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91. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

[A]. 230 m

[B]. 240 m

[C]. 260 m

[D]. 270 m

✅ The correct answer is option D.
Speed =

72 x
5
m/sec
= 20 m/sec.

Time = 26 sec.
Let the length of the train be x metres.

Then,
x + 250
= 20

x + 250 = 520
x = 270.

62. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

[A]. 230 m

[B]. 240 m

[C]. 260 m

[D]. 320 m

✅ The correct answer is option A.
Relative speed = (120 + 80) km/hr

200 x
5
m/sec

500
m/sec.

Let the length of the other train be x metres.

Then,
x + 270
=
500

9
9

x + 270 = 500
x = 230.

64. Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:

[A]. 2 : 3

[B]. 4 : 3

[C]. 6 : 7

[D]. 9 : 16

✅ The correct answer is option B.
Let us name the trains as A and B. Then,
(A’s speed) : (B’s speed) = b : a = 16 : 9 = 4 : 3.

66. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

[A]. 48 km/hr

[B]. 54 km/hr

[C]. 66 km/hr

[D]. 82 km/hr

✅ The correct answer is option D.
Let the speed of the second train be x km/hr.

Relative speed
= (x + 50) km/hr

(x + 50) x
5

m/sec

250 + 5x

m/sec.

Distance covered = (108 + 112) = 220 m.

220
= 6

250 + 5x

250 + 5x = 660
x = 82 km/hr.

68. A train 125 m long passes a man, running at 5 km/hr 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

✅ The correct answer is option B.
Speed of the train relative to man =

125
m/sec

25
m/sec.

25
x
18
km/hr

2
5

= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x – 5) km/hr.
x – 5 = 45 x = 50 km/hr.

70. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

[A]. 3.6 sec

[B]. 18 sec

[C]. 36 sec

[D]. 72 sec

✅ The correct answer is option C.
Speed of train relative to jogger = (45 – 9) km/hr = 36 km/hr.

36 x
5
m/sec

= 10 m/sec.
Distance to be covered = (240 + 120) m = 360 m.

Time taken =

360
sec
= 36 sec.

72. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

[A]. 9

[B]. 9.6

[C]. 10

[D]. 10.8

✅ The correct answer is option D.
Relative speed = (60 + 40) km/hr =

100 x
5
m/sec
=

250
m/sec.

18
9

Distance covered in crossing each other = (140 + 160) m = 300 m.

Required time =

300 x
9
sec
=
54
sec = 10.8 sec.

250
5

74. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

[A]. 50 m

[B]. 150 m

[C]. 200 m

[D]. Data inadequate

✅ The correct answer is option B.
Let the length of the train be x metres and its speed by y m/sec.

Then,
x
= 15 y =
x
.

y
15

x + 100
=
x

25
15

15(x + 100) = 25x
15x + 1500 = 25x
1500 = 10x
x = 150 m.

76. A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

[A]. 66 km/hr

[B]. 72 km/hr

[C]. 78 km/hr

[D]. 81 km/hr

✅ The correct answer is option D.
4.5 km/hr =

4.5 x
5

m/sec =
5
m/sec = 1.25 m/sec, and

18
4

5.4 km/hr =

5.4 x
5

m/sec =
3
m/sec = 1.5 m/sec.

18
2

Let the speed of the train be x m/sec.
Then, (x – 1.25) x 8.4 = (x – 1.5) x 8.5
8.4x – 10.5 = 8.5x – 12.75
0.1x = 2.25
x = 22.5

Speed of the train =

22.5 x
18

km/hr = 81 km/hr.

78. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

[A]. 40 sec

[B]. 42 sec

[C]. 45 sec

[D]. 48 sec

✅ The correct answer is option A.
Formula for converting from km/hr to m/s:
X km/hr =

X x
5

m/s.

Therefore, Speed =

45 x
5
m/sec
=
25
m/sec.

18
2

Total distance to be covered = (360 + 140) m = 500 m.

Formula for finding Time =

Distance

Speed

Required time =

500 x 2
sec
= 40 sec.

Author name: Admin