Aptitude Archives

61. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

[A]. 120 metres

[B]. 180 metres

[C]. 324 metres

[D]. 150 metres

✅ The correct answer is option D.
Speed =

60 x
5
m/sec
=

50
m/sec.

18
3

Length of the train = (Speed x Time).

Length of the train =

50
x 9
m = 150 m.

Video Explanation: https://youtu.be/q6Xy5JXNp-k

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.

63. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

[A]. 45 m

[B]. 50 m

[C]. 54 m

[D]. 72 m

✅ The correct answer is option B.
2 kmph =

2 x
5

m/sec =
5
m/sec.

18
9

4 kmph =

4 x
5

m/sec =
10
m/sec.

18
9

Let the length of the train be x metres and its speed by y m/sec.

Then,

= 9 and

= 10.

y –
5

y –
10

9y – 5 = x and 10(9y – 10) = 9x
9y – x = 5 and 90y – 9x = 100.
On solving, we get: x = 50.
Length of the train is 50 m.

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.

65. Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

[A]. 12 sec

[B]. 24 sec

[C]. 48 sec

[D]. 60 sec

✅ The correct answer is option B.
Relative speed =
= (45 + 30) km/hr

75 x
5

m/sec

125

m/sec.

We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.

So, distance covered = Length of the slower train.

Therefore, Distance covered = 500 m.

Required time =

500 x
6

= 24 sec.

125

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.

67. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

[A]. 69.5 km/hr

[B]. 70 km/hr

[C]. 79 km/hr

[D]. 79.2 km/hr

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

Then,
x
= 8 x = 8y

Now,
x + 264
= y

8y + 264 = 20y
y = 22.

Speed = 22 m/sec =

22 x
18

km/hr = 79.2 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.

69. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

[A]. 9 a.m.

[B]. 10 a.m.

[C]. 10.30 a.m.

[D]. 11 a.m.

✅ The correct answer is option B.
Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x – 1) hours = 25(x – 1) km.
20x + 25(x – 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.

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.