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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়45 minutes
মোট প্রশ্ন২১
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 · ২১ প্রশ্ন

১.
A motorboat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
  1. ক
    ক) 4
  2. খ
    খ) 5
  3. গ
    গ) 6
  4. ঘ
    ঘ) 7
  5. ঙ
    ঙ) 8
ব্যাখ্যা

Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr

30/(15 + x) +30/(15 - x) = 4(1/2)
900/(225 - X2) = 9/2
9X2 = 225
X2 = 25
X = 5 km/hr

২.
A train has a length of 150 metres. It is passing a man who is moving at 2 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) 182 km/hr
  3. গ
    গ) 152 km/hr
  4. ঘ
    ঘ) 180 km/hr
  5. ঙ
    ঙ) 108 km/hr
ব্যাখ্যা

Length of the train = 150 m
Speed of the man = 2 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 + 2
= 182 km/hr

৩.
A train 360 metre long runs with a speed of 45 km/hr. What time will it take to pass a platform 140 metre long?
  1. ক
    ক) 44 seconds
  2. খ
    খ) 40 seconds
  3. গ
    গ) 30 seconds
  4. ঘ
    ঘ) 38 seconds
  5. ঙ
    ঙ) 25 seconds
ব্যাখ্যা

Speed = 45 km/hr = 45 × 5/18
= 25/2 m/s
Distance travelled = Length of the train + Length of the platform
= 360 + 140
= 500 metre.
Time taken to cross the platform = 500/(25/2)
= 40 seconds

৪.
A man can row three-quarters of a kilometre against the stream in 11(1/4) minutes and down the stream in 7(1/2) minutes. The speed (in km/hr) of the man in still water is -
  1. ক
    ক) 2
  2. খ
    খ) 3
  3. গ
    গ) 4
  4. ঘ
    ঘ) 5
  5. ঙ
    ঙ) 6
ব্যাখ্যা

We can write three-quarters of a kilometre as 750 metres, 11(1/4) minutes as 675 seconds and 7(1/2) minutes as 450 seconds.

Rate upstream = (750/675) m/sec = 10/9 m/sec
Rate downstream = (750/450) m/sec = 5/3 m/sec
Rate in still water = (1/2) (10/9 + 5/3) m/sec
= 25/18 m/sec
= (25/18 × 18/5) km/hr
= 5km/hr

৫.
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 metre?
  1. ক
    ক) 99 seconds
  2. খ
    খ) 100 seconds
  3. গ
    গ) 89 seconds
  4. ঘ
    ঘ) 98 seconds
  5. ঙ
    ঙ) 97 seconds
ব্যাখ্যা
Speed of the train = 240/24 = 10 m/s
Required time = (240 + 650)/10 = 89 seconds
৬.
A man rows to a place 48 km distant and comes back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
  1. ক
    ক) 1.5 km/hr
  2. খ
    খ) 1 km/hr
  3. গ
    গ) 2.5 km/hr
  4. ঘ
    ঘ) 2 km/hr
  5. ঙ
    ঙ) 5.2 km/hr
ব্যাখ্যা

Suppose he moves 4 km downstream in x hours.
Then,
Speed downstream = (4/x) km/hr
Speed upstream = (3/x) km//hr

So, 48/(4/x) + 48/(3/x) = 14
or, 12x + 16x = 14
or, 6x + 8x = 7
or, x = 1/2
So, Speed downstream = 8 km/hr
Speed upstream = 6km/hr

Rate of the stream = (1/2) (8-6) km/hr = 1km/hr

৭.
Two trains, each 500 metre long, are running in opposite directions on parallel tracks. If their speeds are 45 km/hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is -
  1. ক
    ক) 22 seconds
  2. খ
    খ) 54 seconds
  3. গ
    গ) 24 seconds
  4. ঘ
    ঘ) 38 seconds
  5. ঙ
    ঙ) 32 seconds
ব্যাখ্যা

Relative speed = ( 45 + 30 )
= 75 km/hr
= (75 × 5)/18 m/s
= 125/6 m/s

We are calculating the time taken by the slower train to pass the driver of the faster one.

Hence, distance = length of the slower train = 500 metre
Time = 500/( 125/6)
= 24 seconds

৮.
A boatman goes 2 km against the current of the stream in 2 hour and goes 1km along the current in 20 minutes. How long will it take to go 5 km in stationary water?
  1. ক
    ক) 4 hr 25 min
  2. খ
    খ) 3 hr 25 min
  3. গ
    গ) 2 hr 30 min
  4. ঘ
    ঘ) 1 hr 15 min
  5. ঙ
    ঙ) 3 hr 53 min
ব্যাখ্যা

Speed upstream = 2/2 = 1 km/hr
Speed downstream = 1/(20/60) = 3 km/hr
Speed in still water = (1/2)(3+1) = 2 km/hr
Time taken to travel 5 km in still water = 5/2
= 2(1/2)
= 2 hr 30 min

৯.
A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?
  1. ক
    ক) 180
  2. খ
    খ) 175
  3. গ
    গ) 190
  4. ঘ
    ঘ) 185
  5. ঙ
    ঙ) 200
ব্যাখ্যা

Speed = 40 km/hr = (40 × 5/18) m/s = 100/9 m/s
Time = 18 seconds
Distance Covered = 100/9 × 18 = 200 m
Therefore,
Length of the train = 200 m

১০.
A boat covers a certain distance downstream in 1 hour, while it comes back in 1 (1/ 2) hours. If the speed of the stream is 3 kmph, what is the speed of the boat in still water?
  1. ক
    ক) 13 kmph
  2. খ
    খ) 17 kmph
  3. গ
    গ) 19 kmph
  4. ঘ
    ঘ) 11 kmph
  5. ঙ
    ঙ) 15 kmph
ব্যাখ্যা

Let speed of the water in still water = x kmph
Given that speed of the stream = 3 kmph

Speed downstream = (x + 3) kmph
Speed upstream = (x - 3) kmph

He travels a certain distance downstream in 1 hour and comes back in 1 (1/ 2) hour. That is, (distance travelled downstream in 1 hour = distance travelled upstream in 1 (1 /2) hour).

Since, distance = speed × time ; we have,
(x + 3) × 1 = (x − 3) × (3/2)
⇒ 2 (x + 3) = 3 (x − 3)
⇒ 2x + 6 = 3x − 9
⇒ x = 6 + 9 = 15

১১.
Two trains are running in opposite directions at the same speed. The length of each train is 120 metre. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
  1. ক
    ক) 20
  2. খ
    খ) 28
  3. গ
    গ) 42
  4. ঘ
    ঘ) 36
  5. ঙ
    ঙ) 48
ব্যাখ্যা

Distance covered = (120 + 120) = 240 metre
Time = 12 seconds
Relative speed = 240/ 12
= 20 m/s
= 20 × 18 /5 km/hr
= 72 km/hr
Relative speed in this case is the sum of the speeds of the trains and each train has same speed,
speed of each train = 72 /2
= 36 km/hr

১২.
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?
  1. ক
    ক) 50 metre
  2. খ
    খ) 60 metre
  3. গ
    গ) 40 metre
  4. ঘ
    ঘ) 45 metre
  5. ঙ
    ঙ) 35 metre
ব্যাখ্যা

Let 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
⇒ 2 x/36 = 50/18
⇒ x = 50

১৩.
A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
  1. ক
    ক) 2 : 1
  2. খ
    খ) 1 : 2
  3. গ
    গ) 1 : 3
  4. ঘ
    ঘ) 3 : 1
  5. ঙ
    ঙ) 2 : 3
ব্যাখ্যা

Let speed upstream = x
Then,
Speed downstream = 2 x
Speed in still water = (2 x + x) /2 = 3x/2
Speed of the stream = (2 x − x)/2 = x/2
Speed in still water : Speed of the stream
= 3x/2 : x/2
= 3 : 1

১৪.
A boat travelled upstream and then returned, stopping 4 km short of the place from which it started. Speed of the stream is 2 km/hr. If total time taken by the boat is 6 hour and its speed in still water is 4 km/hr, distance travelled upstream is :
  1. ক
    ক) 12 km
  2. খ
    খ) 8 km
  3. গ
    গ) 6 km
  4. ঘ
    ঘ) 9 km
  5. ঙ
    ঙ) 10 km
ব্যাখ্যা

Let distance travelled upstream be x km
x/(4 − 2) +( x − 4)/( 4 + 2) = 6
⇒ x/2 + (x − 4)/6 = 6
⇒ 3 x + x − 4 = 36
⇒ 4 x = 40
⇒ x = 10

১৫.
A boatman can row 96 km downstream in 8 hour. If the speed of the current is 4 km/hr, then find the time required to cover 8 km upstream?
  1. ক
    ক) 1 hr
  2. খ
    খ) 4 hrs
  3. গ
    গ) 2 hrs
  4. ঘ
    ঘ) 6 hrs
  5. ঙ
    ঙ) 3 hrs
ব্যাখ্যা

Speed downstream = 96/8 = 12 km/hr
Speed of current = 4 km/hr
Speed of the boatman in still water = 12 − 4 = 8 km/hr
Speed upstream = 8 − 4 = 4 km/hr
Time taken to cover 8 km upstream = 8/4 = 2 hrs

১৬.
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) 45
  2. খ
    খ) 50
  3. গ
    গ) 55
  4. ঘ
    ঘ) 65
  5. ঙ
    ঙ) 60
ব্যাখ্যা

Let length and speed of the train be x metre and v kmph respectively.
x/9 = (v − 2) × 5/18 ⋯ ( 1 )
x/10 = (v − 4) × 5/18 ⋯ ( 2 )
Dividing (1) by (2) gives,
10/9 = (v − 2)/(v − 4)
⇒ 10v − 40 = 9v − 18
⇒ v = 22
Substituting the value of v in (1)
x/9 = 100/18
⇒ x = 50

১৭.
The speed of a boat in still water is 25 kmph. If it can travel 10 km upstream in 1 hr, what time would it take to travel the same distance downstream?
  1. ক
    ক) 21 minute
  2. খ
    খ) 22 minute
  3. গ
    গ) 30 minute
  4. ঘ
    ঘ) 35 minute
  5. ঙ
    ঙ) 15 minute
ব্যাখ্যা

Speed of boat in still water = 25 km/hr
Speed upstream = 10 km/hr
Speed of the stream = (25 − 10) = 15 km/hr
Speed downstream = (25 + 15) = 40 km/hr

Time taken to travel 10 km downstream = 10/40 hour
= (10 × 60)/40
= 15 minute

১৮.
A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up than to row down the river. Find the rate of stream -
  1. ক
    ক) 5.2 km/hr
  2. খ
    খ) 2.5 km/hr
  3. গ
    গ) 3.5 km/hr
  4. ঘ
    ঘ) 5.3 km/hr
  5. ঙ
    ঙ) None of these
ব্যাখ্যা

Let rate of stream be y km/hr, distance be d km
time upstream = 2 (time downstream)
⇒ d/(7.5 − y) = 2d/(7.5 + y)
⇒ 2( 7.5 − y ) = 7.5 + y
⇒ 15 − 2 y = 7.5 + y
⇒ 3 y = 7.5
⇒ y = 2.5

১৯.
A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other 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?
  1. ক
    ক) 80 km/hr
  2. খ
    খ) 91 km/hr
  3. গ
    গ) 88 km/hr
  4. ঘ
    ঘ) 81 km/hr
  5. ঙ
    ঙ) 92km/hr
ব্যাখ্যা

Let length and speed of the train be x metre and y kmph
x/8.4 = (y − 4.5) × 5/18 ⋯ (1)
x/8.5 = (y − 5.4) × 5/18 ⋯ (2)
Dividing (1) by (2) gives,
8.5/8.4 = (y − 4.5)/(y − 5.4)
⇒ 8.4y − 8.4 × 4.5 = 8.5y − 8.5 × 5.4
⇒ 0.1y = 8.5 × 5.4 − 8.4 × 4.5
⇒ 0.1y = 45.9 − 37.8 = 8.1
⇒ y = 81

২০.
Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
  1. ক
    ক) 11 a.m.
  2. খ
    খ) 10.30 a.m
  3. গ
    গ) 9.10 a.m.
  4. ঘ
    ঘ) 8 a.m
  5. ঙ
    ঙ) 10 a.m.
ব্যাখ্যা

Assume both trains meet x hours after 7 a.m.
Distance covered by train starting from P in x hours = 20 x km
Distance covered by train starting from Q in (x − 1) hours = 25 (x − 1) km
Total distance = 110 km
⇒ 20 x + 25 (x − 1) = 110
⇒ 45 x = 135
⇒ x = 3
Hence, they meet 3 hours after 7 a.m.
i.e., they meet at 10 a.m.

Alternative method:
Distance travelled by first train in 1 hour = 20 km
Therefore, at 8 a.m., both trains will be (110 − 20) = 90 km apart.
Since the relative speed is (20 + 25) = 45 kmph,
they will cover this distance in 90/ 45 = 2 hours.
I.e. They will meet at 10 a.m.

২১.
A train, 800 metre long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in metres)?
  1. ক
    ক) 430 metre
  2. খ
    খ) 440 metre
  3. গ
    গ) 260 metre
  4. ঘ
    ঘ) 450 metre
  5. ঙ
    ঙ) 500 metre
ব্যাখ্যা

Let length of the tunnel = x metre
Then, distance = (800 + x) metre
Time = 1 minute = 60 seconds
Speed = 78 km/hr
= 78 × 5 /18 m/s
= 65/3 m/s

800 + x = 60 × 65/3
⇒ 800 + x = 1300
⇒ x = 500