31. Trains A and B travel 900 km in 20 hours and 25 hours respectively. Length of train A is 150 m more than that of train B. They can cross each other travelling in opposite direction in 1 minute. Find the length of A. 

ट्रेन A और B क्रमशः 20 घंटे और 25 घंटे में 900 किमी की यात्रा करती हैं। ट्रेन A की लंबाई ट्रेन B से 150 मीटर अधिक है। वे विपरीत दिशा में यात्रा करने पर एक-दूसरे को 1 मिनट में पार कर सकती हैं। A की लंबाई ज्ञात कीजिए।

Option “D” is correct.

Given:

Trains A and B travel 900 km in 20 hours and 25 hours respectively. Length of A is 150 m more than that of B. They can cross each other travelling in opposite direction in 1 minute.

Formula Used:

When two trains are travelling in opposite direction, relative speed = sum of their individual speed.

When two trains are travelling in same direction, relative speed = difference of their individual speed.

Time = Distance / speed

Calculation:

Speed of A = 900 / 20 = 45 kmph = 12.5 m / s

Speed of B = 900 / 25 = 36 kmph = 10 m / s

Let the lengths of train A and B be ‘l + 150’ m and ‘l’ m respectively.

⇒ (l + 150 + l) / (22.5) = 60

⇒ 2l + 150 = 22.5 × 60

⇒ 2l = 1350 – 150 = 1200

⇒ l = 600 m

∴ Length of train A = (l + 150) m = (600 + 150) m = 750 m

32. A train is moving with a uniform speed. Train crosses a bridge of length 243 meters in 30 seconds and a bridge of length 343 meters in 36 seconds. What is the speed of the train?

एक ट्रेन एकसमान गति से चल रही है। ट्रेन 243 मीटर लंबाई वाले पुल को 30 सेकंड में और 343 मीटर लंबाई वाले पुल को 36 सेकंड में पार करती है। ट्रेन की गति क्या है?

Option “A” is correct.

Given:

Train is moving with a uniform speed.

Train crosses a bridge of length 243 meters in 30 seconds and a bridge of length 343 meters in 36 

Seconds

Formula used:

Speed = Distance/Time

Calculation:

Let the length of the train be x meter

⇒ (x + 243)/30 = (x + 343)/36

⇒ 36x + 8748 = 30x + 10290

⇒ x = 257

∴ Speed =  (x + 243)/30 = (257 + 243)/30 = 16.66 meter per seconds

16.66 × (18/5) = 59.97 km/hr

⇒ From options, speed of the train = 60 km/hr

33. If a train runs with the speed of 65 km/h, it reaches its destination late by 20 minutes. But, if it speed is 75 km/h, it is late by only 2 minutes. The correct time for the train to cover its journey is:

यदि कोई ट्रेन 65 किमी/घंटा की गति से चलती है, तो वह 20 मिनट की देरी से अपने गंतव्य तक पहुँचती है। लेकिन, यदि इसकी गति 75 किमी/घंटा है, तो यह केवल 2 मिनट की देरी से पहुँचती है। ट्रेन का यात्रा तय करने का सही समय है:

Option “C” is correct.

Given:

First speed of train (s1) = 65 km/h

Second speed of train (s2) = 75 km/h

Let, the time = t minutes

Formula used:

Speed =  Distance/Time

Calculations:

⇒ First speed of train (s1) = Distance/time

⇒ s1 = distacne/(t + 20)

⇒ Distacne = 65 × (t + 20)      —-(1)

⇒ Second speed of train (s2) = 75 km/h

⇒ s2 = distacne/(t + 2)

⇒ Distacne = 75 × (t + 2)      —-(2)

From equation (1) and (2)

⇒ 65 × (t + 20) = 75 × (t + 2) 

⇒ 13t + 260 = 15t + 30

⇒ 2t = 230

⇒ t = 115 minutes

∴ The correct time for the train to cover its journey is 115 minutes.

34. To travel 612 km, Train A takes 9 hours more than Train B. If the speed of the Train A is doubled, it takes 3 hours less than Train B. The speed (in km/h) of Train B is:

612 किमी की दूरी तय करने के लिए ट्रेन A ट्रेन B से 9 घंटा अधिक लेती है। यदि ट्रेन A की गति दोगुनी हो जाती है, तो यह ट्रेन B से 3 घंटा कम समय लेती है। तो ट्रेन B की गति (किमी/घंटा में) क्या है?

Option “D” is correct.

Given:

Total Distance = 612 km 

Train A takes 9 hours more than Train B

If the speed of Train A is doubled, it takes 3 hours less than Train B

Formula Used:

Distance = Speed/Time

Calculation:

Let the speed of B be x km/hour

So, the time taken by B to travel 612 km = (612/x) hours

⇒ The time taken by A to travel 612 km = [(612/x) + 9] hours

⇒ The speed of A = 612/[(612/x) + 9] km/hour

Now, according to question

612 = 2 × [612/{(612/x) + 9}] × (612/x – 3)

⇒ (612/x + 9) = 2 (612/x – 3)

⇒ 612/x = 15

⇒ x = 40.8

∴ The speed of train B is 40.8 km/hour

35. Two trains are running on parallel lines in the same direction at speeds of 80 km/h and 65 km/h respectively. The faster train crosses a man in the slower train in 72 seconds. If the length of the faster train is 3/4th of the slower train, find the length of the slower train

सामानांतर पटरियों पर समान दिशा में दो ट्रेनें क्रमशः 80 किमी/घंटा और 65 किमी/घंटा की गति से चल रही हैं। तेज़ ट्रेन, धीमी ट्रेन में बैठे एक व्यक्ति को 72 सेकंड में पार करती है। यदि तेज़ ट्रेन की लंबाई, धीमी ट्रेन की लंबाई की तीन-चौथाई है, तो धीमी ट्रेन की लंबाई ज्ञात कीजिये।

Option “A” is correct.

Let the length of the slower train be 4x m

∴ The length of the faster train will be 3x m

Relative speed = (80 – 65) = 15 km/h = 15 × 5/18 = 25/6 m/s

According to the question,

⇒ 3x = 72 × 25/6

⇒ 3x = 300

⇒ x = 100

∴ Length of the slower train = 4 × 100 = 400 m

36. A train crosses a 300 meters long platform in 15 seconds running at 50% of its normal speed and crosses a pole in 6 seconds running at its normal speed. What is the length of the train?

एक रेलगाड़ी अपनी सामान्य गति के 50%  गति से चलने पर 15 सेकंड में 300 मीटर लंबे प्लेटफॉर्म को पार करती है और रेलगाड़ी अपनी सामान्य गति से 6 सेकंड में एक खंभे को पार करती है। रेलगाड़ी की लंबाई कितनी है?

Option “B” is correct.

GIVEN:

A train crosses a 300 meters long platform in 15 seconds running at 50% of its normal speed and crosses a pole in 6 seconds running at its normal speed.

FORMULA USED:

Time = Distance/Speed

CALCULATION:

Suppose the speed of train is ‘x’ m/s and the length of the train is ‘L’ meters.

So,

L = 6x     —- (1)

And

L + 300 = 0.5x × 15

⇒ L + 300 = 7.5x      —- (2)

From equation 1 and 2:

⇒ 1.5x = 300

⇒ x = 200

So,

L = 6 × 200 = 1200 m

∴ Length of the train = 1200 meters

37. Two trains A and B are running between two points. If the speed of train A is 50% more than the speed of train B, then to cover that distance, A takes 15 minutes less than B. If A covers double the distance and B covers the same distance as earlier then A takes 18 minutes more than B. How much time will train A take to cover the distance?

दो ट्रेनें A और B दो स्थानों के बीच चल रही हैं। यदि ट्रेन A की गति ट्रेन B की गति से 50% अधिक है, तो उस दूरी को तय करने के लिए A, B से 15 मिनट कम समय लेती है। जब B उसी दूरी को पहले की तरह ही तय करती है तब A ने उसी दूरी को दोगुना तय कर लिया है, तो वह B से 18 मिनट अधिक लेती है। A दूरी को तय करने में कितना समय लेगी?

Option “B” is correct.

Given:

Speed of train A = 150% of Speed of train B

Calculations:

Time taken by train A= Ta

Time taken by train B= Tb

⇒ Tb – Ta = 15 minutes      …(i)

If train A takes ‘Ta’ time to travel a distance, it will take ‘2Ta’ time to travel double the distance

⇒ 2Ta – Tb = 18 minutes      …(ii)

Adding (i) and (ii),

⇒ Ta = 33 minutes

∴ The train A will cover the distance in 33 minutes

Shortcut Trick A takes 15 min less time than B to cover the distance.

B takes 15 min more than A  to complete the distance.

If A covered double the distance when B covers the same distance as earlier then A takes 18 minutes more than B. 

So, A ‘s time taken to cover the double  distance = 15 min (as A completed the distance 15 min earlier than B) + 18 min = 33 min

So total time taken by A to cover the double distance = 15 + 18 = 33 minutes

38. A train a whose length is 800 m can cross the pole in 32 seconds and cover the x distance in 4 hours. If the other train b can cover the same distance in 2.5 hour, how much time the train b require to pass the pole? Consider the length of both trains is same.

एक ट्रेन जिसकी लम्बाई 800 मीटर है, किसी स्तम्भ को 32 सेकेंड में पार कर सकती है और चार घंटों में x दूरी को पार कर सकती है। यदि ट्रेन b समान दूरी को 2.5 घंटे में पूरा करती है, तब ट्रेन b को स्तम्भ को पार करने में कितना समय लगेगा? मान लीजिए कि दोनों ट्रेनों की लम्बाई समान है।

Option “A” is correct.

For the speed of the train a,

Distance travelled = 800 m

Time taken = 32 seconds

Speed of train a = 800/32 = 25 m/s = 25 × 18/5 = 90 kmph

For the distance of x,

Speed of train a = x/4

⇒ 90 × 4 = x

⇒ x = 360 km

Speed of train b = 360/2.5 = 144kmph

For time taken by train b to cross the pole,

Convert speed in m/s,

Speed of train b = 144 × 5/18 = 40 m/s

∴ Time require to cross the pole = 800/40 = 20 seconds

39. A train running at a speed of 70 km/hr crosses a pole in 12 sec and a platform in 21 sec, Find in how much time it will cross a platform of triple length?

70 किमी/घंटे की चाल से चलने वाली ट्रेन 12 सेकंड में एक खंबे को और 21 सेकंड में एक प्लेटफ़ॉर्म को पार करती है, ज्ञात कीजिए कि ट्रेन तीन गुने लंबे प्लेटफॉर्म को कितने समय में पार करेगी?

Option “A” is correct.

GIVEN:

A train running at a speed of 70 km/hr crosses a pole in 12 sec and a platform in 21 sec

CONCEPT:

Distance covered will be the sum of the length of train and platform

FORMULA USED:

Distance = speed × time

CALCULATION: 

Speed = 70 × 5/18 m/sec

Length of train = 70 × 5/18 × 12 = 700/3 m

Distance in 21 sec = 70 × 5/18 × 21 = 1225/3 m

Length of platform = 70 × 5/18 × 21 – 70 × 5/18 × 12 = 70 × 5/18 × 9 = 175 m

Platform of triple length = 525 m

Time = (525 + 700/3)/ (70 × 5/18) = 39 seconds

40. Train x running at 84 km/h crosses another train y running at 52 km/h in opposite direction in 12 seconds. If the length of train y is two-third that of x then find the length of train x.

ट्रेन x 84 किमी/घंटा की गति से चलते हुए 52 किमी / घंटा की गति से चल रही एक अन्य ट्रेन y को विपरीत दिशा  12 सेकंड में पार करती है। यदि ट्रेन y की लंबाई x की तुलना में दो-तिहाई है तो ट्रेन x की लंबाई ज्ञात कीजिये।

Option “C” is correct.

Length of train x = L1

Length of train y = L2

Speed of train x = 84 km/h

Speed of train y = 52 km/h

Relative speed = 84 + 52 = 136 × 5/18 m/s

Length of train x and y = time × relative speed

Length of train x and y = 12 × 136 × 5/18 = 1360/3

L1 + L2 = 1360/3

L1 + {L1 × (2/3)} = 1360/3

5/3 L1 =1360/3

L1 = 272 m

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