ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Speed downstream = (14 + 5) km/hr = 19 km/hr.

Time taken to travel 76 km downstream = (76/19) hours  
                                                                  = 4 hours

Here
Length of a train is 1300m
Train took 130 sec to cross a tree
Length of a platform is 800m

Speed of the train = 1300/130 = 10 m/sec
Total distance = 1300 + 800 = 2100 m

Time = distance/speed
        = 2100/10 = 210 sec

∴ Time required to cross a platform is 210 sec.

Rate downstream = (24/3) km/hr. = 8 km/hr.
Rate upstream = (24/4) km/hr. = 6 km/hr.

 The speed of the boat in still water = (1/2)(8 + 6) km/hr.
                                                          = (1/2) × 14 km/hr.
                                                           = 7 km/hr.

⇒ Speed of train = 54 × (5/18) = 15m/s
⇒ Distance covered in 43 seconds = 15 × 43 = 645 m
⇒ Length of train = 110m

∴ The initial distance of the pole from the front end of the train = 645 - 110 = 535 m

Let the speed of the boat in still water be x kmph.
Then,
Speed downstream = (x + 5) kmph,
Speed upstream = (x - 5) kmph.

Now 
(x + 5) x 1 =(x - 5)(7/2)
2(x + 5) = 7(x - 5)
2x + 10 = 7x - 35 
7x - 2x = 35 +10 
5x = 45
x = 9 kmph

Let the length of the platform be x

The speed of the train = (750 + 250)/20
                                    = 1000/20
                                    = 50 m/sec
Now, Again according to the question
The train crosses the platform in 16 seconds
250 + x = 50 × 16
⇒ x = 800 - 250
⇒ x = 550 m

∴ The length of the platform is 550 m.

Speed upstream = 7.5 kmph.
Speed downstream = 12.5 kmph.


∴ Total time taken =(112.5/7.5) +(112.5/12.5) 
                               = (15 + 9) hours 
                                = 24 hours

Length of platform = 405 m
Length of train = 225 m
Time taken to cover the length of train = 21 seconds
Distance need to cover = Length of platform + length of train
                                      = 405 + 225
                                     = 630 m
Speed of train = 630/21 = 30 m/s

∴ Speed of train = 30 × (18/5) = 6 × 18 = 108 km/hr.

Speed downstream =(5 + 1)kmph=6kmph
Speed upstream =(5 - 1)kmph=4kmph
Let the required distance be x km.

x/6 + x/4 = 1
2x+ 3x = 12
5x = 12 
x = 12/5 
x = 2.4

Let the length of the train be x m.
The train passes a bridge of length 400 m in 110 sec.
Speed of the train = (x + 400)/110...........(1)
The train passes another bridge of length 160 m in 60 sec.
Speed of the train = (x + 160)/60..............(2)

Equating equation (1) and (2),
⇒ (x + 400)/110 = (x + 160)/60
⇒ (x + 400) × 60 = (x + 160) × 110
⇒ (60x + 24000) = (110x + 17600)
⇒ 110x – 60x = 24000 – 17600
⇒ 50x = 6400
⇒ x = 6400/50
⇒ x = 128 m

Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.

(200 + 200)/8= 3x
400/8 = 3x
x = (400/(3 × 8)
x = 50/3

Speed of the slower train = (50/3) × (18/5)
                                          = 60 km/hr

Speed of the train relative to man
= (64 - 4) km/hr
= 60 km/hr
= 60× (5/18) sec
= 50/3 sec

Time taken to pass the man
=450 ×(3/50)
= 27 sec

Let the speed of stream be x km/hr.
⇒ Speed of boat in still water =30 km/hr
⇒ Speed of boat in upstream = 25/5 = 5 km/hr

Also, speed of boat in upstream = speed of boat in still water - speed of stream
 5 = 30 - x
x = 30 - 5 
x = 25 
∴ The speed of stream is 25 km/hr.

Speed of first train = 180/18 m/sec
                               = 10 m/sec

Let the speed of second train be x m/sec
Relative speed = (10 + x) m/sec

Here
360/(10 + x) = 12
12(10 + x) = 360
120 + 12x = 360
12x = 360 - 120 
12x = 240 
x = 20 m/sec
x = 20 × (18/5) km/hr
x = 72 km/hr

Distance covered by a man by swimming in still water = 360 m
Time taken by man = 4 minutes = 240 seconds
Speed of man = 360/240 = (3/2) m/sec
Speed of stream is = 1 m/sec.

Time taken in upstream 
= 180/[(3/2) - 1)]
 = 180/(1/2)
= 360 seconds
⇒ Time = 6 minutes

∴ He will cover 150 m upstream in 6 minutes

Length of train = 240 m
Length of platform = (3 × 240) m = 720m

∴Speed of train (240 + 720)/60 m/sec
                          = 960/60 m/sec
                          = 16 × (18/5) km/hr
                           = 57.6 km/hr

The boat covers 15 km upstream in 5 hours and 24 km downstream in 4 hours
According to the question,
Downstream speed = 30/5 = 6 km/h
Upstream speed = 18/6 = 3 km/h

∴ Speed of the Boat in still water = 1/2 × (6 + 3) = 4.5 km/h

Speed of the man in still water = 12 km/h
Speed of the current = 4 km/h
Speed of the man along the current = (12 + 4) km/h = 16 km/h
Speed of the man against the current = (12 -  4) km/h = 8 km/h


Let, The distance is x km
Now
 x/8 – x/16 = 3
=(2x - x)/16 = 3
= x/16 = 3 
∴ x = 48 km

Relative speed = (72 - 60) km/hr
                       = 12 km/hr
                       = 12 × (5/18) m/sec
                       = 10/3 m/sec

Total distance covered = Sum of lengths of trains = (210 + 210) m = 420 m
Time taken = (420 × 3)/10sec=126sec

Speed of the boat in downstream  = 55/2.5
                                                       =(55 × 10)/25 = 22km/hr.

Speed of the boat in upstream = 22/2.2= (22 × 10)/22 =10km/hr.


∴ Speed of the boat in still water = (22 + 10)/2 = 16km/hr.
                                                      =  16km/hr.

Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
Now
2x  =(150 + 150)/15
2x = 300/15
2x = 20 
x = 10 


Speed of each train = 10 m/sec
                                = 10 × (18/5) km/hr    
                                 = 36 km/hr

Relative speed = (60 + 40) km/hr 
                        = 100 km/hr 
                       = 100 × (5/18) m/sec
                       = 250/9 m/sec

Distance covered in crossing each other = (180 + 170) m = 350 m

Required time = 350 × (9/250) 
                       = 12.6 sec

Let the speed of the boat in still water be x kmph 
Then Speed downstream = (x + 6) kmph 
Speed up stream = (x - 6) kmph 

Now 
(x + 6) × 4 = (x - 6) × 6 
4x + 24 = 6x - 36
6x - 4x = 36 + 24 
2x = 60
x = 30 kmph

Relative speed = (120 + 80) km/hr
                          = 200 km/hr
                          = 200 ×(5/18) m/sec
                           = 500/9 m/sec

Let the length of the other train be x metres.
Now
(x + 280)/9 = 500/9
x + 280 = 500
x  = 500 - 280 
x = 220

Let speed upstream be x kmph
Then speed downstream = 3x kmph
Speed in still water = (1/2)​(3x + x)kmph
                              =2x kmph

Now 
2x = 34/3
x  = (34/3) × 2
x = 17/3

So Speed upstream = 17/3 km/hr
Speed downstream = 17 km/hr

Hence speed of the current =(1/2){17 - (17/3)} km/hr.
                                             = (1/2)(51 - 17)/3 km/hr.
                                            = (1/2)(34/3) km/hr.
                                              = 17/3 km/hr.

Let the length of the train be x m.
Length of the bridge = 204 m

Now
⇒ (x + 204)/50 = x/20
(x + 204)/5 = x/2
⇒ 2x + 408 = 5x
5x - 2x = 408 
3x = 408
x = 136

∴ Length of the train is 136 m