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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-5 section-1

41
Two trains of lenths 120 m and 90 m are running with speed of 80 km/hr and 55 km/hr respectively towards each other on parallel lines. If they are 90 m apart, after how many seconds they will cross each other?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{Relative speed}} \cr & {\text{ = (80 + 55)km/hr}} \cr & {\text{ = 135 km/hr}} \cr & {\text{ = }}\left( {135 \times \frac{5}{{18}}} \right)m/\sec \cr & = \left( {\frac{{75}}{2}} \right)m/\sec \cr & {\text{Distance covered}} \cr & {\text{ = (120 + 90 + 90)m}} \cr & {\text{ = 300m}} \cr & {\text{Required time}} \cr & {\text{ = }}\left( {300 \times \frac{2}{{75}}} \right)\sec \cr & = 8\sec \cr} $$
42
Two trains are coming from opposite directions with speed of 75 km/hr and 100 km/hr on to parallel tracks. At some moment the distance between them is 100km. After T hours, distance between them is again 100 km. T is equal to?
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{Relative speed}} \cr & {\text{ = (75 + 100)km/hr}} \cr & {\text{ = 175 km/hr}} \cr & {\text{Time taken to cover 175 km}} \cr & {\text{at relative speed = 1 hr}} \cr & \therefore {\text{T = Time taken to cover 200 km}} \cr & {\text{ = }}\left( {\frac{1}{{175}} \times 200} \right)\, \text{hr} \cr & = \frac{8}{7}\, \text{hr} \cr & = 1\frac{1}{7}\, \text{hr} \cr} $$
43
A train, 240 m long, crosses a man walking alone the line in opposite direction at the rate of 3 kmph in 10 seconds. The speed of the train is?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{Speed of the train relative to man}} \cr & {\text{ = }}\left( {\frac{{240}}{{10}}} \right){\text{m/sec}} \cr & {\text{ = 24 m/sec}} \cr & {\text{ = }}\left( {24 \times \frac{{18}}{5}} \right){\text{ km/sec}} \cr & {\text{ = }}\frac{{432}}{5}{\text{km/hr}} \cr & {\text{Let the speed of the train be x kmph}}{\text{.}} \cr & {\text{Then relative speed = }}\left( {x + 3} \right){\text{kmph}} \cr & \therefore x{\text{ + 3 = }}\frac{{432}}{5} \cr & \Rightarrow x = \frac{{432}}{5} - 3 \cr & \Rightarrow x = \frac{{417}}{5} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 83.4\,{\text{kmph}} \cr} $$
44
Two trains of equal length are running on parallel lines in the same directions at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is?
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{Let the length of each train be }}x{\text{ metres}} \cr & {\text{Then distance covered}} \cr & {\text{ = 2x metres}} \cr & {\text{Relative speed}} \cr & {\text{ = (46}} - {\text{36)km/hr}} \cr & {\text{ = }}\left( {10 \times \frac{5}{{18}}} \right)m/\sec \cr & = \left( {\frac{{25}}{9}} \right)m/\sec \cr & \therefore \frac{{2x}}{{36}} = \frac{{25}}{9} \Leftrightarrow 2x = 100 \Leftrightarrow x = 50 \cr} $$
45
Two trains of equal lengths takes 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 miters, in what time ( in seconds) will they cross each other traveling in opposite direction?
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{Speed of the train}} \cr & {\text{ = }}\left( {\frac{{120}}{{10}}} \right){\text{ m/sec}} \cr & {\text{ = 12 m/sec}} \cr & {\text{Speed of the second train}} \cr & {\text{ = }}\left( {\frac{{120}}{{15}}} \right){\text{ m/sec}} \cr & {\text{ = 8 m/sec}} \cr & {\text{Relative speed}} \cr & {\text{ = (12 + 8)m/sec}} \cr & {\text{ = 20 m/sec}} \cr & \therefore {\text{Required time}} \cr & {\text{ = }}\frac{{\left( {120 + 120} \right)}}{{20}}\,\sec \cr & = 12\,\sec \cr} $$
46
A train B speeding with 120 kmph crosses another train C running in the same direction, in 2 minutes. If the lengths of the trains B and C be 100m and 200m respectively, what is the speed (in kmph) of the train C?
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & {\text{Relative speed of the trains }} \cr & {\text{ = }}\left( {\frac{{100 + 200}}{{2 \times 60}}} \right){\text{m/sec}} \cr & {\text{ = }}\left( {\frac{5}{2}} \right){\text{m/sec}} \cr & {\text{Speed of train B}} \cr & {\text{ = 120 kmph}} \cr & = \left( {120 \times \frac{5}{{18}}} \right){\text{m/sec}} \cr & {\text{ = }}\left( {\frac{{100}}{3}} \right){\text{m/sec}} \cr & {\text{Let the speed of second train be }}x{\text{ m/sec}} \cr & {\text{Then, }} \frac{{100}}{3} - x = \frac{5}{2} \cr & \Rightarrow x = \left( {\frac{{100}}{3} - \frac{5}{2}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{185}}{6}} \right){\text{m/sec}} \cr & \therefore {\text{Speed of second train}} \cr & {\text{ = }}\left( {\frac{{185}}{6} \times \frac{{18}}{5}} \right){\text{ kmph}} \cr & {\text{ = 111 kmph}} \cr} $$
47
What is the speed of a train if it overtakes two persons who are walking in the same direction at the rate of a m/s and (a + 1) m/s and passes them completely in b seconds and (b + 1) seconds respectively?
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{Let the length of the train be }}x{\text{ metres}} \cr & {\text{and its speed be }}y{\text{ m/s}} \cr & {\text{Then,}} \cr & {\text{ }}\frac{x}{{y - a}}{\text{ = b}}\,\,{\text{and}}\, \cr & \,\frac{x}{{y - \left( {a + 1} \right)}} = \left( {b + 1} \right) \cr & \Leftrightarrow {\text{ }}x{\text{ = }}b\left( {y - a} \right){\text{ and}} \cr & \,\,\,\,\,\,\,\,\,\,{\text{ }}x = \left( {b + 1} \right)\left( {y - a - 1} \right) \cr & \Leftrightarrow b\left( {y - a} \right) = \left( {b + 1} \right)\left( {y - a - 1} \right) \cr & \Leftrightarrow by - ba = by - ba - b + y - a - 1 \cr & \Leftrightarrow y = \left( {a + b + 1} \right) \cr} $$
48
A train passes a 50 meter long platform in 14 seconds and a man standing on platform 10 seconds.The speed of the train is?
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & {\text{Distance travelled in 14 sec}} \cr & {\text{ = 50 + }}l \cr & {\text{Distance travelled in 10 sec}} \cr & {\text{ = }}l \cr & {\text{So speed of train}} \cr & {\text{ = }}\frac{{50}}{{14 - 10}}{\text{m/sec}} \cr & {\text{ = }}\frac{{50}}{4} \times \frac{{18}}{5}{\text{km/hr}} \cr & {\text{ = 45 km/hr}} \cr} $$
49
A train is moving at a speed of 132 km/hr. If the length of the train is 110 meters, how long it will take to cross a railway platform 165 meter long?
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{Speed = 132 km/hr }} \cr & {\text{ = 132}} \times \frac{5}{{18}}{\text{m/sec}} \cr & {\text{ = }}\frac{{110}}{3}m/\sec \cr & T = \frac{D}{S} \cr & \,\,\,\,\,\, = \frac{{110 + 165}}{{\frac{{100}}{3}}} \cr & \,\,\,\,\,\, = \frac{{3\left( {275} \right)}}{{110}} \cr & \,\,\,\,\,\, = 7.5\sec \cr} $$
50
A train of length 500 feet crosses a platform of length 700 feet in 10 seconds. The speed of the train is?
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & {\text{Speed of the train}} \cr & {\text{ = }}\frac{{700 + 500}}{{10}} \cr & {\text{ = 120 ft/second}} \cr} $$