111. The speed of train A is 20% more than that of train B and the time taken by train A covers y km is equal to the time taken by train B covers(y-50) km. Find the value of y?

ट्रेन A की गति ट्रेन B की गति से 20% अधिक है और ट्रेन A द्वारा y किमी की दूरी तय करने में लिया गया समय ट्रेन B द्वारा (y-50) किमी की दूरी तय करने के लिये लिए गए समय के बराबर है। y का मान ज्ञात कीजिये?

A. 420
B. 300
C. 360
D. 240
E. None of these

Option “B” is correct.

Let the speed of train B = 5s

And the speed of train A = 5s * 120/100 = 6s

y/6s = (y – 50)/5s

5y = 6y – 300

y = 300
112. Train A with length of 100 m crosses train B travelling in opposite direction in 5 seconds and train A crosses a pole in 5 seconds. Find the speed of train B, if the ratio of the length of train A to B is 5:9?

100 मीटर की लंबाई वाली ट्रेन A विपरीत दिशा में चल रही ट्रेन B को 5 सेकंड में पार करती है और ट्रेन A एक खंभे को 5 सेकंड में पार करती है। ट्रेन B की गति ज्ञात कीजिए, यदि ट्रेन A से B की लंबाई का अनुपात 5:9 है?

A. 60 m/sec
B. 36 m/sec
C. 45 m/sec
D. 24 m/sec
E. None of these

Option “B” is correct.

The length of train A = 100 m

And the length of train B = 100 * 9/5 = 180 m

The speed of train A = 100/5 = 20 m/sec

And the speed of train B = x m/sec

100 + 180 = (x + 20) * 5

280 /5 = x + 20

56 = x + 20

x = 36

The speed of train B = 36 m/sec
113. Train A and Train B crosses each other travelling in opposite direction in 9.8 seconds and the sum of their speeds is 50 m/s and the length of Train A is 50 m more than that of Train B. If the time taken by Train A to cross a bridge of length of 240 m is 17 seconds, find the speed of Train B.

ट्रेन A और ट्रेन B विपरीत दिशा में यात्रा करते हुए एक दूसरे को 9.8 सेकंड में पार करती है और उनकी गति का योग 50 मीटर/सेकंड है और ट्रेन A की लंबाई ट्रेन B की लंबाई से 50 मीटर अधिक है। यदि ट्रेन A द्वारा 240 मीटर लंबे पुल को पार करने में लिया गया समय 17 सेकंड है, तो ट्रेन B की गति ज्ञात कीजिए।

A. 25 m/s
B. 30 m/s
C. 15 m/s
D. 20 m/s
E. None of these

Option “D” is correct.

Let the length of Train A be x m

Length of Train B = (x – 50) m

(x + x – 50)/50 = 9.8

2x – 50 = 490

2x = 540

x = 270 m

Length of Train A = 270 m

Length of train B = 220 m

Let the speed of Train A be y m/s

(270 + 240)/y = 17

510/y = 17

y = 30 m/s

Speed of Train B = 50 – 30 = 20 m/s
114. A train crosses a pole in 12 seconds and the same train crosses a man running in the opposite direction at the speed of x km/hr in 8 seconds. Find the speed of the man, if the speed of the train is 30 m/sec.

एक ट्रेन एक खम्भे को 12 सेकंड में पार करती है और वही ट्रेन x किमी/घंटा की गति से विपरीत दिशा में चल रहे एक व्यक्ति को 8 सेकंड में पार करती है। व्यक्ति की गति ज्ञात कीजिए, यदि ट्रेन की गति 30 मीटर/सेकंड है।

A. 15 km/hr
B. 24 km/hr
C. 30 km/hr
D. 54 km/hr
E. None of these

Option “D” is correct.

Let the speed of the man = a m/sec

The length of the train = 12 * 30 = 360 m

360 = (30 + a) * 8

30 + a = 45

a = 15

The speed of the man = 15 m/sec

x = 15 * 18/5 = 54 km/hr
115. The ratio of the length of train A to train B is 5:6 and the time taken by train B to cross a pole is 50% more than the time taken by train A to cross the same pole. If the sum of the speed of train A and B is 45 m/sec, then find the speed of train A?

ट्रेन A से ट्रेन B की लंबाई का अनुपात 5:6 है और ट्रेन B द्वारा एक खंभे को पार करने में लिया गया समय ट्रेन A द्वारा उसी खंभे को पार करने में लिए गए समय से 50% अधिक है। यदि ट्रेन A और B की गति का योग 45 मीटर/सेकंड है, तो ट्रेन A की गति ज्ञात कीजिए?

A. 42 m/sec
B. 25 m/sec
C. 51 m/sec
D. 36 m/sec
E. None of these

Option “B” is correct.

Let the length of train A = 5x

And the length of train B = 6x

The time taken by train A to cross a pole = 2y

The time taken by train B to cross a pole = 2y * 150/100 = 3y

The speed of train A = z

The speed of train B = (45 – z)

5x = z * 2y

x = z * 2y/5 —(1)

6x = (45 – z) * 3y —(2)

From (1) and (2),

6 * (z * 2y/5) = (45 – z) * 3y

12zy = 15y * (45 – z)

4zy = 225y – 5zy

9zy = 225y

z = 25

The speed of train A = 25 m/sec
116. Ratio of the time taken by a train to cross a platform of half of train’s length to time taken by the train to cross a man travelling in the opposite direction with a speed of 20 m/s is 5:2. Find the speed of the train in km/hr.

ट्रेन द्वारा ट्रेन की लंबाई के आधे लंबाई के प्लेटफॉर्म को पार करने में लगने वाले समय से ट्रेन द्वारा 20 मीटर/सेकेंड की गति से विपरीत दिशा में यात्रा कर रहे एक व्यक्ति को पार करने के लिए लगने वाले समय का अनुपात 5:2 है। किमी/घंटा में ट्रेन की गति ज्ञात करें।

A. 90 km/hr
B. 72 km/hr
C. 126 km/hr
D. 108 km/hr
E. None of these

Option “D” is correct.

Let the length of platform be x and the length of the train be 2x m.

Let the speed of the train be y m/s

((x + 2x)/y)/(2x/(y + 20)) = 5/2

(3x/y)/(2x/(y + 20)) = 5/2

3y + 60 = 5y

2y = 60

y = 30 m/s

Speed of the train = 30 * 18/5 = 108 km/hr
117. A train crosses a platform in 25 seconds and the same train crosses an electric pole in 10 seconds. If the length of the platform is 50 m more than the length of the train, find the speed of the train in km/hr.

एक ट्रेन 25 सेकंड में एक प्लेटफॉर्म को पार करती है और वही ट्रेन 10 सेकंड में एक बिजली के खंभे को पार करती है। यदि प्लेटफार्म की लंबाई ट्रेन की लंबाई से 50 मीटर अधिक है, तो ट्रेन की गति किमी/घंटा में ज्ञात करें।

A. 36 km/hr
B. 54 km/hr
C. 72 km/hr
D. 60 km/hr
E. None of these

Option “A” is correct.

Let the speed of the train = x m/sec

And the length of the train = y m

And the length of the platform = (y + 50) m

y + y + 50 = x * 25

2y + 50 = 25x —(1)

y = x * 10

y = 10x — (2)

From (1) and (2),

2 * (10x) + 50 = 25x

20x + 50 = 25x

5x = 50

x = 10

Therefore, speed of the train in (km/hr) = 10 * 18/5 = 36 km/hr
118. Train A crosses Train B travelling in opposite direction in 14 seconds and the ratio of the speed of Train A to Train B is 2:1. Find the sum of the speeds of Train A and Train B, if the length of Train A and Train B is 440 m and 400 m?

ट्रेन A विपरीत दिशा में यात्रा कर रही ट्रेन B को 14 सेकंड में पार करती है और ट्रेन A से ट्रेन B की गति का अनुपात 2:1 है। ट्रेन A और ट्रेन B की गति का योग ज्ञात कीजिए, यदि ट्रेन A और ट्रेन B की लंबाई 440 मीटर और 400 मीटर है?

A. 60 m/s
B. 45 m/s
C. 36 m/s
D. 48 m/s
E. None of these

Option “A” is correct.

Speed of Train A = 2x

Speed of Train B = x

(440 + 400)/3x = 14

840 = 42x

x = 20

Speed of Train A = 2 * 20 = 40 m/s

Speed of Train B = 20 m/s

Required sum = 40 + 20 = 60 m/s
119. A train crosses 450 m platform in 30 seconds and also crosses a man running with a speed of 36 km/hr in same direction in 17.5 seconds. Find the speed of the train.

एक ट्रेन 450 मीटर प्लेटफॉर्म को 30 सेकंड में पार करती है और समान दिशा में 36 किमी/घंटा की गति से दौड़ रहे एक व्यक्ति को 17.5 सेकंड में पार करती है। ट्रेन की गति ज्ञात करें ।

A. 20 m/sec
B. 36 m/sec
C. 15 m/sec
D. 22 m/sec
E. None of these

Option “D” is correct.

Let the speed of the train = a

And the length of the train = b

The speed of the man in m/sec = 36 * 5/18 = 10 m/sec

b + 450 = a * 30

b + 450 = 30a —(1)

b = (a – 10) * 17.5

b = 17.5a – 175 —(2)

From (1) and (2),

17.5a – 175 + 450 = 30a

12.5a = 275

a = 22

Therefore, the speed of the train = 22 m/sec
120. A train of length 360 m crosses a bridge of length x m in 24 seconds and the train also crosses a platform of length (x + 100) m in 28 seconds. Find the speed of the train.

360 मीटर की लंबाई वाली एक ट्रेन 24 सेकंड में x मीटर लंबाई के पुल को पार करती है और ट्रेन (x + 100) मीटर लंबाई के प्लेटफॉर्म को भी 28 सेकंड में पार करती है। ट्रेन की गति ज्ञात करें।

A. 25 m/s
B. 20 m/s
C. 30 m/s
D. 18 m/s
E. None of these

Option “A” is correct.

Let the speed of the train be a m/s

(360 + x)/24 = (360 + x + 100)/28

(360 + x)/6 = (460 + x)/7

2520 + 7x = 2760 + 6x

x = 240 m

Speed of the train = (360 + 240)/24 = 600/24 = 25 m/s

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