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Problems On Trains - Aptitude MCQ Questions and Solutions with Explanations

Problems On Trains MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Problems On Trains with easy and logical explanations. Problems On Trains MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc. Page-8 section-1

71
A man sitting in a train is counting the pillars of electricity. The distance between two pillars is 60 meters, and the speed of the train is 42 km/hr. In 5 hours, how many pillars will he count?
Discuss
Answer & Solution
Answer: Option A
Solution:
Distance covered by the train in 5 hours
= (42 × 5) km
= 210 km
= 210000 m
∴ Number of pillars counted by the man
= $$\left( {\frac{{210000}}{{60}} + 1} \right)$$
= 3500 + 1
= 3501
72
A 120 meter long train is running at a speed of 90 km/hr. It will cross a railway platform 230 m long in :
Discuss
Answer & Solution
Answer: Option D
Solution:
Speed = $$\left( {90 \times \frac{5}{{18}}} \right)$$   m/sec = 25 m/sec
Total distance covered
= (120 + 230) m
= 350 m
∴ Required time
= $$\frac{{350}}{{25}}$$ seconds
= 14 seconds
73
A 50 meter long train passes over a bridge at the speed of 30 km per hour. If it takes 36 seconds to cross the bridge, what is the length of the bridge?
Discuss
Answer & Solution
Answer: Option B
Solution:
Speed = $$\left( {30 \times \frac{5}{{18}}} \right)$$  m/sec = $$\frac{{25}}{3}$$ m/sec
Time = 36 second
Let the length of the bridge be x meters.
Then, $$\frac{{50 + {\text{x}}}}{{36}}$$   = $$\frac{{25}}{3}$$
⇒ 3(50 + x) = 900
⇒ 50 + x = 300
⇒ x = 250 meters
74
A train takes 5 minutes to cross a telegraphic post. Then the time taken by another train whose length is just double of the first train and moving with same speed to cross a platform of its own length is :
Discuss
Answer & Solution
Answer: Option C
Solution:
Let the length of the train be x metres.
Time taken to cover x meters = 5 min
= (5 × 60) sec
= 300 sec
Speed of the train = $$\frac{{\text{x}}}{{300}}$$ m/sec
Length of the second train = 2x meters
Length of the platform = 2x meters
∴ Required time
$$\eqalign{ & = \left[ {\frac{{2{\text{x}} + 2{\text{x}}}}{{\left( {\frac{{\text{x}}}{{300}}} \right)}}} \right]{\text{sec}} \cr & = \left( {\frac{{4{\text{x}} \times 300}}{{\text{x}}}} \right){\text{sec}} \cr & = 1200\,{\text{sec}} \cr & = \frac{{1200}}{{60}}\,{\text{min}} \cr & = 20\,{\text{minutes}} \cr} $$
75
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Discuss
Answer & Solution
Answer: Option B
Solution:
Speed = $$\left( {54 \times \frac{5}{{18}}} \right)$$  m/sec = 15 m/sec
Length of the train = (15 × 20) m = 300 m
Let the length of the platform be x meters
Then, $$\frac{{{\text{x}} + 300}}{{36}}$$  = 15
⇒ x + 300 = 540
⇒ x = 240 meters
76
A train speeds past a pole in 20 seconds and speeds past a platform 100 meters in length in 30 seconds. What is the length of the train?
Discuss
Answer & Solution
Answer: Option D
Solution:
Let the length of the train be x meters and its speed be y m/sec.
Then, $$\frac{{\text{x}}}{{\text{y}}}$$ = 20
⇒ y = $$\frac{{\text{x}}}{{20}}$$
∴ $$\frac{{{\text{x}} + 100}}{{30}}$$  = $$\frac{{\text{x}}}{{20}}$$
⇒ 30x = 20x + 2000
⇒ 10x = 2000
⇒ x = 200 meters
77
The time taken by a train 180 m long, travelling at 42 kmph, in passing a person walking in the same direction at 6 kmph, will be
Discuss
Answer & Solution
Answer: Option A
Solution:
Speed of train relative to man
= (42 - 6) kmph = 36 kmph
= $$\left( {36 \times \frac{5}{{18}}} \right)$$  m/sec
= 10 m/sec
∴ Time taken to pass the man
= $$\frac{{180}}{{10}}$$ sec
= 18 sec
78
Two trains 200 meters and 150 meters long are running on parallel rails in the same direction at speed of 40 km/hr and 45 km/hr respectively. Time taken by the faster train to cross the slowed train will be:
Discuss
Answer & Solution
Answer: Option D
Solution:
Relative speed = (45 - 40) km/hr = 5 km/hr
= $$\left( {5 \times \frac{5}{{18}}} \right)$$  m/sec
= $$\frac{{25}}{{18}}$$ m/sec
Total distance covered = Sum of lengths of trains = (200 + 150) m = 350 m
∴ Time taken
= $$\left( {350 \times \frac{{18}}{{25}}} \right)$$   sec
= 252 seconds
79
A train with 90 km/hr crosses a bridge in 36 seconds. Another train 100 meters shorter crosses the same bridge at 45 km/hr. What is the time taken by the second train to cross the bridge?
Discuss
Answer & Solution
Answer: Option D
Solution:
Let the lengths of the train and the bridge be x meters and y meters respectively.
Speed of the first train
= 90 km/hr
= $$\left( {90 \times \frac{5}{{18}}} \right)$$  m/sec
= 25 m/sec
Speed of the second train = 45 km/hr
= $$\left( {45 \times \frac{5}{{18}}} \right)$$  m/sec
= $$\frac{{25}}{2}$$ m/sec
Then, $$\frac{{{\text{x}} + {\text{y}}}}{{36}}$$ = 25
⇒ x + y = 900
∴ Required time
$$\eqalign{ & = \left[ {\frac{{\left( {{\text{x}} - 100} \right) + {\text{y}}}}{{\frac{{25}}{2}}}} \right]{\text{sec}} \cr & = \left[ {\frac{{\left( {{\text{x}} + {\text{y}}} \right) - 100}}{{\frac{{25}}{2}}}} \right]{\text{sec}} \cr & = \left( {800 \times \frac{2}{{25}}} \right){\text{sec}} \cr & = 64\,{\text{sec}} \cr} $$
80
A train 125 m long passes a man, running at 5 kmph in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Discuss
Answer & Solution
Answer: Option B
Solution:
Speed of the train relative to man
$$\eqalign{ & = \frac{{125}}{{10}}{\text{m/sec}} \cr & = \frac{{25}}{2}{\text{m/sec}} \cr & = \left( {\frac{{25}}{2} \times \frac{{18}}{5}} \right){\text{m/sec}} \cr & = 45\,{\text{km/hr}} \cr} $$
Let the speed of the train be x kmph.
Then, relative speed = (x - 5) kmph
∴ x - 5 = 45 or
x = 50 km/hr