ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 29x metres
and length of the second train = 17y metres
∴ (29x+17y)/(x+y) = 23
⇒ 29x+17y = 23x+23y
⇒ 6x=6y
⇒ x/y= 1/1

Train’s speed = 120/12 = 10 m/s
The train has to cover = (120 + 450) = 570 m.
∴ Required time = 570/10 = 57 seconds

Let the speed of the boat in still water be x kmph
Then, Speed downstream = (x+4) kmph.
Speed upstream = (x-4) kmph.
∴ (x+4)× 9 = (x-4)×10
⇒ 9x+36 = 10x-40 ⇒ x = 76 ⇒ x = 76 kmph.

Let the speed of the first train be x km/hr.
Then,
Sum of lengths of trains = (66 + 88)m = 154 m.

Relative speed of two trains = (x - 40) km/hr
= {(x - 40) × (5/18)} m/s

∴ 154/{(x - 40) × (5/18)} = 0.168 × 60
⇒ 5(x - 40) = (154 × 18)/10.08
⇒ 5(x - 40) = 275
⇒ x - 40 = 55
⇒ x = 95 km/hr.

Let the speed of boat in still water = x km/hr,
and Speed of current = y km/hr
Rate downstream = (x + y) km/hr, and Rate upstream = (x – y) km/hr
Distance = Speed × Time
∴ (x−y) × 2t = (x+y)×t
⇒ 2x−2y = x+y
⇒ 2x−x = 2y+y
⇒ x = 3y
⇒ x/y = 3/1 = 3:1

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.
So,(120 + 120)/8 = 3x
⇒ 24x = 240
⇒ x = 10
So, speed of the faster train
= 20 m/sec
= (20) x (18/5) km/hr
=72 km/hr.

Speed of boat in still water = (x+y)/2
Where (x = downstream speed) and (y = upstream speed)
∴ Boat's speed = (24+16)/2 = 40/2 = 20 km/hr

Speed of boat along the stream = 8 + 4 = 12 km/h
Speed of boat against stream = 8 - 4 = 4 km/h
ATQ, 
x/12 + x/4 = 10
⇒ (x+3x)/12 = 10
⇒ 4x = 120
⇒ x = 30 km

Notice that the distance between the two boats one minute before they collide is equal to the total distance traveled by the two boats in one minute.

In 1 minute, the boat with speed of 5 km/hr will have traveled 5 x 1/60 = 5/60 km.
Similarly, the boat with speed of 10 km/hr will have traveled 10 x 1/60 = 10/60 km in 1 minute.
Therefore, 1 minute before they collide, they are 5/60 + 10/60 = 15/60 = 1/4 km apart.

Length of the train = 150 m
Speed of the man = 4 km/hr
Relative speed = 150/3 = 50 m/s
= 50 × 18/5
= 180 km/hr
Relative speed = Speed of train - Speed of the man (as both are moving in the same direction).
Therefore,
Speed of the train = Relative speed + Speed of the man
= 180 + 4
= 184 km/hr

ঢাকা থেকে চট্টগ্রামগামী ট্রেনটি 1 ঘন্টায় 59 km. যায়।
চট্টগ্রাম থেকে ঢাকাগামী ট্রেনটি 1 ঘন্টায় 43 km. যায়।
∴ 1 ঘন্টায় দুটি বিপরীতমুখী ট্রেন মোট যায় (59 + 43)
= 102 km. দূরত্ব অতিক্রম করে।
অর্থাৎ মুখোমুখি হওয়ার 1 ঘন্টা আগে তাদের দুরত্ব = 102 km.

Given: Speed of slow train = 60 km/hr, speed of fast train = 40 km/hr
Here both the trains move in same direction. Hence their relative speed is obtained by subtracting the individual speeds of trains.
Relative speed = 60–40 = 20 km/hr
1) Convert km/hr into m/s
20x(5/18)=100/18= 5.56 m/s
2) Distance (Length of faster train) = Speed x Time
Length of faster train = 5.56 x 10 m = 55.6 m

Given: Speed of the person = 5 km/hr, length of train = 100 m, speed of train = 60 km/hr
Speed of train relative to walking person = (60–5) = 55 km/hr
Convert km/hr into m/s
55 km/hr = 55 x(5/18) = 15.27 m/s
Distance to be covered by the train = 200 + 150 = 350 m
Therefore, time taken by the train to cross the person
= Distance over speed =350/15.27 = 22.92 sec

Given that,
The speed of a boat in still water is 40 km/hr
The speed of the stream is 8 km/hr.
Then,
The speed downstream = (40 + 8) km/hr
= 48 km/hr
The distance travelled in half an hour = 48 x 1/2
= 24 km
Hence the distance travelled by the boat is 24 km.

Let,
the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (48 - 38) km/hr
                        = (10 x 5/18) m/sec    [km/hr  কে m/sec পরিণত করতে 5/18  গুণ করতে হয় ]
                          = (25 /9) m/sec 

∴ 2x/ 54 = 25 /9
⇒ 2x = 150
     x = 75 

Speed of the boat in still water = 12 km/hr.
Speed downstream = 45/3 = 15 km/hr.
Speed of the stream = (15 -12) km/hr.
= 3 km/hr.
Speed upstream = (12 - 3)
= 9 km/hr.
Time is taken to cover 45 km upstream = 45/9 hr.
= 5 hrs.

Let the speed of the train be v km/hr.
(v - 2) : (v - 4) = 10 : 9 [speed and time are inversely proportional]
⇒ 9v - 18 = 10v - 40
⇒ v = 22 km/hr.
Length of the train
= (22 - 2) × (5/18) × 9
= 50 meter.

Speed of the boat in still water = 6 km/hr
Speed of the stream = 2 km/hr
Speed downstream = (6 + 2) = 8 km/hr
Speed upstream = (6 − 2) = 4 km/hr
Total journey time = 40/8 + 40/4 = 15 hr

Let the length of train x m
Speed of train = (length of train + length of bridge)/time taken in crossing
According to information we get,
⇒ (x + 600)/100 = (x + 250)/60
⇒ 60 (x + 600) = 100(x + 250)
⇒ 3 (x + 600) = 5(x + 250)
⇒ 5x + 1250 = 3x + 1800
⇒ 5x - 3x = 1800 - 1250
⇒ 2x = 550
⇒ x = 275 m

We know speed = distance/time
Given distance = 10 miles
Speed = 50 miles per hour
Time = distance/speed = ⅕ hours = 12 min
Total time = 20 min
Time left = 20 – 12 = 8 min = 2/15 hour

So the train has to cover 10 miles in 8 minutes.
Speed = distance/time
           = 10/(2/15)
           = 10(15/2)
           = 75 miles per hour

Hence option b is the answer.