41. The length of train A is 150 m and that of train B is 250 m. These two trains are running in the opposite direction with the velocities of 50 km/hr and 70 km/hr respectively. Find the time taken to cross each other?

ट्रेन A की लंबाई 150 मीटर है और ट्रेन B की 250 मीटर है। ये दोनों ट्रेनें विपरीत दिशा में क्रमशः 50 किमी/घंटा और 70 किमी/घंटा की गति से चल रही हैं। एक दूसरे को पार करने में लगने वाला समय ज्ञात कीजिये?

A. 15 seconds
B. 18 seconds
C. 21 seconds
D. 12 seconds
E. None of these

Option “D” is correct.

T = D/S

T = (150 + 250)/[(50 + 70)*(5/18)]

T = (400*18)/(120*5)

T = 12 sec
42. Two trains of equal length are running on parallel lines in the same direction at 53 km/h and 41 km/h. The faster train passes the slower train in 33 sec. The length of each train is

समान लंबाई की दो ट्रेनें समान दिशा में 53 किमी/घंटा और 41 किमी/घंटा की गति से समानांतर रेखाओं पर चल रही हैं। तेज गति वाली ट्रेन धीमी गति की ट्रेन को 33 सेकंड में पार करती है। प्रत्येक ट्रेन की लंबाई _____ है|

A. 55 m
B. 50 m
C. 45 m
D. 60 m
E. 72 m

Option “A” is correct.

Same direction means speed minus

D = S × T × 5/18

(D1 + D2) = (53 – 41) × 33 × 5/18

(D1 + D2) = 110 m 

D = 55 m (D1 = D2)
43. The ratio of length of two trains is 3: 4 and the ratio of speed is 4: 5.Find the time taken by them to cross each other in opposite direction. (Consider the lengths are in m and speeds are in kmph)

दो ट्रेनों की लंबाई का अनुपात 3: 4 है और गति का अनुपात 4: 5 है। उनके द्वारा विपरीत दिशा में एक दूसरे को पार करने में लिया गया समय ज्ञात कीजिए। (मान लें कि लंबाई मीटर में है और गति किमी प्रति घंटे में है)

A. 1.4 s
B. 5.6 s
C. Data inadequate
D. 2.8 s
E. None of these

Option “C” is correct.

Distance = speed * time

The ratio of length = 3: 4(3x, 4x)

The ratio of speed = 4: 5 (4y, 5y)

(3x + 4x) = (5y + 4y) * 5/18 * time

14x/5y = time

We can’t find the answer.
44. A 200m long train A crosses another 180m long train B running in the same direction in 36 seconds. If the speed of the train A is 60kmph, What is the speed of the train B, if speed of train A is faster than that of Train B?

200 मीटर लंबी ट्रेन A, समान दिशा में चल रही 180 मीटर लंबी ट्रेन B को 36 सेकंड में पार करती है। यदि ट्रेन A की गति 60 किमी प्रति घंटा है, तो ट्रेन B की गति क्या है, यदि ट्रेन A की गति ट्रेन B की गति से तेज है?

A. 22 kmph
B. 24 kmph
C. 33 kmph
D. 28 kmph
E. None of these

Option “A” is correct.

(200+180) = (60-x)*5/18*36

38 = (60-x)

X = 22kmph
45. Two trains A and B of length 130 and 70 m respectively running in same direction cross each other in 80 seconds. If the speed of the fastest train A is 47 kmph, find the distance covered by train B in 150 minutes.

एक ही दिशा में चलने वाली क्रमशः 130 और 70 मीटर लंबाई की दो ट्रेनें A और B एक दूसरे को 80 सेकंड में पार करती हैं। यदि सबसे तेज ट्रेन A की गति 47 किमी प्रति घंटा है, तो ट्रेन B द्वारा 150 मिनट में तय की गई दूरी ज्ञात कीजिए।

A. 57 km
B. 90 km
C. 75 km
D. 85 km
E. 95 km

Option “E” is correct.

Distance = speed * time

(130 + 70) = (47 – x) * 5/18 * 80

9 = 47 – x

x = 38 kmph

The distance covered by B in 2.5 hours = 38 * 2.5 = 95 km
46. Two trains of equal length moves towards each other at the speed of 40 km/hr and 50 km/hr respectively. If they cross each other in 12 seconds, then find the length of each train?

समान लंबाई की दो ट्रेनें क्रमशः 40 किमी/घंटा और 50 किमी/घंटा की गति से एक-दूसरे की ओर बढ़ती हैं। यदि वे एक दूसरे को 12 सेकंड में पार करते हैं, तो प्रत्येक ट्रेन की लंबाई ज्ञात कीजिए?

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

Option “A” is correct.

Let the train length be x,

12 = (x + x) / [(40 + 50) * (5/18)]

12 = (2x * 18) / (90 * 5)

(12 * 90 * 5) / 36 = x

X = 150 m
47. Two trains of equal length, which is equal to 400 m, running in opposite direction on parallel tracks. The speeds of two trains are 50 km/hr and 70 km/hr respectively. Find the time taken by slower train to pass the driver of the faster one?

समान लंबाई की दो ट्रेनें, जो 400 मीटर के बराबर हैं, समानांतर पटरियों पर विपरीत दिशा में चल रही हैं। दो ट्रेनों की गति क्रमशः 50 किमी/घंटा और 70 किमी/घंटा है। धीमी ट्रेन द्वारा तेज गति वाले ट्रेन के चालक को पार करने में लिया गया समय ज्ञात कीजिये?

A. 12 seconds
B. 15 seconds
C. 18 seconds
D. 21 seconds
E. None of these

Option “A” is correct.

Relative speed = (50 + 70) * (5/18) = 100/3 m/s

We have to find the time taken by slower train to cross the driver of the faster one. They didn’t mean to cross full faster train. They told only to cross the driver. So,

The distance covered = The length of slower train = 400 m

Required time = 400/(100/3) = 12 seconds
48. Two trains A and B running in opposite direction cross a man standing on the platform in 12 seconds and 20 seconds respectively. Both the trains cross each other in 15 seconds. Find the ratio of their speeds?

विपरीत दिशा में चल रही दो ट्रेनें A और B प्लेटफॉर्म पर खड़े एक व्यक्ति को क्रमशः 12 सेकंड और 20 सेकंड में पार करती हैं। दोनों ट्रेनें एक दूसरे को 15 सेकंड में पार करती हैं। उनकी गति का अनुपात ज्ञात कीजिए?

A. 7 : 5
B. 5 : 3
C. 4 : 1
D. 9 : 7
E. None of these

Option “B” is correct.

Let the speed of two trains be x m/s and y m/s respectively,

Then, the length of train A = 12x

The length of train B = 20y

[(12x + 20y) / (x + y)] = 15

12x + 20y = 15x + 15y

20y – 15y = 15x – 12x

5y = 3x

x / y = 5 / 3

The ratio of speed of train A and B = 5 : 3
49. Two trains cross each other. The length of each train is 150 meters. When they cross each other in same direction they take 54 seconds while in opposite direction they cross each in 12 seconds. Then find the speed of the two trains in km/hr?

दो ट्रेनें एक दूसरे को पार करती हैं। प्रत्येक ट्रेन की लंबाई 150 मीटर है। जब वे एक दूसरे को एक ही दिशा में पार करते हैं तो वे 54 सेकंड लेते हैं जबकि विपरीत दिशा में वे 12 सेकंड में एक दूसरे को पार करते हैं। तो दोनों ट्रेनों की गति किमी/घंटा में ज्ञात कीजिए?

A. 25 km/hr, 40 km/hr
B. 30 km/hr, 45 km/hr
C. 40 km/hr, 50 km/hr
D. 55 km/hr, 35 km/hr
E. None of these

Option “D” is correct.

 Let the speed of two trains be X and Y

Same direction,

54 = (150+150)/[(X – Y)*5/18]

54 = (300*18)/[(X – Y)*5]

X – Y = 20 — (1)

Opposite direction

12 = (150+150)/[(X + Y)*5/18]

12 = (300*18)/[(X + Y)*5]

X + Y = 90 — (2)

By solving the equation (1) and (2), we get,

Y= 35 km/hr, X= 55km/hr
50. Two Stations A and B are 462 km apart. A train leaves from station A to station B and at the same time another train leaves station B to A. Both the trains meet 5.5 hours after they start moving. If the train that starts from station A is 28 km/hr faster than the other one, what is the ratio of the speeds of both the trains?

दो स्टेशन A और B एक दूसरे से 462 किमी दूर हैं। एक ट्रेन स्टेशन A से स्टेशन B के लिए निकलती है और उसी समय दूसरी ट्रेन स्टेशन B से A के लिए निकलती है। दोनों ट्रेनें चलना शुरू करने के 5.5 घंटे बाद मिलती हैं। यदि स्टेशन A से चलने वाली ट्रेन दूसरे की तुलना में 28 किमी/घंटा तेज है, तो दोनों ट्रेनों की गति का अनुपात क्या है?

A. 3: 5
B. 4: 7
C. 2: 1
D. 5: 8
E. None of these

Option “C” is correct.

Let the speed of the first train be x and that of the second train be y

Then, x-y= 28…… (i)

Time = Distance/Speed

5.5 = 462/(x + y)

x + y = 462/5.5

x + y = 84…… (ii)

By solving,

2x= 112

x= 56, y= 28

Ratio of their speed= 56: 28= 2 : 1

 

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