61. The time taken by a train to cross a car travelling in the opposite direction is 9/10th of the time taken by the train to cross an electric pole and the time taken by the train to cross a bridge of length 180 m in 10 seconds. Find the length of the train, if the speed of the car is 5 m/s.

एक ट्रेन द्वारा विपरीत दिशा में यात्रा कर रही कार को पार करने में लिया गया समय, ट्रेन द्वारा बिजली के खंभे को पार करने में लगने वाले समय का 9/10वां है और ट्रेन द्वारा 180 मीटर लंबे पुल को पार करने में लिया गया समय 10 सेकंड है। ट्रेन की लंबाई ज्ञात करें, अगर कार की गति 5 मीटर/सेकेंड है।

A. 320 m
B. 270 m
C. 300 m
D. 350 m
E. None of these

Option “B” is correct.

Let the length of the train be x m and the speed of the train be y m/s.

x/(y + 5) = (9/10) * (x/y)

10y = 9y + 45

y = 45 m/s

(x + 180)/45 = 10

x + 180 = 450

x = 270 m
62. A train crosses 160 m platform in 12 seconds and the same train crosses (160+x) m tunnel in 20 seconds. If the speed of train is 30 m/sec, then find the value of x?

एक ट्रेन 12 सेकंड में 160 मीटर प्लेटफॉर्म को पार करती है और वही ट्रेन (160+x) मीटर सुरंग को 20 सेकंड में पार करती है। यदि ट्रेन की गति 30 मीटर/सेकंड है, तो x का मान ज्ञात कीजिए?

A. 180
B. 300
C. 240
D. 150
E. None of these

Option “C” is correct.

Let the length of the train = y

y + 160 = 30 * 12

y = 360 – 160

y = 200

200 + (160 + x) = 30 * 20

360 + x = 600

x = 600 – 360

x = 240
63. The difference between the time taken by Train A and Train B to cross a bridge is 2 seconds and the speed of the Train A and Train B is 25 m/s and 35 m/s respectively. Find the length of the bridge, if the ratio of length of Train A and Train B is 2:3 and the length of the bridge is 50 m less than that of Train A.

ट्रेन A और ट्रेन B द्वारा एक पुल को पार करने में लिए गए समय के बीच का अंतर 2 सेकंड है और ट्रेन A और ट्रेन B की गति क्रमशः 25 मीटर/सेकेंड और 35 मीटर/सेकंड है। पुल की लंबाई ज्ञात कीजिए, यदि ट्रेन A और ट्रेन B की लंबाई का अनुपात 2:3 है और पुल की लंबाई ट्रेन A की लंबाई से 50 मीटर कम है।

A. 300 m
B. 250 m
C. 450 m
D. 350 m
E. None of these

Option “B” is correct.

Length of Train A = 2x

Length of Train B = 3x

Length of the bridge = 2x – 50

(2x + 2x – 50)/25 – (3x + 2x – 50)/35 = 2

(7(4x – 50) – 5(5x – 50))/175 = 2

28x – 350 – 25x + 250 = 350

3x = 450

x = 150

Length of the bridge = 2 * 150 – 50 = 250 m
64. A train T running at speed of 115 km/hr crosses a boy, who running in the opposite direction at speed of 25 km/hr in 12.6 seconds. If the speed of train T increased by 40% and it takes 42 seconds to cross another train U, which runs at speed of 98 km/hr in same direction. Find the length of train U?

115 किमी/घंटा की गति से चल रही एक ट्रेन T विपरीत दिशा में 25 किमी/घंटा की गति से दौड़ रहे एक लड़के को 12.6 सेकंड में पार करती है। यदि ट्रेन T की गति में 40% की वृद्धि होती है और एक अन्य ट्रेन U, जो समान दिशा में 98 किमी/घंटा की गति से चलती है को पार करने में 42 सेकंड का समय लगता है। ट्रेन U की लंबाई ज्ञात कीजिए?

A. 195 meters
B. 420 meters
C. 245 meters
D. 315 meters
E. None of these

Option “C” is correct.

Let the length of train T = T meters

Then, according to the question,

(115 + 25) × (5/18) = T/12.6

T = 140 × (5/18) × 12.6

T = 490 meters

New speed of train T = 115 × (140/100) => 161 km/hr

Let length of train U = U meters

Then, according to the question,

(161 – 98) × (5/18)= (490 + U)/42

490 + U = 63 × (5/18) × 42

U = 735 – 490 => 245 meters

Hence, the required answer = 245 meters.
65. 240 m length of Train A cross a man standing on the platform of length 300 m in 8 sec. Find the speed of the train in km/hr?

240 मीटर लंबाई वाली ट्रेन A, 300 मीटर लंबे प्लेटफॉर्म पर खड़े एक व्यक्ति को 8 सेकंड में पार करती है। किमी/घंटा में ट्रेन की गति ज्ञात कीजिए?

A. 108 km/hr
B. 92 km/hr
C. 84 km/hr
D. 76 km/hr
E. None of these

Option “A” is correct.

Speed of train = (240/8) = 30 m/s

= > 30 * (18/5) = 108 km/hr
66. A train crosses the bridge which has double the length of train A in 36 seconds and the same train crosses a man running in opposite direction at the speed of 30 kmph in 8 seconds. Find the length of the bridge.

एक ट्रेन 36 सेकंड में उस पुल को पार करती है जिसकी लंबाई ट्रेन A से दोगुनी है और वही ट्रेन 30 किमी प्रति घंटे की गति से विपरीत दिशा में दौड़ रहे एक व्यक्ति को 8 सेकंड में पार करती है। पुल की लंबाई ज्ञात कीजिए।

A. 400 m
B. 480 m
C. 360 m
D. 280 m
E. 200 m

Option “A” is correct.

Let Length of the train =x

Length of the bridge=2x

Speed of the train=y

(x + 2x)=y * 5/18 * 36

10y=3x

x=(y + 30) * 5/18 * 8

9x=20y + 600

Thus, 30y=20y + 600

10y=600

y=60 kmph

3x=10 * 60

x=200

Hence, Length of bridge=2 * 200=400 m
67. If the ratio of the length of the train A to B is 4:5 and the speed of train A and B is 30 kmph and 30 kmph respectively. Train A crosses the train B running in opposite direction in 27 seconds. If train A crosses a platform in 48 seconds, find the length of the platform?

यदि ट्रेन A से B की लंबाई का अनुपात 4:5 है और ट्रेन A और B की गति क्रमशः 30 किमी प्रति घंटा और 30 किमी प्रति घंटा है। ट्रेन A विपरीत दिशा में चल रही ट्रेन B को 27 सेकंड में पार करती है। यदि ट्रेन A एक प्लेटफॉर्म को 48 सेकंड में पार करती है, तो प्लेटफॉर्म की लंबाई ज्ञात कीजिए?

A. 150 m
B. 200 m
C. 250 m
D. 100 m
E. None of these

Option “B” is correct.

Distance = speed * time

The ratio of the length of the train A to B = 4: 5 (4x, 5x)

9x=60 * 5/18 * 27

x =50

Length of train A=4 * 50=200 m

Length of the platform=y

200 + y=30 * 5/18 * 48

y =200 m
68. A train can cross a platform of length 650 m in 72 seconds. It can cross a tree in 20 seconds. Find the time taken by the train to cross another train of length 450 m coming from the opposite direction with the speed of 25 Km/h.

एक ट्रेन 72 सेकंड में 650 मीटर लंबे प्लेटफॉर्म को पार कर सकती है। यह एक पेड़ को 20 सेकंड में पार कर सकती है। 25 किमी/घंटा की गति से विपरीत दिशा से आने वाली 450 मीटर लंबाई की एक अन्य ट्रेन को पार करने में ट्रेन द्वारा लिया गया समय ज्ञात कीजिए।

A. 36 seconds
B. 42 seconds
C. 40 seconds
D. 45 seconds
E. None of these

Option “A” is correct.

Let, length of the train = l metre

And speed of the train = s Km/h

(l + 650) = s x 5/18 x 72

=> l + 650 = 20s ——— (i)

l = s x 5/18 x 20

=> l = 50s/9 ———– (ii)

From (i) and (ii)

50s/9 + 650 = 20s

=> 20s – 50s/9 = 650

=> (180s – 50s)/9 = 650

=> 130s/9 = 650

=> s = 650 x 9/130

=> s = 45 Km/h

From (ii)

l = 50 x 45/9

=> l = 250 m

Let, required time taken = t seconds

(250 + 450) = (45 + 25) x 5/18 x t

=> 700 = 70 x 5/18 x t

=> t = 700 x 18/5 x 1/70

=> t = 36 seconds
69. A train crosses 200 m long platform in 36 seconds and the same train crosses a man standing in the platform in 18 seconds. What is the time taken by the same train crosses another 300 m train running in opposite direction at the speed of 40 kmph?

एक ट्रेन 200 मीटर लंबे प्लेटफॉर्म को 36 सेकंड में पार करती है और वही ट्रेन प्लेटफॉर्म पर खड़े एक व्यक्ति को 18 सेकंड में पार करती है I उसी ट्रेन द्वारा 40 किमी प्रति घंटे की गति से विपरीत दिशा में चल रही एक और 300 मीटर की ट्रेन को पार करने में कितना समय लगता है?

A. 18.5 seconds
B. 19.5 seconds
C. 20.5 seconds
D. 21.5 seconds
E. 22.5 seconds

Option “E” is correct.

Length of train = x

Speed of train = y

x + 200 = y * 5/18 * 36

x + 200 = 10y

x = y * 5/18 * 18

x = 5y

x + 200 = 2x

x = 200

y = 200/5 = 40 kmph

Required time = (300 + 200)/[80 * 5/18] = 22.5 seconds
70. Train A crosses train B running opposite direction in 16.8 seconds and train A crosses a man standing in the platform in 10 seconds. Ratio of the length of train A to B is 5:9 and the train A crosses 200 m long platform in 18 seconds, then find the speed of train B?

ट्रेन A विपरीत दिशा में चल रही ट्रेन B को 16.8 सेकंड में पार करती है और ट्रेन A प्लेटफॉर्म पर खड़े एक व्यक्ति को 10 सेकंड में पार करती है। ट्रेन A से B की लंबाई का अनुपात 5:9 है और ट्रेन A 200 मीटर लंबे प्लेटफॉर्म को 18 सेकंड में पार करती है, तो ट्रेन B की गति ज्ञात कीजिए?

A. 40 kmph
B. 50 kmph
C. 60 kmph
D. 80 kmph
E. 90 kmph

Option “C” is correct.

Length of train A = 5x

Length of train B = 9x

Speed of train A = y

Speed of train B = z

5x = y * 5/18 * 10

9x = 5y

5x + 200 = y * 5/18 * 18

5x + 200 = 9x

4x = 200

x = 50

Length of train A = 50 * 5 = 250 m

Length of train B = 50 * 9 = 450 m

Speed of train A = 90 kmph

250 + 450 = (90 + z) * 5/18 * 16.8

z = 60 kmph

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