31.
A train 150 m long passes a km stone in 15 seconds and another train of the same length travelling in opposite direction in 8 seconds. The speed of the second train is:
• A.
60 km/hr
• C.
72 km/hr
• B.
66 km/hr
• D.
99 km/hr
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Explanation :

Speed of first train =
 150 15
m/sec = 10 m/sec.

Let the speed of second train be x m/sec.

Relative speed = (10 + x) m/sec.

 300 10 + x
= 8 300 = 80 + 8x x =
 220 8
=
 55 2
m/sec.

So, speed of second train =
 55 2
x
 18 5
kmph = 99 kmph.

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32.
How long does a train 110 metres long running at the speed of 72 km/hr take to cross a bridge 132 meters in length?
• A.
9.8 sec
• C.
12.42 sec
• B.
12.1 sec
• D.
14.3 sec
• Report
Explanation :

Speed =   72 x
 5 18
m/sec = 20 m/sec.

Total distance covered = (110 + 132) m = 242 m.

Required time =
 242 20
sec = 12.1 sec.

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33.
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
• A.
200m
• C.
245 m
• B.
225 m
• D.
250 m
• Report
Explanation :

Speed =   45 x
 5 18
m/sec =
 25 2
m /sec; Time = 30 sec.

Let the length of bridge be x meters.

Then,
 130 + x 30
=
 25 2
2(130 + x) = 750 x = 245 m.

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34.
A train overtakes two persons walking along a railway rack. 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
• C.
78 km/hr
• B.
72 km/hr
• D.
81 km/hr
• Report
Explanation :

4.5 km/hr =   4.5 x
 5 18
m/sec =
 5 4
m/sec = 1.25 m/sec, and

5.4 km/hr =   5.4 x
 5 18
m/sec =
 3 2
m/sec = 1.5 m/sec.

Let the speed of the rain be x m/sec.

Then, (x � 1.25) x 84 = (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 5
km/hr = 81 km/hr.

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35.
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
• A.
50 m
• C.
200 m
• B.
150 m
• D.
• Report
Explanation :

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

They,
 x y
= 15 y =
 x 15

 x + 100 25
=
 x 15
x = 150 m.

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