Train Questions for IIFT PDF
Download important IIFT Train Questions PDF based on previously asked questions in IIFT and other MBA exams. Practice Train questions and answers for IIFT exam.
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Question 1: Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southwest of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to
a) 6 : 15 am
b) 6 : 30 am
c) 6 :45 am
d) 7 : 00 am
e) 7 : 15 am
Question 2: Train X departs from station A at 11 a.m. for station B, which is 180 km so far. Train Y departs from station B at 11 a.m. for station A. Train X travels at an average speed of 70 km/hr and does not stop anywhere until it arrives at station B. Train Y travels at an average speed of 50 km/hr, but has to stop for 15 min at station C, which is 60 km away from station B enroute to station A. Ignoring the lengths of the trains, what is the distance, to the nearest kilometre, from station A to the point where the trains cross each other?
a) 112 km
b) 118 km
c) 120 km
d) None of these
Question 3: Only a single rail track exists between stations A and B on a railway line. One hour after the northbound super fast train N leaves station A for station B, a south-bound passenger train S reaches station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day, N leaves for B from A, 20 min behind the normal schedule. In order to maintain the schedule, both N and S increased their speeds. If the super fast train doubles its speed, what should be the ratio (approximately) of the speeds of passenger train to that of the super fast train so that the passenger train S reaches exactly at the scheduled time at A on that day?
a) 1 : 3
b) 1 : 4
c) 1 : 5
d) 1 : 6
Question 4: A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is 3/8 of the distance AB measured from the entrance A. When the train whistles the cat runs. If the cat moves to the entrance of the tunnel A, the train catches the cat exactly at the entrance. If the cat moves to the exit B, the train catches the cat at exactly the exit. What is the ratio of speed of train and cat ?
a) 3 : 1
b) 4 :1
c) 5 : 1
d) None of these
Question 5: Two trains are traveling in opposite direction at uniform speed 60 and 50 km per hour respectively. They take 5 seconds to cross each other. If the two trains had traveled in the same direction, then a passenger sitting in the faster moving train would have overtaken the other train in 18 seconds. What are the lengths of trains (in metres)?
a) 112.78
b) 97.78, 55
c) 102.78, 50
d) 102.78, 55
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Question 6: An express train travelling at 80 km/hr overtakes a goods train, twice as long and going at 40 km/hr on a parallel track, in 54 s. How long will the express train take to cross a platform of 400 m long?
a) 36 s
b) 45 s
c) 27 s
d) None of these
Question 7: It takes 15 seconds for a train travelling at 60 km/hour to cross entirely another train half its length and travelling in opposite direction at 48 km/hour. It also passes a bridge in 51 seconds. The length of the bridge is
a) 550 m
b) 450 m
c) 500 m
d) 600 m
Question 8: The duration of the journey from your home to the College in the local train varies directly as the distance and inversely as the velocity. The velocity varies directly as the square root of the diesel used per km., and inversely as the number of carriages in the train. If, in a journey of 70 km. in 45 minutes with 15 carriages, 10 litres of diesel is required, then the diesel that will be consumed in a journey of 50 km. in half an hour with 18 carriages is
a) 2.9 litres
b) 11.8 litres
c) 15.7 litres
d) None of the above
Question 9: A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train’s departure. The distance (in km) from his home to the railway station is
Question 10: Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance between X and Z is three-fifths of that between X and Y. How many hours does train T take for its journey from X to Y?
Answers & Solutions:
1) Answer (B)
According to given conditions angle between AC and AB is 30 degrees and between AB and BC is 60 degrees. So the triangle formed is a 30-60-90 triangle.
So, total time taken by train is 5 hrs, hence the train reaches at 1 pm. Accordingly, Rahim has to reach C fifteen minutes before i.e. at 12:45 PM.
Time taken by Rahim to travel by car is around 6.2 hrs. So, the latest time by which Rahim must leave A and still be able to catch the train is 6:30 am.
2) Answer (A)
Distance between A-B , A-C, C-B is 180, 120 and 60 km respectively.
Let x be the distance from A where the 2 trains meet.
According to given condition we have
$\frac{x}{70}=\frac{60}{50} + \frac{1}{4} + \frac{120-x}{50}$.
Solving the equation we get x around 112 km.
3) Answer (D)
Let the speed of an express train be 4x, normal train be 2x and passenger train be x.
Let the distance between the 2 stations be D.
Since there is only 1 railway track, train N must reach station B before train S leaves.
Therefore, D/4x + D/x = 60
5D/4x = 60
D/x = 48
Train N leaves 20 minutes late. Therefore, the 2 trains must have covered the distance within 40 minutes on this particular day.
Train N doubles its speed. Therefore, speed of train N will be 8x. Let the new speed of the passenger train be y.
D/8x + D/y = 40
48/8 + D/y = 40
D/y = 34.
Speed of super fast train = D/8x = 6
Speed of passenger train = D/y = 34
Ratio of the speeds = 6/34 = 3/17.
The ratio is approximately equal to 1:6. Therefore, option D is the right answer.
4) Answer (B)
Let the length of the tunnel be x and distance of the train to entrance A be y. Let the speeds of train and cat be t and c respectively.
Hence, when the cat runs 3x/8, the train covers y.
=> (3x/8)/c = y/t — (1)
When the cat runs 5x/8 to the other end, the train covers x+y
=>(5x/8)/c = (x+y)/t —(2)
Taking ratio of (1) to (2)
3/5 = y/(x+y) => 3x = 2y —(3)
Substituting (3) in (1)
(2y/8)/c = y/t
=> t = 4c
Hence the ratio t:c is 4:1.
5) Answer (C)
let’s $l_s$ is length of slower train and $l_f$ is length of faster train.
So according to second condition when two trains are moving in same direction
$l_s = v_{fs} \times t$ (where $v_{fs}$ is relative velocity of faster train w.r.t. slower train and t is time taken to cross it)
or $l_s = \frac{(60-50) \times 5}{18} \times 18$ = 50 meter
Only option which has length of slower train as 50 is C.
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6) Answer (C)
Let’s say length of express train = $x$
So length of goods train = $2x$
Total length travelled by express train = $3x = ((80-40) \times \frac{5}{18}) \times 54 $ (Where $(80-40) \times \frac{5}{18})$ = relative velocity of express train w.r.t. goods train in meter/sec.)
So $x =200$ meter.
Now crossing a plateform of length 400 m., total length travelled by train = 600 m=$t\times(80 \times \frac{5}{18})$
$t = 27$ sec.
7) Answer (A)
Speed of train 1 = 60 km/hr = 50/3 m/s
Speed of train 2 = 48 km/hr = 40/3 m/s
Thus, their relative speed = 90/3 = 30 m/s
Let, Length of train 1 = l
Thus, the length of train 2 will be 0.5 l
Time taken by them to cross each other = 15 s
Thus, $ 15*30 = 1.5l$
Thus, $ l = 300 $
Train 1 takes 51s to cross a bridge
Let the length of the bridge be b
Thus, $\frac{50*51}{3} = 300+b $
Hence, $ 850 = 300+b $
Hence, $b = 550$ m
Thus, option A is the correct answer.
8) Answer (B)
Let D be the distance, T be the time, V be the velocity, N be the number of carriages and X be the liters of Diesel required.
Given T$\ltimes \dfrac{D}{V}$
Also given that, V $\ltimes \dfrac{\sqrt{\frac{X}{D}}}{N}$
Thus, T = $\dfrac{k*N*D^{\frac{3}{2}}}{\sqrt{X}}$
Given when in a journey of 70 km, in 45 minutes with 15 carriages, 10 litres of diesel is required
Thus, 45 = $\dfrac{k*15*70^{\frac{3}{2}}}{\sqrt{10}}$
Thus, k = $\dfrac{3}{70\sqrt{7}}$
In a journey of 50 km, in half an hour with 18 carriages
30 = $\dfrac{3}{70\sqrt{7}}*\dfrac{50\sqrt{50}*18}{\sqrt{X}}$
Thus, $\sqrt{X} = \dfrac{9*\sqrt{50}}{7*\sqrt{7}}$
Thus, X = 11.8
Hence, option B is the correct answer.
9) Answer: 20
We see that the man saves 20 minutes by changing his speed from 12 Km/hr to 15 Km/hr.
Let d be the distance
Hence,
$\frac{d}{12} – \frac{d}{15} = \frac{1}{3}$
$\frac{d}{60} = \frac{1}{3}$
d = 20 Km.
10) Answer: 15
Train T starts at 3 PM and train S starts at 4 PM.
Let the speed of train T be t.
=> Speed of train S = 0.75t.
When the trains meet, train t would have traveled for one more hour than train S.
Let us assume that the 2 trains meet x hours after 3 PM. Trains S would have traveled for x-1 hours.
Distance traveled by train T = xt
Distance traveled by train S = (x-1)*0.75t = 0.75xt-0.75t
We know that train T has traveled three fifths of the distance. Therefore, train S should have traveled two-fifths the distance between the 2 cities.
=> (xt)/(0.75xt-0.75t) = 3/2
2xt = 2.25xt-2.25t
0.25x = 2.25
x = 9 hours.
Train T takes 9 hours to cover three-fifths the distance. Therefore, to cover the entire distance, train T will take 9*(5/3) = 15 hours.
Therefore, 15 is the correct answer.
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