Aptitude

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📘 Height-and-Distance
📘 series
📘 Time and Distance
📘 Time and Work
📘 Train

82. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

by
[A]. 50 m
[B]. 72 m
[C]. 80 m
[D]. 82 m
✅ The correct answer is option A.
Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 – 36) km/hr

   =

10 x
5
m/sec

18

   =

25
m/sec

9

2x
=
25

36
9

2x = 100
x = 50.

83. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

by
[A]. 30 km/hr
[B]. 45 km/hr
[C]. 60 km/hr
[D]. 75 km/hr
✅ The correct answer is option C.
Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.

(100 + 100)
= 3x

8

24x = 200

x =
25
.

3

So, speed of the faster train =
50
m/sec

3

   =

50
x
18
km/hr

3
5

   = 60 km/hr.

84. How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

by
[A]. 25
[B]. 30
[C]. 40
[D]. 45
✅ The correct answer is option B.
Speed of the train relative to man
= (63 – 3) km/hr

= 60 km/hr

=

60 x
5

m/sec

18

=

50

m/sec.

3

Time taken to pass the man

=

500 x
3

sec

50

= 30 sec.

85. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

by
[A]. 36
[B]. 45
[C]. 48
[D]. 49
✅ The correct answer is option C.
Relative speed = (60+ 90) km/hr

   =

150 x
5
m/sec

18

   =

125
m/sec.

3

Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.

Required time =

2000 x
3
sec = 48 sec.

125

86. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

by
[A]. 10
[B]. 12
[C]. 15
[D]. 20
✅ The correct answer is option B.
Speed of the first train =

120

m/sec = 12 m/sec.

10

Speed of the second train =

120

m/sec = 8 m/sec.

15

Relative speed = (12 + 8) = 20 m/sec.

Required time =

(120 + 120)

sec = 12 sec.

20

87. A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

by
[A]. 400 m
[B]. 450 m
[C]. 560 m
[D]. 600 m
✅ The correct answer is option A.
Let the length of the first train be x metres.

Then, the length of the second train is

x

metres.

2

Relative speed = (48 + 42) kmph =

90 x
5

m/sec = 25 m/sec.

18

[x + (x/2)]
= 12 or
3x
= 300     or     x = 200.

25
2

Length of first train = 200 m.
Let the length of platform be y metres.

Speed of the first train =

48 x
5

m/sec =
40
m/sec.

18
3

(200 + y) x
3
= 45

40

600 + 3y = 1800
y = 400 m.

89. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

by
[A]. 23 m
[B]. 23 2 m 9
[C]. 27 7 m 9
[D]. 29 m
✅ The correct answer is option C.
Relative speed = (40 – 20) km/hr =

20 x
5

m/sec =

50

m/sec.

18
9

Length of faster train =

50
x 5

m =
250
m = 27
7
m.

9
9
9

90. Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:

by
[A]. 10
[B]. 18
[C]. 36
[D]. 72
✅ The correct answer is option C.
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.

So, 2x =
(120 + 120)

12

2x = 20
x = 10.

Speed of each train = 10 m/sec =

10 x
18

km/hr = 36 km/hr.

5