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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়30 minutes
মোট প্রশ্ন২০
সিলেবাস
Math - 08: Problems on Boats & Streams, Trains
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২০ প্রশ্ন

১.
Two trains running in opposite directions cross a man standing on the platform in 29 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is -
  1. ক
    ক) 1:3
  2. খ
    খ) 3:2
  3. গ
    গ) 3:4
  4. ঘ
    ঘ) 1:1
ব্যাখ্যা
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
২.
A 120 m long train passed a pole in 12 seconds. How long will it take to pass a 450 m long platform?
  1. ক
    ক) 89 sec
  2. খ
    খ) 57 sec
  3. গ
    গ) 59 sec
  4. ঘ
    ঘ) 61 sec
ব্যাখ্যা
Train’s speed = 120/12 = 10 m/s
The train has to cover = (120 + 450) = 570 m.
∴ Required time = 570/10 = 57 seconds
৩.
A boat takes 10 hours to cover a distance while traveling upstream, whereas while travelling downstream it takes 9 hours. If the speed of the current is 4 kmph, what is the speed of the boat in still water?
  1. ক
    ক) 74 kmph
  2. খ
    খ) 76 kmph
  3. গ
    গ) 78 kmph
  4. ঘ
    ঘ) 79 kmph
ব্যাখ্যা
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.
৪.
A moving train, 66 metres long, overtakes another train of 88 metres long, moving in the same direction in 0.168 minutes. If the second train is moving at 40 km/hr, at what speed is the first train moving ?
  1. ক
    ক) 95 km/hr
  2. খ
    খ) 85 km/hr
  3. গ
    গ) 75 km/hr
  4. ঘ
    ঘ) 79 km/hr
ব্যাখ্যা
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.
৫.
A boat takes half time in moving a certain distance downstream than upstream. The ratio of the speed of the boat in still water and that of the current is?
  1. ক
    ক) 2 : 1
  2. খ
    খ) 3 : 2
  3. গ
    গ) 5 : 3
  4. ঘ
    ঘ) 3 : 1
ব্যাখ্যা
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
৬.
Two trains, each 120 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
  1. ক
    ক) 75 km/hr
  2. খ
    খ) 72 km/hr
  3. গ
    গ) 60 km/hr
  4. ঘ
    ঘ) 54 km/hr
ব্যাখ্যা
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.
৭.
A man can row upstream at 24km/hr and downstream at 16km/hr. The man rowing speed in still water is?
  1. ক
    ক) 20 km/hr
  2. খ
    খ) 15 km/hr
  3. গ
    গ) 25 km/hr
  4. ঘ
    ঘ) 27 km/hr
ব্যাখ্যা
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
৮.
A boat can travel from point A to point B and return back to point A in 10 hours. Speed of the boat in still water is 8 km/h and the speed of the stream is 4 km/h. Find the distance between A and B.
  1. ক
    ক) 25 km
  2. খ
    খ) 27 km
  3. গ
    গ) 30 km
  4. ঘ
    ঘ) 29 km
ব্যাখ্যা
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
৯.
Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide?
  1. ক
    ক) 1/12
  2. খ
    খ) 1/6
  3. গ
    গ) 1/4
  4. ঘ
    ঘ) 1/2
ব্যাখ্যা
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.
১০.
A train has a length of 150 metres. It is passing a man who is moving at 4 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train?
  1. ক
    ক) 169 km/hr
  2. খ
    খ) 152 km/hr
  3. গ
    গ) 184 km/hr
  4. ঘ
    ঘ) 180 km/hr
ব্যাখ্যা
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
১১.
A train left Dhaka for Chittagong at 59 km per hour and at the same time another train left Chittagong for Dhaka at 43 km per hour on the same route. How far apart were the two trains one hour before they met?
  1. ক
    ক) 105 km.
  2. খ
    খ) 102 km.
  3. গ
    গ) 110 km
  4. ঘ
    ঘ) 108 km.
ব্যাখ্যা
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.
১২.
Two trains moving in same direction run at a speed of 60 km/hr and 40 km/hr respectively. If a man sitting in slow train is passed by the fast train in 10 seconds, then what is the length of the faster train?
  1. ক
    ক) 53.7 m
  2. খ
    খ) 53.2 m
  3. গ
    গ) 55.6 m
  4. ঘ
    ঘ) 57.2 m
ব্যাখ্যা
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
১৩.
A person is walking at a speed of 5 km/hr along a railway track. If he is 200 m ahead of the train which is 150 m long and runs at a speed of 60 km/hr in same direction, then what is the time required to pass the person?
  1. ক
    ক) 17.34 sec
  2. খ
    খ) 18.47 sec
  3. গ
    গ) 22.92 sec
  4. ঘ
    ঘ) 19.49 sec
ব্যাখ্যা
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
১৪.
A boat covers a certain distance in half an hour downstream with the speed of 40km/hr in still water and the speed of the current is 8km/hr. Then the distance travelled by the boat is:
  1. ক
    ক) 6km
  2. খ
    খ) 7km
  3. গ
    গ) 12km
  4. ঘ
    ঘ) 24km
ব্যাখ্যা
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.
১৫.
Two trains of equal length are running on parallel lines in the same direction at 48km/hr and 38 km/hr. The faster train passes the slower train in 54 seconds. The length of each train is
  1. ক
    ক) 50m
  2. খ
    খ) 75m
  3. গ
    গ) 65m
  4. ঘ
    ঘ) 60m
ব্যাখ্যা
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 
১৬.
The speed of the boat is still water at 12 kmph. It can travel downstream through 45 kms in 3 hrs. In what time would it cover the same distance upstream?
  1. ক
    ক) 4 hours
  2. খ
    খ) 8 hours
  3. গ
    গ) 6 hours
  4. ঘ
    ঘ) 5 hours
ব্যাখ্যা
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.
১৭.
A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
  1. ক
    ক) 65 meter
  2. খ
    খ) 60 meter
  3. গ
    গ) 55 meter
  4. ঘ
    ঘ) 50 meter
ব্যাখ্যা
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.
১৮.
In a river flowing at 2 km/hr, a boat travels 40 km upstream and then returns downstream to the starting point. If its speed in still water is 6 km/hr, find the total journey time.
  1. ক
    ক) 15 hours
  2. খ
    খ) 13 hours
  3. গ
    গ) 12 hours
  4. ঘ
    ঘ) 11 hours
ব্যাখ্যা
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
১৯.
A train passes two bridges of the lengths 600 m and 250 m in 100 seconds and 60 seconds respectively. The length of the train is -
  1. ক
    ক) 152 m
  2. খ
    খ) 125 m
  3. গ
    গ) 275 m
  4. ঘ
    ঘ) 120 m
ব্যাখ্যা
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
২০.
An train travels 10 miles at a speed of 50 miles per hour. How fast must the train travel on the return trip if the round-trip travel time is to be 20 minutes?
  1. ক
    ক) 55 miles/hours
  2. খ
    খ) 75 miles/hours
  3. গ
    গ) 65 miles per hour
  4. ঘ
    ঘ) 78 miles per hour
ব্যাখ্যা
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.