1. 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?

a) 5.6 sec

b) 7.2 sec

c) 8 sec

d) 9 sec.

Explanation:

$$\eqalign{ & {\text{Relative speed}} \cr & {\text{ = (80 + 55)km/hr}} \cr & {\text{ = 135 km/hr}} \cr & {\text{ = }}\left( {135 \times \frac{5}{{18}}} \right)m/\sec \cr & = \left( {\frac{{75}}{2}} \right)m/\sec \cr & {\text{Distance covered}} = (120 + 90 + 90)m \cr & {\text{ = 300m}} \cr & {\text{Required time}} \cr & {\text{ = }}\left( {300 \times \frac{2}{{75}}} \right)\sec \cr & = 8\sec \cr} $$

2. 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?

a) 1 hr

b) $$1\frac{1}{7}$$ hr

c) $$1\frac{1}{2}$$ hr

d) 2 hr

Explanation:

$$\eqalign{ & {\text{Relative speed}} = (75 + 100)km/hr \cr & {\text{ = 175 km/hr}} \cr & {\text{Time taken to cover 175 km}} \cr & {\text{at relative speed = 1 hr}} \cr & {\text{T = Time taken to cover 200 km}} \cr & {\text{ = }}\left( {\frac{1}{{175}} \times 200} \right)\, \text{hr} \cr & = \frac{8}{7}\, \text{hr} \cr & = 1\frac{1}{7}\, \text{hr} \cr} $$

3. 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?

a) 63 kmph

b) 75 kmph

c) 83.4 kmph

d) 86.4 kmph

Explanation:

$$\eqalign{ & {\text{Speed of the train relative to man}} \cr & {\text{ = }}\left( {\frac{{240}}{{10}}} \right){\text{m/sec}} \cr & {\text{ = 24 m/sec}} \cr & {\text{ = }}\left( {24 \times \frac{{18}}{5}} \right){\text{ km/sec}} \cr & {\text{ = }}\frac{{432}}{5}{\text{km/hr}} \cr & {\text{Let the speed of the train be x kmph}}{\text{.}} \cr & {\text{Then relative speed = }}\left( {x + 3} \right){\text{kmph}} \cr & x{\text{ + 3 = }}\frac{{432}}{5} \cr & x = \frac{{432}}{5} - 3 \cr & x = \frac{{417}}{5} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 83.4\,{\text{kmph}} \cr} $$

4. 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?

a) 50 m

b) 72 m

c) 80 m

d) 82 m

Explanation:

$$\eqalign{ & {\text{Let the length of each train be }}x{\text{ metres}} \cr & {\text{Then distance covered}} \cr & {\text{ = 2x metres}} \cr & {\text{Relative speed}} \cr & {\text{ = (46}} - {\text{36)km/hr}} \cr & {\text{ = }}\left( {10 \times \frac{5}{{18}}} \right)m/\sec \cr & = \left( {\frac{{25}}{9}} \right)m/\sec \cr & \frac{{2x}}{{36}} = \frac{{25}}{9} \Leftrightarrow 2x = 100 \Leftrightarrow x = 50 \cr} $$

5. 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?

a) 10

b) 12

c) 15

d) 20

Explanation:

$$\eqalign{ & {\text{Speed of the train}} \cr & {\text{ = }}\left( {\frac{{120}}{{10}}} \right){\text{ m/sec}} \cr & {\text{ = 12 m/sec}} \cr & {\text{Speed of the second train}} \cr & {\text{ = }}\left( {\frac{{120}}{{15}}} \right){\text{ m/sec}} \cr & {\text{ = 8 m/sec}} \cr & {\text{Relative speed}} \cr & {\text{ = (12 + 8)m/sec}} \cr & {\text{ = 20 m/sec}} \cr & {\text{Required time}} \cr & {\text{ = }}\frac{{\left( {120 + 120} \right)}}{{20}}\,\sec \cr & = 12\,\sec \cr} $$

6. 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?

a) 100 meters

b) 150 meters

c) 180 meters

d) 200 meters

Explanation: 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

7. 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

a) 18 sec

b) 21 sec

c) 24 sec

d) 25 sec

Explanation: 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

8. 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:

a) 72 seconds

b) 132 seconds

c) 192 seconds

d) 252 seconds

Explanation: 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

9. 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?

a) 61 seconds

b) 62 seconds

c) 63 seconds

d) 64 seconds

Explanation: 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

$$\eqalign{ & = \left[ {\frac{{\left( {{\text{x}} - 100} \right) + {\text{y}}}}{{\frac{{25}}{2}}}} \right]{\text{sec}} \cr & = \left[ {\frac{{\left( {{\text{x}} + {\text{y}}} \right) - 100}}{{\frac{{25}}{2}}}} \right]{\text{sec}} \cr & = \left( {800 \times \frac{2}{{25}}} \right){\text{sec}} \cr & = 64\,{\text{sec}} \cr} $$.

10. 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:

a) 45 km/hr

b) 50 km/hr

c) 54 km/hr

d) 55 km/hr

Explanation: 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