Learn and practice the chapter "Problems on Trains" with these solved Aptitude Questions and Answers. Each question in the topic is accompanied by a clear and easy explanation, diagrams, formulae, shortcuts and tricks that help in understanding the concept.

Use of Problems on Trains

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1. There are two trains moving towards each other with a speed 15 m/s and 20 m/s. Their lengths are 124 m and 121 m respectively. How much time would they need to cross each other?

a. 7 seconds
b. 11 seconds
c. 35 seconds
d. 49 seconds

Answer: a. 7 seconds

Explanation:

As they are moving in opposite directions,
Relative Speed = 15 + 20 = 35 m/s
Distance covered = Length of train 1 + Length of train 2 = 124+121 = 245 m

Time =

Distance covered

=

245

= 7 seconds

Relative Speed

35

Going further,
If they say that the trains are moving in same direction and how much time is taken by the faster train to cross the slower train, then we can say that Relative Speed = 20-15 = 5 m/s

Time =

Distance covered

=

245

= 49 seconds

Relative Speed

5

2. A train takes 24 seconds to cross a 240 m long bridge and 10 seconds to cross a stationary pole. Find the length and speed of train.

a. Length = 100m; Speed = 10 m/s
b. Length = 160.8m; Speed = 16.08 m/s
c. Length = 171.14m; Speed = 17.14 m/s
d. Length = 200m; Speed = 20 m/s

Answer: c. Length = 171.14m; Speed = 17.14 m/s

Explanation:

D = S x T

∴ S =

D

; T =

D

T

S

In 1^{st} case, distance travelled = length of train = L
In 2^{nd} case, distance travelled = length of train + length of bridge = (L+240) m
Speed of train is same in both cases.
∴ S = S

∴

L

=

L+240

10

10

∴ L = 171.4 m = length of train

∴ Speed of train =

L

=

171.4

= 17.14 m/s

10

10

3. A 150 m long train takes 4 seconds less than a minute to cross a 0.55 km long platform. Find the time it will take to cross a 250 m long platform at the next station.

a. 24 seconds
b. 28 seconds
c. 30 seconds
d. 32 seconds

Answer: d. 32 seconds

Explanation:

D = S x T

∴ S =

D

; T =

D

T

S

Some simplifications before we begin solving the question:
i. 4 seconds less than a minute = 56 seconds
ii. 0.55 km = 550 m

Case 1, distance travelled = length of train + length of platform = 150+550 = 700m
Case 2, distance travelled = 150+250 = 400 m

Speed of train is same in both cases.
∴ S = S

∴

700

=

400

56

?

∴ ? = 32 seconds = Time taken to cross platform of 250m

4. Two trains start from stations A and B at the same time and start moving towards each other. A moves at a speed of 120 km/ hr while B is 20 km/ hr slower than A. They meet at a point but by then one train has already covered a distance of 40 km more than the other one. What is the distance between two stations?

a. 180 kms
b. 220 kms
c. 260 kms
d. 440 kms

Answer: d. 440 kms

Explanation:

Since the difference in speeds is 20km/hr
So, if they meet in say 1 hour, one train travels just 20 kms more than other.
If they meet in 2 hours, it would travel 20kms x 2 = 40kms more than other train.
This is as per given condition.

Now, distance covered in 2 hours by both trains = Distance between A and B
∴ Distance between A and B = (120km/hr x 2 hrs) + (100km/hr x 2hrs) ∴ Distance between A and B = 440 kms.

5. Two trains start from the same starting points and move towards the same destination. The first one starts half an hour earlier than the second one. The first one runs at a speed of 90 km/hr while the second one runs at 30 km/hr faster. At what distance from the starting point will the two trains meet?

a. 150 kms
b. 180 kms
c. 360 kms
d. 450 kms

Answer: b. 180 kms

Explanation:

D = S x T

∴ S =

D

; T =

D

T

S

Since the second train is 30 km/hr faster, it is moving at 120 km/hr
Now, let train A travel T hours before meeting train B.
Time for which train B travels = (T - ½) hrs.
This is because it starts half an hour late
Distance travelled is same.
∴ D = D
∴ 90km/hr x T hrs = 120 km/hr x (T - ½) hrs
∴ 90T = 120T - 60 ∴ T = 2 hours
Distance travelled by train A = 90 km/hr x 2 hours = 180kms. Thus they meet 180 kms from starting point.