# Bank Preparation Problems On Trains Part-1

18

বিভিন্ন ওয়েবসাইট থেকে গুরুত্বপূর্ণ ম্যাথ গুলোই তুলে দেয়া হল। প্র্যাকটিস করতে থাকুন আশা করি কমন পাবেন। কিছু সূত্র জেনে রাখা ভালোঃ

1. km/hr to m/s conversion: $\fn_phv&space;\large&space;\inline&space;\fn_phv&space;\large&space;akm/hr&space;=&space;\left&space;(&space;a\times&space;\frac{5}{18}&space;\right&space;)m/s$
2. m/s to km/hr conversion: $\inline&space;\fn_phv&space;\large&space;\inline&space;\fn_phv&space;\large&space;a&space;m/s&space;=&space;\left&space;(&space;a\times&space;\frac{18}{5}&space;\right&space;)km/hr$
3. Time taken by a train x meters long to pass a pole, standing man, post, etc. = time is taken by the train to travel x meters.
4. If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:

(A’s speed) : (B’s speed) = $\fn_phv&space;\large&space;\inline&space;\fn_phv&space;\large&space;\sqrt{a}:\sqrt{b}$
5. If two trains of length metres and b metres are moving in the same direction at u m/s and v m/s, then:

The time is taken by the faster train to cross the slower train =  $\inline&space;\fn_phv&space;\large&space;\frac{\left&space;(&space;a+b&space;\right&space;)}{\left&space;(&space;u-v&space;\right&space;)}$sec.

6. If two trains of length metres and b metres are moving in opposite directions at u m/s and v m/s, then:

The time taken by the trains to cross each other = $\inline&space;\fn_phv&space;\large&space;\inline&space;\fn_phv&space;\large&space;\frac{\left&space;(&space;a+b&space;\right&space;)}{\left&space;(&space;u+v&space;\right&space;)}$sec.
7. Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.
8. Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u – v) m/s.

এখন ট্রেন নিয়ে গুরুত্বপূর্ণ কিছু ম্যাথ দেখে নেয়া যাকঃ

1. প্রশ্নঃ A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

A. 120 metres
B. 180 metres
C. 324 metres
D. 150 metres

Speed = $\inline&space;\fn_phv&space;\large&space;\fn_phv&space;\large&space;\left&space;(&space;60\times&space;\frac{5}{18}&space;\right&space;)m/sec&space;=&space;\left&space;(&space;\frac{50}{3}&space;\right&space;)m/sec$
Length of the train = (Speed x Time).
∴ Length of the train = $\inline&space;\fn_phv&space;\large&space;\dpi{100}&space;\fn_phv&space;\large&space;\left&space;(&space;\frac{50}{3}&space;\times&space;9\right&space;)m=&space;150m$

2. প্রশ্নঃ A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

A. 45 km/hr
B. 50 km/hr
C. 54 km/hr
D. 55 km/hr

Speed of the train relative to man = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;\frac{125}{10}&space;\right&space;)m/sec$
= $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;\frac{25}{2}&space;\right&space;)m/sec$
= $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;\frac{25}{2}&space;\times&space;\frac{18}{5}\right&space;)km/hr$
= 45 km/hr

Let the speed of the train be x km/hr. Then, relative speed = (x – 5) km/hr.
∴ x – 5 = 45 ⇒ x = 50 km/hr.

3. প্রশ্নঃ Two, trains, one from Dhaka to Khulna and the other from Khulna to Dhaka start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:

A. 2:3
B. 4:3
C. 6:7
D. 9:16

Let us name the trains as A and B. Then,
(A’s speed) : (B’s speed) = $\inline&space;\fn_phv&space;\large&space;\sqrt{a}:\sqrt{b}=&space;\sqrt{16}:\sqrt{9}=&space;4:3$

4. প্রশ্নঃ Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

A. 23m
B. 23(2/9)m
C. 27(7/9)m
D. 29m

Relative speed = (40 – 20) km/hr = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;20\times&space;\frac{5}{18}&space;\right&space;)m/sec=&space;\left&space;(\frac{50}{9}\right&space;)m/sec$
∴ Length of faster train = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;\frac{50}{9}\times&space;5&space;\right&space;)m=&space;\frac{250}{9}m=&space;27\frac{7}{9}m$

5. প্রশ্নঃ A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

A. 45 m
B. 50 m
C. 54 m
D. 72 m

2 kmph = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;2\times&space;\frac{5}{18}&space;\right&space;)m/sec=&space;\frac{5}{9}&space;m/sec$
4 kmph =$\inline&space;\fn_phv&space;\large&space;\inline&space;\fn_phv&space;\large&space;\left&space;(&space;4\times&space;\frac{5}{18}&space;\right&space;)m/sec=&space;\frac{10}{9}&space;m/sec$
Let the length of the train be x metres and its speed by y m/sec.
Then, $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;\frac{x}{y-\frac{5}{9}}&space;\right&space;)=&space;9&space;,and&space;\left&space;(&space;\frac{x}{y-\frac{10}{9}}&space;\right&space;)=&space;10$
Therefore 9y – 5 = x and 10(9y – 10) = 9x
⇒ 9y – x = 5 and 90y – 9x = 100.
On solving, we get: x = 50.
∴ The Length of the train is 50 m.

6. প্রশ্নঃ A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

A. 66 km/hr
B. 72 km/hr
C. 78 km/hr
D. 81 km/hr

4.5 kmph = $\inline&space;\fn_phv&space;\large&space;\inline&space;\fn_phv&space;\large&space;\left&space;(&space;4.5\times&space;\frac{5}{18}&space;\right&space;)m/sec=&space;\frac{5}{4}&space;m/sec=&space;1.25m/sec$
5.4 kmph = $\inline&space;\fn_phv&space;\large&space;\inline&space;\fn_phv&space;\large&space;\inline&space;\fn_phv&space;\large&space;\left&space;(&space;5.4\times&space;\frac{5}{18}&space;\right&space;)m/sec=&space;\frac{3}{2}&space;m/sec=&space;1.5m/sec$
Let the speed of the train be x m/sec.
Then, (x – 1.25) x 8.4 = (x – 1.5) x 8.5
⇒ 8.4x – 10.5 = 8.5x – 12.75
⇒ 0.1x = 2.25
⇒ x = 22.5
∴ Speed of the train = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;22.5\times&space;\frac{5}{18}&space;\right&space;)km/hr=&space;81km/hr$

7. প্রশ্নঃ Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

A. 9 a.m.
B. 10 a.m.
C. 10.30 a.m.
D. 11 a.m.

Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x – 1) hours = 25(x – 1) km.
∴ 20x + 25(x – 1) = 110
⇒ 20x + 25x – 20 = 110
⇒ 45x = 135
⇒ x = 3.
So, they meet at 10 a.m.

8. প্রশ্নঃ A train travelling at 48 kmph completely crosses another train having half its length and travelling in the opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is?

A. 400 m
B. 450 m
C. 560 m
D. 600 m

Let the length of the first train be x metres.
Then, the length of the second train is ( $\inline&space;\fn_phv&space;\large&space;\frac{x}{2}$ ) meters
Relative speed = (48 + 42) kmph = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;90\times&space;\frac{5}{18}&space;\right&space;)m/sec=&space;25m/sec$
$\inline&space;\fn_phv&space;\large&space;\frac{[x+(\frac{x}{2})]}{25}=&space;12&space;,or&space;\frac{3x}{2}=&space;300\therefore&space;x=200$
∴ Length of first train = 200 m.
Let the length of the platform be y metres.
Speed of the first train = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;48\times&space;\frac{5}{18}&space;\right&space;)m/sec=&space;\frac{40}{3}m/sec$
∴ (200 + y) x $\inline&space;\fn_phv&space;\large&space;\frac{3}{40}$ = 45
⇒ 600 + 3y = 1800
⇒ y = 400 m.

9. প্রশ্নঃ How many seconds will a 500-metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

A. 25
B. 30
C. 40
D. 45

Speed of the train relative to man = (63 – 3) km/hr = 60km/hr
= $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;60\times&space;\frac{5}{18}&space;\right&space;)m/sec=&space;\left&space;(&space;\frac{50}{3}&space;\right&space;)m/sec$
∴ Time is taken to pass the man    = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;500\times&space;\frac{3}{50}&space;\right&space;)sec$
=30 sec

10. প্রশ্নঃ Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

A. 12 sec
B. 24 sec
C. 48 sec
D. 60 sec

Relative speed = (45 + 30) km/hr
= $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;75\times&space;\frac{5}{18}&space;\right&space;)m/sec$
= $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;\frac{125}{6}&space;\right&space;)m/sec$

We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.

So, distance covered = Length of the slower train.
Therefore, Distance covered = 500 m.
∴ Required time = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;500\times&space;\frac{6}{125}&space;\right&space;)$sec
= 24sec

11. প্রশ্নঃ A train, 130 metres long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is?

A. 235 metres
B. 245 metres
C. 270 metres
D. 220 metres

Speed = 45km/hr = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;45\times&space;\frac{5}{18}&space;\right&space;)m/sec=&space;12.5\,&space;m/sec$
Time =30 sec
Distance travelled = 12.5 × 30 = 375 m
Length of the bridge = 375 −130 = 245 m

12. প্রশ্নঃ A train 360 metre long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 metre long?

A. 235 metres
B. 245 metres
C. 270 metres
D. 220 metres

Speed = 45km/hr = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;45\times&space;\frac{5}{18}&space;\right&space;)m/sec=&space;12.5\,&space;m/sec$
Distance travelled = Length of the train + Length of the platform = 360 + 140 = 500 metre
Time taken to cross the platform = $\inline&space;\fn_phv&space;\large&space;\left&space;(&space;\frac{500}{12.5}&space;\right&space;)sec$= 40 sec

13. প্রশ্নঃ A train having a length of 240 metre passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 metres?

A. 99 seconds
B. 89 seconds
C. 120 seconds
D. 80 seconds

Speed of the train = 240/24 =10 m/s
Required time = (240 + 650)/10 = 89 seconds

14. প্রশ্নঃ A jogger is running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train. The train is running at 45 kmph in the same direction. How much time does it take for the train to pass the jogger?

A. 46 seconds
B. 22 seconds
C. 18 seconds
D. 36 seconds

Distance to be covered = (240 + 120) = 360 m
Relative speed = (45 − 9) = 36 km/hr
= 36 × 5/18
= 10 m/s

∴ Required time = 360/10 = 36 seconds

15. প্রশ্নঃ Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?

A. 70 seconds
B. 62 seconds
C. 50 seconds
D. 88 seconds

Solution-1:
Let the length of each train = x metre
Total distance covered while passing the slower train = (x + x) = 2x metre
Relative speed = (46 − 36) =10 km/hr
= 10 × 5/18
= 50/18 m/s

Time = 36 seconds
(2x)/36 = 50/18
⇒ x = 50 metre

Solution-2:
Relative speed = (46 − 36) = 10 km/hr
Time = 36/3600 = 1/100 hr

Total distance covered = 10 × (1/100)
= 1/10 km
= 100 m

Since the trains are of equal length, total distance covered must be equal to twice the length of each train.
Therefore, length of each train = 100/2 = 50 metre

পরবর্তী পোস্টে আরও ম্যাথ দেয়া হবে। ভাল লাগলে শেয়ার করে অন্যদের দেখার সুযোগ করে দিন। জ্ঞান প্রসার করুন।

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