25x km resp.
As one train travels 60 km more than the other,
25x – 20x = 60
5x = 60
x = 12 hours
As the two trains are moving towards each other, relative speed = 20 + 25 = 45 km/hr
Therefore, total distance = 45*12 = 540 km.


2)   Two trains of lengths 156.62 and 100 meters are running on parallel lines with respective speeds of 30 km/hr and 36 km/hr. The time of crossing each other, if they run in the opposite direction is __________ .
- Published on 05 May 16

a. 10 sec
b. 62 sec
c. 14 sec
d. 12 sec
e. None of these
Answer  Explanation 

ANSWER: 14 sec

Explanation:
Total distance to be covered = 156.62 + 100 = 256.62 m
Trains are running in opposite directions, hence
Relative speed = 30 + 36 = 66 km/hr = 18.33 m/sec
Time = Distance / Relative Speed
= 256.62 /18.33 sec
= 14 sec
Therefore, the time of crossing each other in the opposite direction is 14 seconds.


3)   Two trains are traveling in the same direction at speeds of 50 kmph and 20 kmph respectively If the faster train passes the driver in the slower train in 20 seconds, What is the length of the faster train?
- Published on 25 Apr 16

a. 150 m
b. 149 m
c. 162 m
d. 166 m
e. None of these
Answer  Explanation 

ANSWER: 166 m

Explanation:
Given :
Speed of fast train = 50 kmph.
Speed of slow train = 20 kmph.
The driver in the slower train is moving with the speed of the slower train which is 20 kmph.
The faster train will pass the driver when it has gained a distance. Distance gained by faster train
in 1 hour = (50 – 20) = 30 km
= 8.33 m/sec
Distance gained by faster train in 20 sec = 20 * 8.33 = 166.6 m.
Therefore, Length of faster train = 166.6 m.


4)   A boy sitting in a train counts the electricity poles along the line as he passes them. If they are 40 m apart and the speed of the train is 48 km/h, how many poles does he pass per minute ?
- Published on 22 Apr 16

a. 14
b. 19
c. 21
d. 24
e. None of these
Answer  Explanation 

ANSWER: 21

Explanation:
Speed of train = 48 km/h = (48 * 1000)/60 m/minute
= 800 m/minute
Thus we have to find the number of poles situated along a distance of 800 with each pole at a distance of 40 m from each other.

|--------40 m-------|--------40 m ---------|
Consider a distance of 80 m. There are 3 poles situated along this distance as shown.
Thus number of poles = 80/40 + 1 = 2 + 1 = 3
Similarly along a distance of 900 m, number of poles situated
= 800/40 + 1 = 21


5)   How long does a train 90 metres long running at the speed of 71 km/hr take to cross a bridge 132 metres in length?
- Published on 06 Apr 16

a. 9.8 sec
b. 11.26 sec
c. 12.42 sec
d. 14.3 sec
Answer  Explanation 

ANSWER: 11.26 sec

Explanation:
Speed = (71 x 5/18) m/sec = 19.72 m/sec
Total distance covered = (90 + 132) m = 222 m.
Required time = (222/19.72) sec = 11.26 sec


6)   A train travels a certain distance by taking 3 stops of 20 minutes each. Considering the period of stoppage, the overall speed of the train comes to 40 kmph; while without consideration of stoppage, it is 60 kmph. How much distance must the train have travelled ?
- Published on 31 Mar 16

a. 170 kms
b. 120 kms
c. 270 kms
d. None of these
e. Cannot be determined
Answer  Explanation 

ANSWER: 120 kms

Explanation:
Let the time taken to travel the distance without taking stops be “b” hours.
Thus, we get,
60 x b = 40(b + 1)
b = 2
Thus, we get 60 x 2 = 120 kms


7)   A train takes 20 seconds to pass completely through a station 160 m long and 15 seconds through another station 110 m long. Find the length of the train.
- Published on 28 Mar 16

a. 100 m
b. 70 m
c. 60 m
d. 40 m
Answer  Explanation 

ANSWER: 40 m

Explanation:
Let the length of the train be x meters.
Therefore (x + 160)/20 = (x + 110)/15 = 15(x + 160) = 20(x+110)
x = 40 m


8)   Two trains 140 metres and 120 metres are running in the same direction with speeds 40 kmph and 60 kmph respectively. In what time will the faster train pass the slower one?
- Published on 06 Jul 15

a. 0.60 minutes
b. 0.36 minutes
c. 0.78 minutes
d. 0.42 minutes
Answer  Explanation 

ANSWER: 0.78 minutes

Explanation:
Total distance = addition of length of the two trains = 140 + 120 = 260 metres
As the two trains are travelling in the same direction, their relative speed is:
v = | v1 – v2 | = | 40 – 60 | = 20 km/hr = 20*1000/60 = 1000/3 metres/min
t = 260/ 1000*3
t = 0.78 minutes


9)   Two trains each of which is 100 m long moving in opposite direction to one another cross each other taking 8 seconds. If speed of one train is twice the speed of other
train find the speed of the faster train.

- Published on 15 Jun 15

a. 48 km/hr
b. 30 km/hr
c. 60 km/hr
d. 40 km/hr
Answer  Explanation 

ANSWER: 60 km/hr

Explanation:
No explanation is available for this question!


10)   A train runs across a post in 15 seconds and across a platform of length 100m in 25 seconds. Determine the length of this train:
- Published on 15 Jun 15

a. A. 50 m
b. C. 200m
c. D. 130m
d. B. 150 m
Answer  Explanation 

ANSWER: B. 150 m

Explanation:
Let us assume for this question that the length of train is x metres and it is assumed to be running at the speed of y m/sec.

A pole is assumed as a point object.

=>Time taken by the train to pass the pole= x/y

=>15=x/y

=>y=x/15

Now, the train passes the platform which is 100 m in length in 25 seconds.

=>x+100/y=25

=>x+100/25=y

Equating speed generated from both cases:

x+100/25=x/15

Therefore x = 150 metres.


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