91. Train A crosses a tree in 20 seconds with a speed of 54 km/hr and the ratio of the speed of Train A and Train B is 3:4 and the length of Train B is 100 m more than that of Train A. Find the time taken by both trains to cross each other, if both trains are travelling in same direction.

ट्रेन A एक पेड़ को 54 किमी/घंटा की गति से 20 सेकंड में पार करती है और ट्रेन A और ट्रेन B की गति का अनुपात 3:4 है और ट्रेन B की लंबाई ट्रेन A से 100 मीटर अधिक है। यदि दोनों ट्रेनें समान दिशा में यात्रा कर रही हैं, तो दोनों ट्रेनों को एक-दूसरे को पार करने में लगने वाला समय ज्ञात कीजिए।

A. 180 seconds
B. 155 seconds
C. 140 seconds
D. 170 seconds
E. None of these

Option “C” is correct.

Speed of Train A = 54 * 5/18 = 15 m/s

Speed of Train B = 15 * 4/3 = 20 m/s

Length of Train A = 15 * 20 = 300 m

Length of Train B = 300 + 100 = 400 m

Time taken to cross each other = 700/(20 – 15) = 140 seconds
92. A train crosses a (L+240) long bridge in 30 sec and crosses a lamp post in 8 sec. If the speed of the train is 54 km/hr. then find the time taken by train to cross the 3L m long platform?

एक ट्रेन (L+240) लंबे पुल को 30 सेकंड में पार करती है और एक लैम्प पोस्ट को 8 सेकंड में पार करती है। यदि ट्रेन की गति 54 किमी/घंटा है। तो 3L मीटर लम्बे प्लेटफार्म को पार करने में ट्रेन द्वारा लिया गया समय ज्ञात कीजिये?

A. 10 sec
B. 18 sec
C. 11 sec
D. 13 sec
E. None of these

Option “B” is correct.

Speed of train = 54 km/hr =54*5/18=15 m/sec.

So, length of train = 15*8=120

So, [120+L+240]/15=30

Or, L=(15*30)-120-240=90

So, required time = 90*3/15 =18 sec.
93. A train running at the speed of 45 m/sec crosses a platform in 20 seconds. If the length of the train is 50% more than that of the platform, then find the time taken by the train to cross 135 m tunnel?

45 मीटर/सेकंड की गति से चल रही एक ट्रेन 20 सेकंड में एक प्लेटफॉर्म को पार करती है। यदि ट्रेन की लंबाई प्लेटफॉर्म की लंबाई से 50% अधिक है, तो ट्रेन द्वारा 135 मीटर सुरंग को पार करने में लगने वाला समय ज्ञात कीजिये?

A. 18 seconds
B. 12 seconds
C. 15 seconds
D. 10 seconds
E. None of these

Option “C” is correct.

Let the length of the platform = 2x

And the length of the train = 2x * 150/100 = 3x

3x + 2x = 45 * 20

5x = 900

x = 180

The length of the train = 3 * 180 = 540 m

The time taken by the train to cross 135 m tunnel = t sec

540 + 135 = 45 * t

t = 675/45

t = 15 seconds
94. The ratio of speed of a man to a train is 2 :7. The length of the train is 490 m and crosses the same man standing on the platform in 5 seconds. Find the time taken by the man to cross a 420 m long stationary train?

एक आदमी की गति से एक ट्रेन की गति का अनुपात 2:7 है। ट्रेन की लंबाई 490 मीटर है और प्लेटफॉर्म पर खड़े उसी व्यक्ति को 5 सेकंड में पार करती है। 420 मीटर लंबी एक स्थिर ट्रेन को पार करने के लिए आदमी द्वारा लिया गया समय ज्ञात कीजिए?

A. 20 seconds
B. 15 seconds
C. 10 seconds
D. 30 seconds
E. None of these

Option “B” is correct.

Let the speed of man = 2x

Speed of train = 7x

According to the question,

490/7x = 5

x = 70/5 = 14

Required time = 420/28 = 15 seconds
95. The ratio of the length of trains A and B is 6:5 respectively and train A can crosses a platform of 540 m long in 15 seconds. If two trains A and B are running at a speed of 60 m/s and 35 m/s respectively, then find the time taken by train B to cross the same platform?

ट्रेन A और B की लंबाई का अनुपात क्रमशः 6:5 है और ट्रेन A 540 मीटर लंबे प्लेटफॉर्म को 15 सेकंड में पार कर सकती है। यदि दो ट्रेनें A और B क्रमशः 60 मीटर/सेकेंड और 35 मीटर/सेकेंड की गति से चल रही हैं, तो ट्रेन B द्वारा उसी प्लेटफॉर्म को पार करने में लिया गया समय ज्ञात करें?

A. 24 seconds
B. 18 seconds
C. 21 seconds
D. 15 seconds
E. None of these

Option “A” is correct.

Length of train A=x

(x+540)/60=15

x=360 m

Length of train B=360*5/6=300 m

Required time=(300+540)/=840/35=24 seconds
96. Train A crosses a man running in the opposite direction in 18 seconds and train A also crosses a 350 m long platform in 32 seconds. If the length of train B is 50 m less than the length of train A and the speed of train B is 60 kmph, then find the time taken by train A to cross train B running in the same direction?

ट्रेन A विपरीत दिशा में दौड़ रहे एक व्यक्ति को 18 सेकंड में पार करती है और ट्रेन A 350 मीटर लंबे प्लेटफॉर्म को भी 32 सेकंड में पार करती है। यदि ट्रेन B की लंबाई, ट्रेन A की लंबाई से 50 मीटर कम है और ट्रेन B की गति 60 किमी प्रति घंटे है, तो ट्रेन A द्वारा समान दिशा में चल रही ट्रेन B को पार करने में लिया गया समय ज्ञात कीजिए?

A. 20 seconds
B. 36 seconds
C. 24 seconds
D. 18 seconds
E. Cannot be determined

Option “E” is correct.

Length of train A = x

Speed of train A = y

Speed of a man = z

x = (y + z) * 5/18 * 18

x = 5 * (y + z)

x + 350 = y * 5/18 * 32

9x + 3150 = 80y

Data inadequate
97. Two trains A and B of length 150 m and 200 m respectively, running in opposite direction with a speed of 75 km/hr and 100 km/hr respectively. Find the time taken to cross each other?

दो ट्रेनों A और B की लंबाई क्रमशः 150 मीटर और 200 मीटर है, जो क्रमशः 75 किमी / घंटा और 100 किमी / घंटा की गति के साथ विपरीत दिशा में दौड़ रही हैं। प्रत्येक दूसरे को पार करने में लिया गया समय ज्ञात कीजिये?

A. 7.2 sec
B. 8.4 sec
C. 9 sec
D. 10.6 sec
E. None of these

Option “A” is correct.

Time required to cross each other

T = (150 + 200) / ((75 + 100) * 5/18)

= > 350 / (175 * (5/18))

= > 36/5

= > 7.2 seconds
98. Two trains A and B are moving in opposite direction along the parallel track. Their speeds are in the ratio 3: 5. If each of the train takes 8 seconds to cross a standing man, find the time taken by the train to cross each other completely.

दो ट्रेनें A और B समानांतर ट्रैक पर विपरीत दिशा में दौड़ रही हैं। उनकी गतियां 3: 5 के अनुपात में है। यदि प्रत्येक ट्रेन, एक खड़े व्यक्ति को पार करने में 8 सेकंड लेती हैं, तो ट्रेन के द्वारा एक दूसरे को पूर्णतया पार करने में लिए गए समय को ज्ञात कीजिए।

A. 5 seconds
B. 6 seconds
C. 7 seconds
D. 8 seconds
E. None of these

Option “D” is correct.

Time taken = (t1x + t2y)/(x + y)

= (8 * 3 + 8 * 5)/(3 + 5)

= 8 seconds
99. Train A takes 20% more time than train B to cover 20% more distance than that of train B. If the sum of the speed of trains A and B is 120 km/hr, then what is the time taken by train A to cover 640 km distance while the speed of the train A is 33.33% more than the usual speed?

ट्रेन A, ट्रेन B की तुलना में 20% अधिक दूरी तय करने के लिए ट्रेन B से 20% अधिक समय लेती है। यदि ट्रेन A और B की गति का योग 120 किमी/घंटा है, तो ट्रेन A द्वारा 640 किमी की दूरी तय करने के लिए लिया गया समय क्या है जबकि ट्रेन A की गति सामान्य गति से 33.33% अधिक है?

A. 5 hours
B. 8 hours
C. 10 hours
D. 12 hours
E. None of these

Option “B” is correct.

The speed of the train B=x/t

The speed of the train A=(120x/100)/(120t/100)=x/t

The ratio of the speed of the trains A and B=x/t:x/t=1:1

The speed of the train A=1/2*120=60 km/hr

The speed of the train B=60 km/hr

Required time=640/(60*4/3)=640/80=8 hours
100. Train A of 240 m length crosses a 220 m long train B, which is in rest in 23 seconds. If the speed of train B is 25% more than the speed of train A and when train B starts running, then find the time taken by train B to cross a 180 m long platform?

240 मीटर लंबाई वाली ट्रेन A 220 मीटर लंबी रुकी हुई ट्रेन B को 23 सेकंड में पार करती है। यदि ट्रेन B की गति ट्रेन A की गति से 25% अधिक है और जब ट्रेन B चलना शुरू करती है, तो ट्रेन B द्वारा 180 मीटर लंबे प्लेटफॉर्म को पार करने में लिया गया समय ज्ञात कीजिए?

A. 9 seconds
B. 11 seconds
C. 10 seconds
D. 16 seconds
E. None of these

Option “D” is correct.

Speed of the train A = (240+220)/23= 20 m/sec.

Speed of train B= 20*125/100=25 m/sec.

Required time = (220+180)/25=16 seconds

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