ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২৭ প্রশ্ন

১.

A motorist can go downstream at 18 km/hr and upstream at 10 km/hr. Find the speed of the stream and the speed of the motorist in still waters.

ক
ক) Motorist = 8 km/hr ; Stream = 28 km/hr
খ
খ) Motorist = 10 km/hr ; Stream = 5 km/hr
গ
গ) Motorist = 14 km/hr ; Stream = 4 km/hr
ঘ
ঘ) Motorist = 28 km/hr ; Stream = 8 km/hr

ব্যাখ্যা

Man's/Boat's Speed = X
Stream/Current/River Speed = Y

∴ Downstream speed = X + Y
Upstream speed = X - Y

X + Y = 18 km/hr and X - Y = 10 km/hr
Adding them we get,
X + Y + X - Y = 28 km/hr

∴ X = 14 km/hr = Speed of Motorist

Y = 18 - 14 = 4 km/hr = Speed of stream

২.

A man can row 9 (1/3) kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. What is the speed of the current?

ক
ক) 3(1/3)km/hr
খ
খ) 3(1/9) km/hr
গ
গ) 4(2/3) km/hr
ঘ
ঘ) 4(1/2) km/hr

ব্যাখ্যা

Let speed upstream be x km/hr
Then, speed downstream = 3x km/hr.

Speed in still water = 1/2 (3x + x) kmph = 2x km/hr.

∴ 2x = 28/3
x = 14/3 km/hr;
Speed downstream = 14 km/hr

Hence, speed of the current
1/2 {14 - (14/3)} km/hr
= 14/3 km/hr
= 4(2/3) km/hr.

৩.

A speedboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the speed of the stream in km/hr?

ক
ক) 2.5 km/hr
খ
খ) 3.5 km/hr
গ
গ) 4 km/hr
ঘ
ঘ) 5 km/hr

ব্যাখ্যা

Let the speed of the stream be x km/hr
Upstream Speed = 15 + x
Downstream Speed = 15 - x

So,
{30/(15+x)} + {30/(15-x)} = 4(1/2)(4 hours 30 minutes)
⇒ {900/(225-x2)} = 9/2
⇒ 9x² = 225
⇒ x² = 25
⇒ x = 5.
Hence, the speed of the stream is 5 km/hr.

৪.

A man rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream at the same time as 3 km against the stream. The rate of the stream is:

ক
ক) 1 km/hr
খ
খ) 1.5 km/hr
গ
গ) 1.8 km/hr
ঘ
ঘ) 3.5 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

∴ 48/(4/x) + 48/(3/x) = 14
⇒ 48x/4 + 48x/3 = 14
⇒ 48{(x/4) + (x/3)} = 14
⇒ 7x/12 = 14/48
⇒ 7x/12 = 7/24
⇒ 7x = (7/24) × 12
⇒ 7x = 7/2
⇒ 14x = 7
⇒ x = 7/14
⇒ x = 1/2

So, speed downstream = 7 km/hr
Rate of the stream = 1/2(8 - 6) km/hr = 1 km/hr.

৫.

A child swims in still water at 4.5 km/hr. The river is flowing at a rate of 1.5 km/hr. Find the average speed of the child if he swims the same distance upstream and downstream.

ক
ক) 3 km/hr
খ
খ) 3.5 km/hr
গ
গ) 4 km/hr
ঘ
ঘ) 6 km/hr

ব্যাখ্যা

Man's/Boat's Speed = X
Stream/Current/River Speed = Y

∴ Downstream speed = X + Y
Upstream speed = X - Y

∴ X+Y = 4.5+1.5 = 6 km/hr and X-Y = 4.5-1.5 = 3 km/hr
Let distance be D km

Downstream time = Distance/Speed = D/6
Upstream time = D/3

Average speed = Total distance/Time taken = (D + D)/(D/6 + D/3)
= (6 × 2D)/3D
= 4 km/hr.

৬.

A man takes 2.2 times as long to row a distance upstream as to row the same distance downstream. If he can row 55 km downstream in 2 hour 30 minutes, what is the speed of the boat in the still water?

ক
ক) 40 km/hr
খ
খ) 8 km/hr
গ
গ) 16m/hr
ঘ
ঘ) 24 km/hr

ব্যাখ্যা

Downstream speed = 55/(5/2) = 11 × 2
= 22 km/hours

Time taken in upstream = 2.2 × 5/2
= 5.5 hours

Upstream speed = 55/5.5
= 10 km/hour

∴ The speed of boat in still water

= (10 + 22)/2
= 32/2
= 16 km/hr.

৭.

P, Q and R are three towns on a river which flows uniformly. Q is equidistant from P and R. I row from P to Q and back in 10 hours and I can row from P to R in 4 hours. Compare the speed of my boat in still water with that of the river.

ক
ক) 4 : 3
খ
খ) 5 : 3
গ
গ) 6 : 5
ঘ
ঘ) 7 : 3

ব্যাখ্যা

Let PQ = Qr = x km
Let speed downstream = a km/hr.
and speed upstream = b km/hr.

Then,
x/a + x/b = 10
x = 10ab/(a + b) .........(i)

And,
2x/a = 4
x = 4a/2
x = 2a .............(ii)

From (i) and (ii) we have:
2a = 10ab/(a + b)
5b = a + b
a = 4b

Required ratio = Speed in the water/Speed of river
= {1/2(a + b)}/{(1/2) (a - b)}
= (a + b)/(a - b)
= (4b + b)/(4b - b)
= 5b/3b
= 5/3

৮.

A fisherman can row his boat to the market for 80 km along the stream. For this he takes 1 hour 20 minutes. His son says that his father’s rowing speed in still water is 45 km/hr. How much time should he take to row the same distance back, against the stream?

ক
ক) 3 hours 10 minutes
খ
খ) 2 hours 40 minutes
গ
গ) 2 hours 30 minutes
ঘ
ঘ) 3 hours 50 minutes

ব্যাখ্যা

Man's/Boat's Speed = X
Stream/Current/River Speed = Y

∴ Downstream speed = X + Y
Upstream speed = X - Y

X+Y = (45+Y) km/hr
1 hour 20 munites = 1 hour + 20/60 = (1 + 1/3) = (4/3) hours
Downstream speed = Distance covered/Time taken

∴ 45 + y = 80/(4/3)
∴ Y = 15 km/hr
X - Y = 45 - 15 = 30 km/hr

Time is taken to go against the stream = 80/30 hours = 2 Hours 40 minutes.

৯.

A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.

ক
ক) 10 km/hr.
খ
খ) 7 km/hr
গ
গ) 5 km/hr
ঘ
ঘ) 2.5 km/hr

ব্যাখ্যা

Given that,
time is taken to travel upstream = 2 × times taken to travel downstream
When the distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream

Let speed upstream = x
Then speed downstream = 2x

we have,
1/2(x + 2x) = speed in still water
⇒ 1/2(3x)=7.5
⇒ 3x = 15
⇒ x = 5
∴ speed upstream = 5 km/hr

∴ Rate of stream = 1/2(2x - x)
= x/2
= 5/2
= 2.5 km/hr.

১০.

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boating till water.

ক
ক) 3 km/hr
খ
খ) 4 km/hr
গ
গ) 8 km/hr
ঘ
ঘ) 6 km/hr

ব্যাখ্যা

Let,
the speed of the stream be = u kmph
the speed of the boat be = v kmph
speed upstream will be = v - u kmph
speed downstream will be = v + u kmph

30 km upstream in time duration = 30 / (v - u) hrs
44 km downstream in time duration = 44 / (v + u) hrs
44/(v + u) + 30/(v - u)
= 10 hrs .........(i)

Similarly,
40 /(v - u) + 55 / (v + u) = 13 hrs Multiply with 3/4:
30/(v - u) + 165 / 4(v + u) = 39/4 .......(ii)

Now (i) - (ii)
⇒ [44 - 165/4] / (v + u) = 10 - 39/4 = 1/4
⇒ v + u = 11 ..........(iii)
Substitute this in (1) to get: 44/11 + 30/(v - u) = 10
⇒ v - u = 30/6 = 5.........(iv)

Solving (iii) and (iv) ,
we get :
v = 8 kmph and
u = 3 kmph

১১.

The speed of the boat in still water is 5 times that of current, it takes 1.1 hour to row to point B from point A downstream. The distance between point A and point B is 13.2 km. How much distance (in km) will it cover in 312 minutes upstream?

ক
ক) 43.2 km
খ
খ) 48 km
গ
গ) 41.6 km
ঘ
ঘ) 44.8 km

ব্যাখ্যা

Let the speed of the current be x kmph
Then speed of the boat in still water = 5x

∴ Downstream speed
= (5x + x) = 6x km/hr.
Upstream speed
= (5x - x)
= 4x km/hr

Now,
According to the question,
1.1 × 6x = 13.2 km
6.6x = 13.2
x = 13.2/6.6
x = 2 km/hr.

Upstream speed
= 4x = 4 × 2 = 8 km/hr

∴ 312 minutes
= 312/60 hours
= 5(1/5) hours

∴ Required Distance travelled upstream
= Speed × Time
= 8 × (26/5)
= 41.6 km

১২.

A boat can travel with a speed of 12 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream -

ক
ক) 4.5 hr
খ
খ) 4 hr
গ
গ) 6 hr
ঘ
ঘ) 4.25 hr

ব্যাখ্যা

Speed of the boat in still water = 12 km/hr.
Speed of the stream = 4 km/hr.
Speed downstream = (12 + 4)
= 16 km/hr.
Time is taken to travel 68 km downstream
= 68/16
=17/4
= 4.25 hrs.

১৩.

Practicing for a competition, a swimmer saw that he could swim 20 km downstream in just 1 hr while it took 2 hrs to swim upstream. Find the speed of the river and that of the swimmer respectively.

ক
ক) 4 km/hr ; 16 km/hr
খ
খ) 5 km/hr ; 15 km/hr
গ
গ) 6 km/hr ; 14 km/hr
ঘ
ঘ) 8 km/hr ; 12 km/hr

ব্যাখ্যা

Man's/Boat's Speed = X
Stream/Current/River Speed = Y

∴ Downstream speed = X + Y
Upstream speed = X - Y

Downstream Speed = Distance covered/Time taken
= 20/1
= 20 km/hr
Upstream Speed = 20/2 = 10 km/hr

X + Y = 20 km/hr
and, X - Y = 10 km/hr

Adding them we get,
X + Y + X - Y = 30 km/hr
∴ X=15 km/hr = Speed of swimmer in still water

∴ Y = 20 - 15 = 5 km/hr = Speed of river.

১৪.

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 30 km/hr, at what speed is the first train moving ?

ক
ক) 85 km/hr
খ
খ) 50 km/hr
গ
গ) 55 km/hr
ঘ
ঘ) 45 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 - 30) km/hr
= {(x - 30) × (5/18)} m/s

∴ 154/(x - 30) × (5/18) = 0.168 × 60
⇒ 5(x - 30) = (154 × 18)/10.08
⇒ 5(x - 30) = 275
⇒ x - 30 = 55
⇒ x = 85 km/hr.

১৫.

A train 125 m long passes a person, running at 8 kmph in the same direction in which the train is going in 25 seconds. The speed of the train is:

ক
ক) 22 km/hr.
খ
খ) 36 km/hr.
গ
গ) 30 km/hr.
ঘ
ঘ) 26 km/hr.

ব্যাখ্যা

Speed of the train relative to Person
= (125/25) m/s.
= 5 m/s.

∴ 5 × (18/5) km/hr
= 18 km/hr

Let the speed of the train be x km/hr.
then, relative speed = (x - 8) km/hr.

So, (x - 8) = 18
⇒ x = 26 km/hr.

১৬.

Time is taken by two trains running in opposite directions to cross a man standing on the platform in 28 seconds and 18 seconds respectively. It took 26 seconds for the trains to cross each other. What is the ratio of their speeds?

ক
ক) 2 : 3
খ
খ) 3 : 2
গ
গ) 1 : 4
ঘ
ঘ) 4 : 1

ব্যাখ্যা

Let the speed one train be x and the speed of the second train be y
Length of the first train = Speed × Time = 28x
Length of second train = Speed × Time = 18y

So, {(28x + 18y)/(x + y)} = 26
⇒ 28x + 18y = 26x + 26y
⇒ 2x = 8y

Therefore,
x : y = 4 : 1.

১৭.

If a train takes 1.5 sec to cross a telegraph post and 1.75 to overtake a cyclist racing along the parallel road to the track at 10 m/s , then the length of the train is:

ক
ক) 105 m
খ
খ) 115 m
গ
গ) 125 m
ঘ
ঘ) 135 m

ব্যাখ্যা

Let the length of the train be x metres and its speed be y m/sec.
Then,
x/y = 1.75
⇒ x = 1.75y

Since the train takes less time to pass a moving object than a stationary object,
it means that the cyclist is moving in a direction opposite to that of the train.

∴ x/(y + 10) = 1.5
⇒ x = 1.5 y + 15
⇒ 1.75 y = 1.5 y + 15
⇒ 0.25 y = 15
⇒ y = 15/0.25
⇒ y = 60.

Length of the train = 1.75 y = (1.75 × 60) m
= 105 m.

১৮.

Two trains start from the same starting points and move towards the same destination. The first one starts half an hour earlier than the second one. The first one runs at a speed of 90 km/hr while the second one runs at 30 km/hr faster. At what distance from the starting point will the two trains meet?

ক
ক) 150 km
খ
খ) 180 km
গ
গ) 360 km
ঘ
ঘ) 450 km

ব্যাখ্যা

We know,
Distance(D) = Speed(S) × Time(T)
⇒ D = S × T
∴ S = D/T; T = D/S

Since the second train is 30 km/hr faster, it is moving at 120 km/hr
Now, let train A travel T hours before meeting train B.
Time for which train B travels = (T - 1/2) hrs.
This is because it starts half an hour late
Distance travelled is same.

∴ D = D
∴ 90 km/hr × T hrs = 120 km/hr × {T - (1/2} hrs
∴ 90T = 120T - 60
∴ T = 2 hours

Distance travelled by train A = 90 km/hr × 2 hours = 180km.
Thus they meet 180 km from starting point.

১৯.

A train, 800metre 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)?

ক
ক) 440 metre
খ
খ) 260 metre
গ
গ) 500 metre
ঘ
ঘ) 430 metre

ব্যাখ্যা

Let the length of the tunnel = x metre
Then, distance = (800 + x) metre.
Time = 1 minute = 60 seconds.

∴ Speed = 78 km/hr
= 78 × (5/18)
= (65/3) m/s

According to the question,
800 + x = {60 × (65/3)}
⇒ 800 + x = 1300
⇒ x = 500 metre.
Hence, The length of the tunnel is 500 metre.

২০.

Two trains, 130 and 110 meters long, are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass each other completely in 3 seconds. Find the speed of the faster train.

ক
ক) 38 m/sec.
খ
খ) 42 m/sec.
গ
গ) 46 m/sec.
ঘ
ঘ) 50 m/sec.

ব্যাখ্যা

Let the speeds of the faster and slower trains be x m/sec and y m/sec respectively.
Then,
240/(x - y) = 60
⇒ x - y = 4 ........(i)

And, 240/(x + y) = 3
⇒ x + y = 80 ........(ii)

Adding (i) and (ii), we get
2x = 84
⇒ x = 42
Putting x = 42 in (i), we get:
42 - y = 4
⇒ y = 38

Hence, speed of the faster train = 42 m/sec.

২১.

The distance between two stations is 240 km. When it strikes 5 pm in the clock, a train starts from each of these stations and travels towards the other one. They meet at a junction after 12 hrs. One of the trains is slower to the other one by 14km/hr. Find the speed of the slower train.

ক
ক) 3 km/hr
খ
খ) 5 km/hr
গ
গ) 7 km/hr
ঘ
ঘ) 13 km/hr

ব্যাখ্যা

Let the speed of slower train = S km/hr
Speed of faster = (S + 14) km/hr
Trains meet after 12 hours.

Distance travelled by slower train in 12 hrs. = 12S
Distance travelled by faster train in 12 hrs. = 12(S + 14)

The total distance to be travelled between the two stations is given.
So, 12S + 12(S + 14) = 240
2S + 14 = 20
S = 3 km/hr.

Hence, The speed of the slower train is 3 km/hr.

২২.

Train A passes a lamp post in 9 seconds and 700 meter long platform in 30 seconds. How much time will the same train take to cross a platform which is 800 meters long?

ক
ক) 32 seconds
খ
খ) 31 seconds
গ
গ) 33 seconds
ঘ
ঘ) 30 seconds

ব্যাখ্যা

Let the length of the train is x m. and its speed is v. m/s.

Distance = Speed × time [S = V × T]
x = v × 9 .........(i).
(x+700) = v × 30 ........(ii).

Dividing the eqn. (i) by (ii).

x/(x+700)= 3/10.
⇒ 10x=3x + 2100.
⇒ 7x=2100.
⇒ x= 2100/7.
⇒ x= 300. m.

putting x = 300 in eqn. (1).
300 = v × 9
⇒ v = 300/9
⇒ v = 100/3 m/s.

Let the train crosses a 800 m. long platform in t seconds.
(x + 800) = v × t .........(iii) [ S = V × T]
⇒ (300 + 800) = (100/3) × t. [putting x= 300. and v= 100/3.]
⇒ t = (1100×3)/100
⇒ t = 33 seconds.

২৩.

Two trains of lengths 120 m and 90 m are running with speed of 80 km/hr and 55 km/hr respectively towards each other on parallel lines. If they are 90 m apart, after how many seconds will they cross each other?

ক
ক) 5.6 sec.
খ
খ) 7.2 sec.
গ
গ) 8 sec.
ঘ
ঘ) 9 sec.

ব্যাখ্যা

Relative speed
= (80 + 55) km/hr
= 135 km/hr.
= 135 × (5/18) m/sec
= (75/2) m/sec.

Distance covered = (120 + 90 + 90)
= 300 m.

∴ Required time = {300 × (2/75)}
= 8 sec.

২৪.

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

ক
ক) 500 metre
খ
খ) 480 metre
গ
গ) 400 metre
ঘ
ঘ) 360 metre

ব্যাখ্যা

Speed of the first train = 48 km/hr.
Let the length of the first train = 2x metre.

Speed of the second train = 42 km/hr.
Let the length of the second train = x metre.

Distance = (2x + x) = 3x metre.
Time = 12 seconds

Relative speed = 48 + 42 = 90 km/hr.
= 90 × (5/18) = 25 m/s.
3x = 25 × 12
⇒ x = 100 metre.

Length of the first train = 200
Time is taken to cross the platform = 45 seconds.
Speed of first train = 48 km/hr
= 48 × (5/18)
= 40/3 m/s.

Let the length of the platform = y metre.
Distance = 200 + y metre.
⇒ 200 + y = 45 × (40/3)
⇒ 200 + y = 600
⇒ y = 400 metre.

২৫.

If a train stops on the way, its speed is 35 km/hr but if it doesn't, its speed is 40 km/hr. Find the number of minutes the train halts per hour.

ক
ক) 4 minutes
খ
খ) 6 minutes
গ
গ) 7.5 minutes
ঘ
ঘ) 8 minutes

ব্যাখ্যা

The difference in speed due to stopping = Speed without stoppage - Speed with stoppage
∴ Difference = 40-35 = 5km/hr
Thus, in 1-hour train covers 5 km less.

Time taken to cover 4km = 5km/(40 km/hr)
= 1/8 hours.
= (1/8 × 60) minutes.
= 7.5 minutes.

Hence, The train halts 7.5 minutes per hour.

২৬.

Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train is 120 metres, in what time (in seconds) will they cross each other travelling in the opposite direction?

ক
ক) 10
খ
খ) 12
গ
গ) 15
ঘ
ঘ) 20

ব্যাখ্যা

Speed of the first train
= 120/10 m/sec.
= 12 m/sec.

Speed of the second train
= 120/15 m/sec.
= 8 m/sec.

Relative speed = 12 + 8 = 20 m/sec.

∴ Required time
= (120 + 120)/20 sec.
= 240/20 sec.
= 12 sec.

২৭.

What is the speed of a train if it overtakes two persons who are walking in the same direction at the rate of a m/s and (a + 1) m/s and passes them completely in b seconds and (b + 1) seconds respectively?

ক
ক) (a + b) m/s
খ
খ) (a + b + 1) m/s
গ
গ) (2a + 1) m/s
ঘ
ঘ) (2a + 1)/2 m/s

ব্যাখ্যা

Let the length of the train be x metres and its speed be y m/s.
Then,
x/(y - a) = b and x/{y - (a + 1) = (b + 1)
⇒ x = b (y - a) and x = (b + 1)(y - a - 1)
⇒ b (y - a) = (b + 1) (y - a - 1)
⇒ by - ba = by - ba - b + y - a - 1
⇒ y = (a + b + 1).