Time and Speed - Train and Boat

PrepBank · পাতা ৩ / ১৫ · ২০১–৩০০ / ১,৪৩৯

২০১.

Subarna express normally reaches its destination at 60 km/h in 8 hours. Find the speed at which it travels to reduce the time by 3 hours?

ক
96 km/h
খ
106 km/h
গ
90 km/h
ঘ
85 km/h

ব্যাখ্যা

Question: Subarna express normally reaches its destination at 60 km/h in 8 hours. Find the speed at which it travels to reduce the time by 3 hours?

Solution:
Distance to be covered = Speed × Time
= 60 × 8
= 480 km

Time = (8 - 3) hours
= 5 hours

∴ Required Speed = 480/5
= 96 km/h

২০২.

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

ক
300 m
খ
400 m
গ
500 m
ঘ
600 m

ব্যাখ্যা

Question: A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is-

Solution:
relative speed = 48 + 42 kmph
= 90 kmph
= (90 × 1000)/3600 m/s
= 25 m/s

let, length of train travelling at 48 kmph is x m

x + x/2 = 25 × 12 = 300
⇒ 3x = 600
∴ x = 200 m

speed = 48 kmph = (48 × 1000)/3600 = 40/3 m/s

ATQ,
(40/3) × 45 = 200 + length of platform
length of platform = 600 - 200
= 400 m

২০৩.

An airplane flies along the four sides of a square at the speeds of 200, 400, 600 and 800 kmh. Find the average speed of the plane around the field.

ক
ক) 432 km/hr
খ
খ) 375 km/hr
গ
গ) 384 km/h
ঘ
ঘ) 221 km/hr

ব্যাখ্যা

Speed of aeroplane is 200, 400, 600 and 800 km/h respectively
Let the side of side be LCM of (200, 400, 600 and 800) = 2400
Time taken by aeroplane to travel the side at the speed of 200 km/hr
⇒ 2400/200 = 12 hours
Time taken by aeroplane to travel the side at the speed of 400 km/hr
⇒ 2400/400 = 6 hours
Time taken by aeroplane to travel the side at the speed of 600 km/hr
⇒ 2400/600 = 4 hours
Time taken by aeroplane to travel the side at the speed of 800 km/hr
⇒ 2400/800 = 3 hours

Average speed = (Total Distance travelled)/(Total time taken)
∴ Average speed = (4×2400)/25 = 384 km/hr

২০৪.

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-

ক
3 : 1
খ
2 : 1
গ
3 : 2
ঘ
3 : 4

ব্যাখ্যা

Question: 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-

Solution:
Let,
man's rate upstream be = a kmph
Then, his rate downstream = 2a kmph

Now,
(speed in still water) : (Speed of stream)
= {(2a + a)/2 : (2a - a)/2}
= (3a/2) : (a/2)
= 3 : 1

২০৫.

A man rows a certain distance along the stream and against the stream in 1 hour and 1.5 hours respectively. If the velocity of the current is 3 km/hr, what is the speed of the man in still water?

ক
ক) 12 km/hr
খ
খ) 15 km/hr
গ
গ) 18 km/hr
ঘ
ঘ) 13 km/hr

ব্যাখ্যা

Let the speed of the man in still water = x
Given that, speed of the stream = 3 km/h
So, Speed downstream = (x + 3) km/h
and, Speed upstream = (x – 3) km/h
ATQ,
(x + 3) × 1 = (x - 3) × 1.5
Or, x + 3 = 1.5x – 4.5
Or, 0.5x = 7.5
∴ x = 15

২০৬.

A boat covers 800 meters in 600 seconds against the stream and returns downstream in 5 minutes. What is the speed of the boat in still water?

ক
1 m/s
খ
1.5 m/s
গ
2 m/s
ঘ
2.5 m/s

ব্যাখ্যা

Question: A boat covers 800 meters in 600 seconds against the stream and returns downstream in 5 minutes. What is the speed of the boat in still water?

Solution:
Speed in upstream = 800/600 = 8/6 m/s
Speed in downstream = 800/(5 × 60) = 800/300 = 8/3 m/s

Apply formula: Speed in still water = (1/2)(speed downstream + speed upstream)
∴ Speed in still water = (1/2) (8/3 + 8/6)
= (1/2){(16 + 8)/6}
= (1/2)(24/6)
= 24/12
= 2 m/s

২০৭.

A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of total time, to cover the remaining distance in the remaining time, his speed in kmph must be-

ক
10 kmph
খ
12 kmph
গ
15 kmph
ঘ
20 kmph

ব্যাখ্যা

Question: A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of total time, to cover the remaining distance in the remaining time, his speed in kmph must be-

Solution:
Remaining distance = (6 - 3) km
= 3 km

∴ remaining time = (1/3) × 45
= 15 min
= 15/60 hr
= 1/4 hr

∴ Required speed = 3/(1/4) kmph
= 12 kmph

২০৮.

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.

২০৯.

The speed of a train is 220% of the speed of a car. The car covers a distance of 950 km in 19 hours. How much distance will the train cover in 2.5 hours?

ক
190 km
খ
275 km
গ
385 km
ঘ
450 km
ঙ
525 km

ব্যাখ্যা

Question: The speed of a train is 220% of the speed of a car. The car covers a distance of 950 km in 19 hours. How much distance will the train cover in 2.5 hours?

Solution:
Speed of car = 950/19
= 50 km/h

Speed of train = 220% × speed of car
= (220/100) × 50
= 110 km/h

Distance covered by the train = 110 × 2.5
= 110 × (25/10)
= 275 km

২১০.

In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is-

ক
1 hour
খ
2 hours
গ
3 hours
ঘ
4 hours
ঙ
5 hours

ব্যাখ্যা

Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is-

Solution:
Let the duration of the flight be x hours.
Then,
600/x - 600/(x + 1/2) = 200
⇒ 600/x - 1200/(2x + 1) = 200
⇒ 3/x - 6/(2x + 1) = 1
⇒ (6x + 3 - 6x){x(2x + 1)} = 1
⇒ x(2x + 1) = 3
⇒ 2x² + x - 3 = 0
⇒ 2x² + 3x - 2x - 3 = 0
⇒ x(2x + 3) - 1(2x + 3) = 0
⇒ (2x + 3)(x - 1) = 0
∴ x = 1 hr. [neglecting the (- ve) value of x]

২১১.

How long will a 150m long train running at a speed of 60 kmph take to cross a bridge of 300m?

ক
ক) 7 seconds
খ
খ) 13 seconds
গ
গ) 17 seconds
ঘ
ঘ) 20 seconds
ঙ
ঙ) 27 seconds

ব্যাখ্যা

Total Distance = 300 + 150 = 450 m
Speed = 60 kmph = 60×(5/18)=(50/3) m/sec
Distance = Speed×Time
450 =(50/3)×Time
Time = 27 seconds

২১২.

A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr. And the sum of times taken by them is 14 hours. Then A’s speed is equal to -

ক
ক) 3 km/hr
খ
খ) 4 km/hr
গ
গ) 5 km/hr
ঘ
ঘ) 6 km/hr

ব্যাখ্যা

Let,
A's speed = x km/hr.
Then,
B's speed = (7 - x) km/hr.
So,
24/x + 24/(7 - x) = 14
⇒ {24(7 - x) + 24x} = 14x(7 - x)
⇒ 168 - 24x + 24x = 98x - 14x²
⇒ 14x² - 98x + 168 = 0
⇒ x² - 7x + 12 = 0
⇒ x² - 4x - 3x + 12 = 0
⇒ x(x - 4) - 3(x - 4) = 0
⇒ (x - 3) (x - 4) = 0
⇒ x = 3 or x = 4
Since A is faster than B, so A's speed = 4 km/hr and B's speed = 3 km/hr.

২১৩.

Mithila travels the first 4 hours of her journey at a speed of 80 miles/hr and the remaining distance in 6 hours at a speed of 30 miles/hr. What is her average speed in miles/hr?

ক
50 miles/ hr
খ
60 miles hr
গ
75 miles/hr
ঘ
92 miles/hr

ব্যাখ্যা

i.e. Average speed = Total distance / Time
Distance =Time x Speed

Total distance covered by Mithila = Distance covered in first 4 hours + distance covered in next 6 hours
= (80 x 4) + (30 x 6)
= 500 miles / hr

Total time taken to complete the journey = 4 + 6 = 10 hrs

Therefore,
Average speed = Total Distance/Time
= 500 / 10
= 50 miles/hr

২১৪.

In a 200m race, Joy defeats Bishal by 5 seconds. If the speed of Joy is 18 kmph, then the speed of Bishal is-

ক
16 kmph
খ
15 kmph
গ
14.45 kmph
ঘ
15.56 kmph

ব্যাখ্যা

Question: In a 200m race, Joy defeats Bishal by 5 seconds. If the speed of Joy is 18 kmph, then the speed of Bishal is-

Solution:
speed of Joy = 18 kmph = 18/3.6 = 5 mph
time taken by Joy = 200/5 = 40 sec

time taken by Bishal = 40 + 5
= 45 sec
speed of Bishal = 200/45 mph
= 4.44 mph
= 16 kmph

২১৫.

A truck covers a distance of 540 meters in 1 minute where as a bus covers a distance of 56.7 km in 45 minutes. The ratio of their speeds is-

ক
4 : 7
খ
2 : 9
গ
3 : 7
ঘ
5 : 11

ব্যাখ্যা

Question: A truck covers a distance of 540 meters in 1 minute where as a bus covers a distance of 56.7 km in 45 minutes. The ratio of their speeds is-

Solution:
Speed of truck = 540/60 = 9 m/s
Speed of bus = (56.7 × 1000)/(45 × 60) = 21 m/s

∴ Ratio of speed = 9 : 21 = 3 : 7

২১৬.

A train crosses a platform 300 meters long in 50 seconds and another platform 150 meters long in 35 seconds. What is the length of the train?

ক
320 meters
খ
280 meters
গ
200 meters
ঘ
240 meters

ব্যাখ্যা

Question: A train crosses a platform 300 meters long in 50 seconds and another platform 150 meters long in 35 seconds. What is the length of the train?

Solution:
Let the length of the train = x meters

Then,
For the first platform, the distance covered by the train = (x + 300) meters
And,
For the second platform, the distance covered by the train = (x + 150) meters

According to the question,
(x + 300)/50 = (x + 150)/35
⇒ 50(x + 150) = 35(x + 300)
⇒ 50x + 7500 = 35x + 10500
⇒ 50x - 35x = 10500 - 7500
⇒ 15x = 3000
⇒ x = 3000/15
⇒ x = 200

∴ The length of the train is 200 meters

২১৭.

Find the speed of the stream when a boat takes 7 hours to travel 40km downstream at a rate of 12km per hour in still water.

ক
2.63
খ
3.72
গ
5.82
ঘ
4.11

ব্যাখ্যা

Let,
The speed of the stream is x km/hr.
Then,
Downstream Speed = (12 + x) km/hr
Upstream Speed = (12 - x) km/hr
The boat covers, 40 km downstream in 7 hours
Then we have,
[ 40/(12 + x) ] + [ 40/(12 - x) ] = 7
⇒ [{40(12 - x) + 40(12 + x)}/{(12 + x)(12 - x)}]
⇒[40(12 - x) + 40(12 + x)] = 7(144 - x²)
⇒ 480 - 40x + 480 + 40x = 1008 - 7x²
⇒ 960 = 1008 - 7x²
⇒ 7x²= 1008 - 960
⇒ 7x² = 48
⇒ x² = 48/7
⇒ x² = 6.92
⇒ x = 2.63
Hence, the speed of the stream is 2.63 km/hr.

২১৮.

A train takes 20 seconds to cross a pole. It takes 50 seconds to cross the platform. What is the ratio of the length of the platform to that of the train?

ক
2 : 3
খ
2 : 5
গ
5 : 2
ঘ
3 : 2
ঙ
None

ব্যাখ্যা

Question: A train takes 20 seconds to cross a pole. It takes 50 seconds to cross the platform. What is the ratio of the length of the platform to that of the train?

Solution:
Let,
The speed of the train is x m/s

While cross the pole the train travels 20 × x meters = 20x meters, which is the length of the train

While cross the platform the train travels 50 × x meters = 50x meters
∴ Length of the platform 50x - 20x = 30x meters

∴ Length of the platform : Length of the train = 30x : 20x = 30 : 20 = 3 : 2

২১৯.

If a man rows at the rate of 7 kmph in still water and his rate against the current is 4 kmph, then the man's rate along the current is-

ক
ক) 3 kmph
খ
খ) 5 kmph
গ
গ) 8 kmph
ঘ
ঘ) 10 kmph

ব্যাখ্যা

Question: If a man rows at the rate of 7 kmph in still water and his rate against the current is 4 kmph, then the man's rate along the current is-

Solution:
Speed of current = 7 - 4 = 3 km
so, the speed in downstream = 7 + 3 = 10 kmph

২২০.

A woman complete a journey in 8 hours. She travels first half of the journey at the rate of 30 km/hr and second half at the rate of 20 km/hr. Find the total journey in km.

ক
292 km
খ
322 km
গ
192 km
ঘ
300 km
ঙ
None of these

ব্যাখ্যা

Question: A woman complete a journey in 8 hours. She travels first half of the journey at the rate of 30 km/hr and second half at the rate of 20 km/hr. Find the total journey in km.

Solution:
Let, Total distance = x
⇒ {(1/2)x/30} + {(1/2)x}/20 = 8
⇒ (x/30) + (x/20) = 16
⇒ (2x + 3x)/60 = 16
⇒ 5x = 16 × 60
⇒ x = (16 × 60)/5
∴ x = 192

So, the total distance is 192 km.

২২১.

A man reduces his speed from 20 kmph to 18 kmph. So, he takes 10 minutes more than the normal time. What is the distance traveled by him?

ক
ক) 30 km
খ
খ) 25 km
গ
গ) 50 km
ঘ
ঘ) 36 km

ব্যাখ্যা

As the speed decreases from 20 kmph to 18 kmph i.e. 10 % increment in usual time.
10% = 10 min
100% = 100 min.

Now,
Distance traveled by him,
= (100/60) × 18
= 30 km.

২২২.

Rahim and Shafiq are standing at two ends of a room with a width of 30 m. They start walking towards each other along the width of the room with a speed of 2 m/s and 1 m/s respectively. Find the total distance travelled by Rahim when he meets Shafiq for the third time.

ক
ক) 110 m
খ
খ) 112 m
গ
গ) 120 m
ঘ
ঘ) 100 m

ব্যাখ্যা

When Rahim meets Shafiq for the third time,
they together would have covered a Distance of 5d, i.e 5 × 30m = 150 m.

The ratio of Speed of Rahim and Shafiq = 2 : 1,
so the total distance traveled by them will also be in the ratio 2 : 1
as the Time is taken is constant.

So the Distance traveled by Rahim will be (2/3) × 150= 100 m.

২২৩.

A man on tour travels first 60 km at 20 km/hr and the next 60 km at 30 km/hr. The average speed for the first 120 km of the tour is :

ক
20 km/hr
খ
24 km/hr
গ
25 km/hr
ঘ
26 km/hr

ব্যাখ্যা

Question: A man on tour travels first 60 km at 20 km/hr and the next 60 km at 30 km/hr. The average speed for the first 120 km of the tour is :

সমাধান:
প্রথম অংশের জন্য সময় = দূরত্ব/গতিবেগ
= 60 কিমি/20 কিমি/ঘন্টা
= 3 ঘন্টা

দ্বিতীয় অংশের জন্য সময় = দূরত্ব/গতিবেগ
= 60 কিমি/30 কিমি/ঘন্টা
= 2 ঘন্টা

মোট অতিক্রান্ত দূরত্ব = 60 কিমি + 60 কিমি = 120 কিমি
মোট সময় = 3 ঘন্টা + 2 ঘন্টা = 5 ঘন্টা

∴ গড় গতিবেগ = 120 কিমি/5 ঘন্টা
= 24 কিমি/ঘন্টা

২২৪.

A man can reach a certain place in 30 hours .If the reduces his speed by 1/15th, he goes 10 km less in that time. Find his speed.

ক
ক) 10 km/hr.
খ
খ) 8 km/hr.
গ
গ) 6 km/hr.
ঘ
ঘ) 5 km/hr

ব্যাখ্যা

Let’s the speed of man = x km/hr.

According to the question
x × 30 - x × (14/15) × 30 = 10
⇒ 30x - 28x = 10
⇒ 2x = 10
⇒x = 10/2
∴ x = 5

২২৫.

An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 100 minutes, it must travel at a speed of:

ক
300 kmph
খ
360 kmph
গ
600 kmph
ঘ
720 kmph

ব্যাখ্যা

Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 100 minutes, it must travel at a speed of:

Solution:
Total Distance = (240 × 5) = 1200 km.
Time = 100 minutes = 100/60 hr
= 5/3 hr

We know that,
Speed = Distance/Time
∴ Required speed = 1200/(5/3) km/hr
= 720 km/hr.

২২৬.

Two, trains, one from Sylhet to Dhaka and the other from Dhaka to Sylhet, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 25 hours respectively. The ratio of their speeds is-

ক
4 : 5
খ
25 : 16
গ
5 : 4
ঘ
16 : 25

ব্যাখ্যা

Question: Two, trains, one from Sylhet to Dhaka and the other from Dhaka to Sylhet, start simultaneously. After they meet, the trains reach their destinations after 16 hours and 25 hours respectively. The ratio of their speeds is-

Solution:

let, they meet at X, and Train A and B have the speed of p and y respectively.

in the time of t,
A covers = pt distance
B covers = qt distance

after meeting at X point,
A covers the rest part in 16 hours and B in 25 hours.
so,
distance covered by A is = 16p
distance covered by B is = 25q

∴ pt = 25q......(i)
and, qt = 16p.......(ii)

from equations (i) and (ii) we we get,
p/q = 25q/16p
p²/q² = 25/16
p/q = 5/4
p : q = 5 : 4

২২৭.

A bus covers a distance of 2500m in just 1/12 hour. What is the speed in km/h?

ক
ক) 25km/h
খ
খ) 30km/h
গ
গ) 35km/h
ঘ
ঘ) 40km/h

ব্যাখ্যা

Question: A bus covers a distance of 2500m in just 1/12 hour. What is the speed in km/h?

Solution:
here,
distance, D = 2500m = 2.5km
time, T = 1/12 hour

We know,
D = S × T
S = D/T
= 2.5km/(1/12)hour
= 2.5 × 12 km/h
= 30 km/h

২২৮.

A man travels equal distances of his journey at 15, 20 and 30 km/hour respectively. What is his average speed for whole journey?

ক
ক) 10
খ
খ) 12
গ
গ) 16
ঘ
ঘ) 20

ব্যাখ্যা

Required average speed
= (3 × 15 × 20 × 30)/(15 × 20 + 20 × 30 + 30 × 15)
= 20 km/hour
----------------------------------------------------------------
Alternative way:
Distance 30 km, Speed 30 km/h, Time 1 Hour
Distance 30 km, Speed 15 km/h, Time 2 Hours
Distance 30 km, Speed 20 km/h, Time 1 hour & 30 minutes.
Total Distance 90 km, Total Time 4.5 Hours,
Average Speed 90/4.5 km/h = 20 km/h
--------------------------------------------------------------
Alternative way:
Let, equal distances travelled by the man be ’s’.
Time taken to travel first distance, s at 15 kmph = s/15
Time taken to travel second distance, s at 20 kmph = s/20
Tine taken to travel last distance, s at 30 kmph = s/30
Therefore, total time taken by the man = s(1/15 +1/20 +1/30)
Total distance travelled by the man = 3s
Hence, average speed of the man
= 3s / [ s(1/15 +1/20 +1/30) ] =3/(1/15 +1/20 +1/30)
= 20 kmph
---------------------------------------------------------------
Alternative way:
Avg speed formula= 3 ÷ (1/x +1/y +1/z)
Now we have 1/30 +1/20 +1/15
L.C.M. of 20, 30 and15 is 60.
Then (3 + 4 + 8)/60=9/60 = 3/20
From above formula, average speed = 3 ÷ 3/20=20 km/h

২২৯.

A man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?

ক
14 km
খ
16 km
গ
18 km
ঘ
12 km
ঙ
None of these

ব্যাখ্যা

Question: A man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?

Solution:
Let the time in which he travelled on foot = x hr
Then the time in which he travelled on bicycle =(9 - x) hr
distance = speed × time
⇒ 4x + 9(9 - x) = 61
⇒ 4x + 81 - 9x = 61
⇒ 5x = 20
⇒ x = 4

∴ The distance travelled on foot = 4 × 4 = 16 km

২৩০.

The speed of a car increases by 2 km after every one hour. If the distance travelled in the first one hour was 30 km, what was the total distance travelled in 10 hours?

ক
390 km
খ
400 km
গ
405 km
ঘ
415 km

ব্যাখ্যা

Question: The speed of a car increases by 2 km after every one hour. If the distance travelled in the first one hour was 30 km, what was the total distance travelled in 10 hours?

Solution:
Total distance travelled in 10 hours =( 30 + 32 + 34 +...... upto 10 terms)
This is an A.P with first term, a = 30 ,
number of terms, n = 10
d = 2

Required distance = (10/2)[(2 × 30) + {(10 - 1) × 2}] km
= 5 (60 + 18) km
= (5 × 78) km
= 390 km

২৩১.

একজন মোটর সাইকেল চালক একটি নির্দিষ্ট দূরত্ব ৫ ঘণ্টায় অতিক্রম করতে পারে। সে এক-তৃতীয়াংশ দূরত্ব ৬০ কি.মি./ঘণ্টা গতিতে এবং বাকি অংশ ৮০ কি.মি./ ঘণ্টা গতিতে সম্পন্ন করে। মোট দূরত্ব কত?

ক
ক) ৩৬০ কি.মি.
খ
খ) ৩৪০ কি.মি.
গ
গ) ৩২০ কি.মি.
ঘ
ঘ) ৩০০ কি.মি.

ব্যাখ্যা

মনেকরি
মোট দূরত্ব = ক কি.মি.

{(ক/৩)/৬০} + {(২ক/৩)/৮০} = ৫
(ক /১৮০) + (ক/১২০) = ৫
(২ক + ৩ক)/৩৬০ = ৫
৫ক/৩৬০ = ৫
ক /৩৬০ = ১
ক = ৩৬০

মোট দূরত্ব = ৩৬০ কি.মি.

২৩২.

The speed of A and B are in the ratio 3 : 4. A takes 30 minutes more than B to reach a destination. Time in which A reach the destination?

ক
100 minutes
খ
105 minutes
গ
110 minutes
ঘ
115 minutes
ঙ
None of the above

ব্যাখ্যা

Question: The speed of A and B are in the ratio 3 : 4. A takes 30 minutes more than B to reach a destination. Time in which A reach the destination?

Solution:
Ratio of speed = 3 : 4
Ratio of time taken = 4 : 3 (As Speed ∝ 1/Time, When distance remains constant)

Let the time taken by A and B be 4x and 3x hours respectively.

Then,
4x - 3x = 30/60
Or, x = 1/2

Hence, time taken by A = 4x = 4 × (1/2) = 2 hours = 120 minutes

২৩৩.

A boat makes a return journey from point A to point B and back in 5 hours 36 minutes. One way it travels with the stream and on the return it travels against the stream. If the speed of the stream increases by 2 km/hr, the return journey takes 9 hours 20 minutes. What is the speed of the boat in still water? (The distance between A and B is 16 km.)

ক
7 km/hr
খ
8.5 km/hr
গ
9 km/hr
ঘ
6 km/hr

ব্যাখ্যা

Question: A boat makes a return journey from point A to point B and back in 5 hours 36 minutes. One way it travels with the stream and on the return it travels against the stream. If the speed of the stream increases by 2 km/hr, the return journey takes 9 hours 20 minutes. What is the speed of the boat in still water? (The distance between A and B is 16 km.)

Solution:
Let x be speed of u/s
and y be the speed of d/s.

∴ (16/x) + (16/y) = (28/5)
and 16/(y+2) + 16/(x-2) = 28/3

Solving these 2 equations,
we get x = 4km/hr
and y = 10km/hr

∴ speed of boat in still water = (4 + 10)/2 = 7 km/hr.

২৩৪.

An aeroplane covers a certain distance at a speed of 400 kmph in 3 hours. To cover the same distance in 3/2 hours, it must travel at a speed of:

ক
650 kmph
খ
720 kmph
গ
800 kmph
ঘ
1000 kmph
ঙ
none of these

ব্যাখ্যা

Question: An aeroplane covers a certain distance at a speed of 400 kmph in 3 hours. To cover the same distance in 3/2 hours, it must travel at a speed of:

Solution:
দেওয়া আছে, প্রথম ক্ষেত্রে গতিবেগ = 400 kmph এবং সময় = 3 hours

আমরা জানি, দূরত্ব = গতিবেগ × সময়
∴ দূরত্ব = 400 × 3 = 1200 km

আবার, দ্বিতীয় ক্ষেত্রে অতিক্রান্ত দূরত্ব একই থাকবে।
দূরত্ব = 1200 km এবং সময় = 3/2 hours

আমরা জানি, গতিবেগ = দূরত্ব/সময়
= 1200/(3/2)
= (1200 × 2)/3
= 400 × 2
= 800 kmph

∴ উড়োজাহাজটিকে 800 kmph গতিবেগে চলতে হবে।

২৩৫.

The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 Km/hr. At what time do they meet?

ক
10 a.m
খ
10:30 a.m
গ
11 a.m
ঘ
11:30 a.m

ব্যাখ্যা

Question: The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 Km/hr. At what time do they meet?

Solution:
Suppose they meet x hrs after 8 a.m
then,
[Distance moved by first in x hrs] + [Distance moved by second in (x - 1) hrs] = 330.
Therefore, 60x + 75(x - 1) = 330
⇒ 60x + 75x - 75 = 330
⇒ 135x = 405
∴ x = 3

So,they meet at (8 + 3) = 11 a.m.

২৩৬.

In a river flowing at 2 km/hr, a boat travels 32 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.

ক
16 hours
খ
14 hours
গ
10 hours
ঘ
12 hours

ব্যাখ্যা

speed of the boat = 6 km/hr
Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 32 km
Total time taken
= Time taken downstream + Time taken upstream
= 32/8 + 32/4
= 4 + 8
= 12 hours.

২৩৭.

A man completes a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

ক
220 km
খ
224 km
গ
230 km
ঘ
234 km
ঙ
236km

ব্যাখ্যা

(1/2)x/21 + (1/2)x/24 = 10
⇒ x/21 + x/24 = 20
⇒ 15x = 168 x 20
∴ x = 224 km

২৩৮.

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.

২৩৯.

Two trains of equal length are running on parallel lines in the same direction at 50 km/hr and 60 km/hr. The faster train passes the slower train in 72 seconds. The length of each train is:

ক
150 m
খ
120 m
গ
80 m
ঘ
100 m

ব্যাখ্যা

Question: Two trains of equal length are running on parallel lines in the same direction at 50 km/hr and 60 km/hr. The faster train passes the slower train in 72 seconds. The length of each train is:

Solution:
Let the length of each train be x metres.
Then, distance covered = 2x metres.

Relative speed = (60 - 50) km/hr
= 10 km/hr
= (10 × 1000)/3600 m/s
= 25/9 m/s

Now,
2x/72 = 25/9
⇒ 18x = 1800
∴ x = 100

২৪০.

The speed of a boat in still water is 10 km/h. The time it takes to travel downstream is one-third the time it takes to travel upstream. What is the speed of the stream?

ক
3 km/h
খ
5 km/h
গ
6 km/h
ঘ
4 km/h

ব্যাখ্যা

Question: The speed of a boat in still water is 10 km/h. The time it takes to travel downstream is one-third the time it takes to travel upstream. What is the speed of the stream?

Solution:
Let the speed of the current be = x km/h

Then,
Downstream speed = (10 + x) km/h
Upstream speed = (10 − x) km/h

We know, time = distance/speed

According to the question:
distance/(10 + x) = distance/{3 × (10 - x)}
⇒ (10 + x) = 3(10 - x)
⇒ 4x = 20
⇒ x = 5
∴ The speed of the current = 5 km/h

২৪১.

A and B can do a piece of work in 45 and 40 days respectively. They began the work together but A leaves after some days and B finished the remaning work in 23 days. After how many days did A leave?

ক
9 days
খ
10 days
গ
11 days
ঘ
12 days

ব্যাখ্যা

Question: A and B can do a piece of work in 45 and 40 days respectively. They began the work together but A leaves after some days and B finished the remaning work in 23 days. After how many days did A leave?

Solution:
Work done by B in 23 days {(1/40) × 23} = 23/40 part

Remaining work = (1 - 23/40) part
= 17/40 part

(A + B)'s 1 day's work = 1/45 + 1/40 = 17/360 part

Now,
17/360 part has done by (A + B) in 1 day
∴ 1 part has done by (A + B) in 360/17 day
∴ 17/40 part has done by (A + B) in {(360/17)(17/40)} days
= 9 days

২৪২.

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 12 seconds respectively and they cross each other in 24 seconds. The ratio of their speeds is:

ক
3 : 1
খ
4 : 1
গ
3 : 2
ঘ
4 : 3

ব্যাখ্যা

Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 12 seconds respectively and they cross each other in 24 seconds. The ratio of their speeds is:

Solution:
Let,
the speeds of the two trains be x m/sec and y m/sec respectively.

Then,
length of the first train = 27x metres,
and length of the second train = 12y metres.

ATQ,
(27x + 12y)/(x + y) = 24
⇒ 27x + 12y = 24x + 24y
⇒ 27x - 24x = 24y - 12y
⇒ 3x = 12y
⇒ x/y = 12/3
∴ x : y = 4 : 1

২৪৩.

Jisan cycled halfway at 3 km/h and the rest at 6 km/h. What was his average speed for the whole trip?

ক
2 km/h
খ
3 km/h
গ
4 km/h
ঘ
4.5 km/h

ব্যাখ্যা

Question: Jisan cycled halfway at 3 km/h and the rest at 6 km/h. What was his average speed for the whole trip?

Solution:
ধরি,
3 কি.মি./ঘণ্টা বেগে অতিক্রম করে = x কি.মি.
এবং 6 km/h বেগে অতিক্রম করে = x কি.মি.
∴ পথের মোট দূরত্ব = x + x = 2x কি.মি.

যাত্রাপথের অর্ধেক দূরত্বে প্রয়োজনীয় সময় = x/3 ঘণ্টা
বাকি অর্ধেক দূরত্বে প্রয়োজনীয় সময় = x/6 ঘণ্টা

∴ সম্পূর্ণ যাত্রায় গড় গতিবেগ = মোট দূরত্ব/মোট সময়
= 2x/{(x/3) + (x/6)}
= 2x/{(2x + x)/6}
= 2x/(3x/6)
= 2x/(x/2)
= 2x × (2/x)
= 4 কি.মি./ঘণ্টা

২৪৪.

Suppose that a person rows a boat in still water at the speed of 10 km/hr and the water runs at the speed of 4 km/hr. This person travels a certain distance & then returns. If it takes 4 hrs more for him to travel upstream than that of downstream then what will be the distance?

ক
16 km
খ
30 km
গ
42 km
ঘ
70 km

ব্যাখ্যা

If a boat takes time 't' hours more in upstream than to move downstream for the same distance, then the distance is given by,
Distance = [(x²– y²) (t)]/(2y) km

Given parameters are:
Speed of a boat in still water = 10 km/hr
Speed of running water = 4 km/hr
Required time = 4 hrs to travel upstream more than downstream

Therefore, we obtain,
D = 4 x (10²– 4²)/(2 x 4)
= 42 km.

২৪৫.

A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is-

ক
71 km/hr
খ
35.55 km/hr
গ
36 km/hr
ঘ
71.11 km/hr
ঙ
None of these

ব্যাখ্যা

Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is-

Solution:
Total time taken = (160/64 + 160/80)hrs
= (5/2 + 2)
= 9/2 hrs.

∴ Average speed = (320 × (2/9) km.hr
= 71.11 km/hr.

২৪৬.

A certain distance is covered at a certain speed. If half the distance is covered in double the time, the ratio of the two speeds is-

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

ব্যাখ্যা

Question: A certain distance is covered at a certain speed. If half the distance is covered in double the time, the ratio of the two speeds is-

Solution:
Let x km be covered in y hours.
Then, speed = x/y km/hr

In the second case, x/2 km is covered in 2y hours.
∴ New speed = (x/2)/2y km/hr
= x/4y

∴ Ratio of speeds = x/y : x/4y
= 1 : 1/4
= 4 : 1

২৪৭.

An individual is cycling at a speed of 37.5 km per hour. He catches his predecessor who had started earlier in two hours. What is the speed of his predecessor who had started 3 hours earlier?

ক
ক) 8 kmph.
খ
খ) 10 kmph.
গ
গ) 15 kmph.
ঘ
ঘ) 12 kmph.

ব্যাখ্যা

Question: An individual is cycling at a speed of 37.5 km per hour. He catches his predecessor who had started earlier in two hours. What is the speed of his predecessor who had started 3 hours earlier?

Question:
The distance covered in two hour,
= 2 × 37.5= 75 km
Time taken by first individual = (3h + 2h) = 5h

Then, the speed of predecessor,
= 75/5
= 15 kmph.

২৪৮.

The driver of an ambulance sees a school bus 40 m ahead of him after 20 seconds, the school bus is 60 meter behind. If the speed of the ambulance is 30 km/h, what is the speed of the school bus?

ক
ক) 10 kmph
খ
খ) 12 kmph
গ
গ) 15 kmph
ঘ
ঘ) 22 kmph
ঙ
ঙ) 21 kmph

২৪৯.

What is the distance covered by a car traveling at a speed of 40 kmph in 15 minutes?

ক
15 km
খ
30 km
গ
20 km
ঘ
10 km

ব্যাখ্যা

Question: What is the distance covered by a car traveling at a speed of 40 kmph in 15 minutes?

Solution:
converting speed into km/min, we get
40 kmph = 40/60 km/min = 2/3 km/min.

Therefore, distance traveled = 15 × (2/3) = 10 km.

২৫০.

A thief steals a car at 1.30 pm and drive it off 40 km/hr. The theft is discovered at 2 pm and the owner sets off in another car at 50 km/hr he will catch the thief at-

ক
2 : 30 pm
খ
3 pm
গ
3 : 30 pm
ঘ
4 pm

ব্যাখ্যা

Question: A thief steals a car at 1.30 pm and drive it off 40 km/hr. The theft is discovered at 2 pm and the owner sets off in another car at 50 km/hr he will catch the thief at-

Solution:
Distance covered by thief in (2 pm - 1.30 pm) = 1/2 hours

1/2 hours at speed of 40 km/h = 40 × (1/2) = 20 km

Their relative speed in same direction = (50 - 40) km/h
= 10 km/h

ATQ,
20 km, is the distance that has to be covered by owner to catch the thief.

Required time = (20/10) hours
=2 hours

Therefore, he will over take the thief at :
= 2 pm + 2 hours
= 4 pm

২৫১.

A train crossing a station in 30 seconds with a speed of 72kmph. If the length of the station is 300m, what is the size of the train?

ক
200m
খ
250m
গ
350m
ঘ
400m
ঙ
None of the above

ব্যাখ্যা

Question: A train crossing a station in 30 seconds with a speed of 72kmph. If the length of the station is 300m, what is the size of the train?

Solution:
Speed = 72kmph
= (72 × 1000)/3600 mps
= 20 mps

total distance covered by the train is = 20 × 30 = 600m

∴ size of the train is = (600 - 300) = 300m

২৫২.

Two trains start at the same time from Chittagong and Sylhet and proceed towards each other at 80 km/h and 100 km/h, respectively. When they meet, it is found that one train has travelled 80 km more than the other. Find the distance between Chittagong and Sylhet.

ক
720 km
খ
520 km
গ
620 km
ঘ
600 km

ব্যাখ্যা

Question: Two trains start at the same time from Chittagong and Sylhet and proceed towards each other at 80 km/h and 100 km/h, respectively. When they meet, it is found that one train has travelled 80 km more than the other. Find the distance between Chittagong and Sylhet.

Solution:
Let the trains meet after t hours.

ATQ,
(100 × t) = (80 × t) + 80
⇒ 100t - 80t = 80
⇒ 20t = 80
∴ t = 4 hours

∴ Distance between Chittagong and Sylhet = (100 × 4) + (80 × 4)
= 400 + 320
= 720 km

∴ The distance between Chittagong and Sylhet is 720 km.

২৫৩.

Samia travels the first 4 hours of her journey at a speed of 80 miles/hr and the remaining distance in 6 hours at a speed of 30 miles/hr. What is her average speed in miles/hr?

ক
40 miles/hour
খ
50 miles/hour
গ
53 miles/hour
ঘ
60 miles/hour
ঙ
55 miles/hour

ব্যাখ্যা

Average speed = Total distance / Time
Distance =Time x Speed

Total distance covered by Mithila = Distance covered in first 4 hours + distance covered in next 6 hours
= (80 x 4) + (30 x 6)
= 500 miles / hr

Total time taken to complete the journey = 4 + 6 = 10 hrs

Therefore,
Average speed = Total Distance/Time
= 500 / 10
= 50 miles/hr

২৫৪.

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

ক
20 km/hr
খ
30 km/hr
গ
40 km/hr
ঘ
50 km/hr

ব্যাখ্যা

Question: A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Solution:
Given distance = 360 km.
Let the speed of the train be x km/hr.
Speed when increased by 5 km/hr = (x + 5) km/hr

ATQ,
(360/x) - {360/(x + 5)} = 1
⇒ [360x + 1800 - 360x]/x(x + 5) = 1
⇒ 1800/x² + 5x = 1
⇒ x² + 5x = 1800
⇒ x² + 5x - 1800 = 0
⇒ x² + 45x - 40x - 1800 = 0
⇒ x(x + 45) - 40(x + 45) = 0
⇒ (x - 40)(x + 45) =0
∴ x = 40, - 45

The speed of the train is 40 km/hr.

২৫৫.

A student walks from his house at a speed of (5/2) km per hour and reaches his school 6 minutes late. The next day he increases his speed by 1 km per hour and reaches 6 minutes before school time. How far is the school from his house?

ক
5/4 km
খ
7/4 km
গ
9/4 km
ঘ
11/4 km

ব্যাখ্যা

Question: A student walks from his house at a speed of (5/2) km per hour and reaches his school 6 minutes late. The next day he increases his speed by 1 km per hour and reaches 6 minutes before school time. How far is the school from his house?

Solution:
Let, the school is at x kilometer distance , usual time is t km/hr

Now
x/(5/2) = t + (6/60)
⇒ 2x/5 = t + (1/10)
⇒ 4x = 10t + 1
⇒ 4x - 10t = 1
⇒ 28x - 70t = 7 [multiplying by 7]

Again
x/{(5/2) + 1} = t - 6/60
⇒ 2x/7 = t - (1/10)
⇒ 20x = 70t - 7 [multiplying by 70]
⇒ 20x - 70t = - 7

28x - 70t - 20x + 70t = 7 + 7
⇒ 8x = 14
⇒ x = 14/8 = 7/4

The school is 7/4 km far from his house.

২৫৬.

A boat travels 90 km downstream in 3 hours. It can cover the same distance upstream in 5 hours. Find speed of the stream.

ক
ক) 4 km/hr
খ
খ) 5 km/hr
গ
গ) 6 km/hr
ঘ
ঘ) 8 km/hr

ব্যাখ্যা

Question: A boat travels 90 km downstream in 3 hours. It can cover the same distance upstream in 5 hours. Find speed of the stream.

Solution:
স্রোতের অনুকূলে নৌকা ৯০ কিমি যায় ৩ ঘণ্টায়
১ ঘণ্টায় যায় ৯০/৩ কিমি
= ৩০ কিমি

নৌকার বেগ + স্রোতের বেগ = ৩০ কিমি/ঘণ্টা

স্রোতের প্রতিকূলে ৫ ঘণ্টায় যায় ৯০ কিমি
১ ঘণ্টায় যায় ৯০/৫ কিমি
= ১৮ কিমি
নৌকার বেগ - স্রোতের বেগ = ১৮ কিমি/ঘণ্টা

নৌকার বেগ + স্রোতের বেগ - নৌকার বেগ + স্রোতের বেগ = ৩০ - ১৮
⇒ ২ × স্রোতের বেগ = ১২
∴ স্রোতের বেগ = ১২/২
= ৬ কিমি/ঘণ্টা

২৫৭.

A boat running upstream takes 4 hours 24 minutes to cover a certain distance, while it takes 2 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

ক
ক) 7 : 4
খ
খ) 6 : 5
গ
গ) 4 : 3
ঘ
ঘ) 8 : 3

ব্যাখ্যা

Question: A boat running upstream takes 4 hours 24 minutes to cover a certain distance, while it takes 2 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

Solution:
Let
The man's rate upstream be x kmph
The man's rate downstream be y kmph.
Distance covered upstream in 4 hrs 24 min = Distance covered downstream in 2 hrs.
x × (22/5) = y × 2
⇒ (22x)/5 = 2y
∴ y = (22x)/10

∴ Required ratio = (y + x)/2 : (y - x)/2
= (y + x) : ( y - x)
= {(22x)/10 + x} : {(22x)/10 - x}
= 32x/10 : 12x/10
= 32x : 12x
= 32 : 12
= 8 : 3

২৫৮.

In a 600 m race, the speeds of two runners, P and Q are in the ratio 5 : 6. If P is given a start of 150m, by how many meters does P win the race?

ক
50m
খ
80m
গ
120m
ঘ
60m

ব্যাখ্যা

Question: In a 600 m race, the speeds of two runners, P and Q are in the ratio 5 : 6. If P is given a start of 150m, by how many meters does P win the race?

Solution:
Total race length = 600 meters.
P is given a start of 150 meters, so P runs 600 - 150 = 450 meters.

Speed ratio P : Q = 5 : 6.

Let, Q runs = X meter

Therefore,
450/X = 5/6
⇒ X = (6 × 450)/5
∴ X = 540m

Remaining distance for Q = 600 - 540 = 60 meters.
Therefore, P wins by 60 meters.

২৫৯.

A motorist travels to a place 150 km away at in average speed of 50 km and returns at 30 km per hour. His average speed for the whole journey in km per hour is:

ক
ক) 35
খ
খ) 37
গ
গ) 37.5
ঘ
ঘ) 40

ব্যাখ্যা

50 কি.মি. যেতে সময় লাগে = 1 ঘণ্টা
150 কি.মি. যেতে সময় লাগে = 150 /50 = 3 ঘণ্টা

30 কি.মি. ফিরে আসতে সময় লাগে = 1 ঘণ্টা
150 কি.মি. ফিরে আসতে সময় লাগে = 150/30 = 5 ঘণ্টা

গড় বেগ = (150 + 150)/(3 + 5) কি.মি./ঘণ্টা
= 300/8 কি.মি./ঘণ্টা
= 37.5 কি.মি./ঘণ্টা

২৬০.

A father and a son started for a shop at the same time. In one minute, the son moved 20 steps forward and in the same time, the father moved 30 steps forward. In one step the son covered 1 ft. and the father covered 1.5 ft. If the son reached the store 10 minutes after his father, what was the distance of the store in ft?

ক
ক) 280
খ
খ) 240
গ
গ) 360
ঘ
ঘ) 320

ব্যাখ্যা

ধরি,
Distance of store = x feet
Now, Distance covered by son in one minute = 1 × 20
= 20 ft. and
Distance covered by father = 30 × 1.5
= 45 ft.
∴ Time taken by son = x/20 minutes = Time taken by father = x/45 minutes.
∴ x/20 = x/45 + 10
⇒ (x/20 - x/45) = 10
⇒ (9x - 4x)/180 = 10
⇒ 5x = 1800
⇒ x = 1800/5
⇒ x = 360 ft.

২৬১.

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?

ক
ক) 4 hours
খ
খ) 8 hours
গ
গ) 6 hours
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.

২৬২.

Two trains travel in opposite directions at 36 km/hr and 45 km/hr and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is:

ক
240 m
খ
90 m
গ
120 m
ঘ
180 m

ব্যাখ্যা

Question: Two trains travel in opposite directions at 36 km/hr and 45 km/hr and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is:

Solution:
As the trains travel in opposite directions then
Relative speed = (45 + 36)km/hr.
= 81 km/hr.
= (81 × 1000)/3600
= 45/2

The length of the faster train = (45/2) × 8
= 180 m

২৬৩.

A bus trip of 450 miles would have taken 1 hour less if the average speed S for the trip had been greater by 5 miles per hour. What was the average speed S, in miles per hour, for the trip?

ক
40
খ
45
গ
50
ঘ
55

ব্যাখ্যা

Question: A bus trip of 450 miles would have taken 1 hour less if the average speed S for the trip had been greater by 5 miles per hour. What was the average speed S, in miles per hour, for the trip?

Solution:
Average Speed = S
∴ Time reqired in Average Speed = 450/S

Time required in speed S for the trip had been greater by 5 miles per hour = 450/(S + 5)

So, we get:
450/S - 450/(S + 5) = 1
⇒ 450/S = 450/(S + 5) + 1
⇒ 450 = 450S/(S + 5) + S
⇒ 450(S + 5) = 450S + S(S + 5)
⇒ 450S + 2250 = 450S + S² + 5S
⇒ 2250 = S² + 5S
⇒ S² + 5S - 2250 = 0
⇒ (S + 50)(S - 45) = 0
∴ S = - 50, OR S = 45
Since the speed can't be negative, the correct answer must be S = 45

২৬৪.

A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour?

ক
3.6
খ
7.2
গ
8.4
ঘ
10

ব্যাখ্যা

Question: A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour?

Solution:
Speed = 600/(5 × 60) m/sec
= 2 m/sec
= 2 × (18/5) km/hr
= 7.2 km/hr

২৬৫.

A boat goes 15 km downstream in 45 minutes. The speed of stream is 3km/hr. The speed of boat in still water is-

ক
15 km/hr
খ
17 km/hr
গ
12 km/hr
ঘ
23 km/hr

ব্যাখ্যা

Question: A boat goes 15 km downstream in 45 minutes. The speed of stream is 3km/hr. The speed of boat in still water is-

Solution:
স্রোতের প্রতিকূলে 45 মিনিটে যায় 15 কি.মি.
স্রোতের প্রতিকূলে 1 মিনিটে যায় 15/45 কি.মি.
স্রোতের প্রতিকূলে 1 ঘণ্টা বা 60 মিনিটে যায় (15 × 60)/45 কি.মি./ঘণ্টা
= 20 কি.মি./ঘণ্টা

স্রোতের বেগ = 3 কি.মি./ঘণ্টা
স্থির পানিতে নৌকার বেগ = (20 - 3) কি.মি./ঘণ্টা
= 17 কি.মি./ঘণ্টা

২৬৬.

A horse covers a distance of 1500 meters in 1 minute 20 seconds. At what speed the horse is running?

ক
67.2 km/hr
খ
67.7 km/hr
গ
67.5 km/hr
ঘ
67.9 km/hr

ব্যাখ্যা

Question: A horse covers a distance of 1500 meters in 1 minute 20 seconds. At what speed the horse is running?

Solution:
Distance = 1500 meters
Time = 1 minute 20 seconds = 60 + 20 = 80 seconds

So, Required Speed = 1500/80 = 75/4 m/s

We need answer in km/hr:
So, Speed in km/hr = (75/4) × (18/5) = 67.5 km/hr

২৬৭.

From two places, 60 km apart, A and B start towards each other at the same time and meet each other after 6 hours. If A traveled with 2/3 of his speed and B traveled with double of his speed, they would have met after 5 hours. The speed of A is:

ক
4 km/h
খ
5 km/h
গ
6 km/h
ঘ
7 km/h
ঙ
8 km/h

ব্যাখ্যা

Question: From two places, 60 km apart, A and B start towards each other at the same time and meet each other after 6 hours. If A traveled with 2/3 of his speed and B traveled with double of his speed, they would have met after 5 hours. The speed of A is:

Solution:
Let the speed of A = x km/h and that of B = y km/h
ATQ,
(x × 6) + (y × 6) = 60
⇒ 6x + 6y = 60
⇒ 6(x + y) = 60
⇒ x + y = 10 .......... (1)

And, (2x/3) × 5 + (2y × 5) = 60
⇒ (10x/3) + 10y = 60
⇒ (10x + 30y)/3 = 60
⇒ 10x + 30y = 180
⇒ 10(x + 3y) 180
⇒ x + 3y = 18 .......... (2)

From equation (1) × 3 - (2)
3x + 3y = 30
⇒ x + 3y = 18
⇒ 2x = 12
∴ x = 6 km/h

২৬৮.

A train starts from a place A at 8 : 00 a.m. and arrives at another place B at 1 : 30 p.m. on the same day. If the speed of the train is 30 km/hr, then what will be the distance (in km) covered by the train?

ক
165
খ
175
গ
150
ঘ
135

ব্যাখ্যা

Question: A train starts from a place A at 8 : 00 a.m. and arrives at another place B at 1 : 30 p.m. on the same day. If the speed of the train is 30 km/hr, then what will be the distance (in km) covered by the train?

Solution:
সকাল ৮ : ০০ টা থেকে দুপুর ১ : ৩০ টা পর্যন্ত
মোট সময় = ৫ ঘণ্টা ৩০ মিনিট = ৫.৫ ঘণ্টা

∴ ট্রেনের মোট অতিক্রান্ত দূরত্ব = ৩০ × ৫.৫ কিলোমিটার
= ১৬৫ কিলোমিটার

২৬৯.

A 240 m long train passed a pole in 24 seconds. How long will it take to pass a 650 m long platform?

ক
ক) 89 sec
খ
খ) 91 sec
গ
গ) 96 sec
ঘ
ঘ) 99 sec

ব্যাখ্যা

Train’s speed = 240/24 = 10 m/s
The train has to cover = (240 + 650) = 890 m.
∴ Required time = 890/10 = 89 seconds

২৭০.

Two stations A and B are on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 Kmph. Another train starts from B at 8 a.m. and travel towards A at a speed of 25 kmph. If they meet at 10 a.m., what is the distance between two stations A and B?

ক
90 km
খ
95 km
গ
100 km
ঘ
110 km

ব্যাখ্যা

Question: Two stations A and B are on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 Kmph. Another train starts from B at 8 a.m. and travel towards A at a speed of 25 kmph. If they meet at 10 a.m., what is the distance between two stations A and B?

Solution:
train started at 7 a.m. traveled for (10 - 7) = 3 hour
so in 3 hour at 20 kmph, the train travelled (20 × 3) = 60 km

train started at 8 a.m. traveled for (10 - 8) = 2 hour
so in 2 hour at 25 kmph, the train travelled (25 × 2) = 50 km

∴ The distance between two station A and B is = (60 + 50) km
= 110 km

২৭১.

A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is-

ক
5.15 kmph
খ
4.4 kmph
গ
4.25 kmph
ঘ
4.14 kmph

ব্যাখ্যা

Question: A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is-

Solution:

A's speed = 5 × (5/18) m/sec = 25/18 m/sec.

Time taken by A to cover 100 m = 100 × (18/25) sec = 72 sec.
∴ Time taken by B to cover 92 m = (72 + 8) = 80 sec.

B's speed = (92/80) ×(18/5) kmph = 4.14 kmph.

২৭২.

A bus is running at 60 km/hr speed. How far the bus will travel in 3 min. 30 sec.?

ক
5 km
খ
4.5 km
গ
3.5 km
ঘ
4 km

ব্যাখ্যা

Question: A bus is running at 60 km/hr speed. How far the bus will travel in 3 min. 30 sec.?

Solution:
3 min. 30 sec. = 180 + 30 sec. = 210 sec.

In 3600 sec. the bus travels 60 km.
∴ In 210 sec. the bus travels (60 × 210)/3600 km.
= 3.5 km.

২৭৩.

Two cyclists start from P towards M, which is 150 km away, at the same time. The first cyclist moves at 30 km/h while the second cyclist moves at 20 km/h. After reaching M, the first cyclist immediately turns back and meets the second cyclist at L. What is the distance between M and L?

ক
25 km
খ
30 km
গ
35 km
ঘ
40 km

ব্যাখ্যা

Question: Two cyclists start from P towards M, which is 150 km away, at the same time. The first cyclist moves at 30 km/h while the second cyclist moves at 20 km/h. After reaching M, the first cyclist immediately turns back and meets the second cyclist at L. What is the distance between M and L?

Solution:
Speed of first cyclist : Speed of second cyclist :: 30:20 :: 3:2

Let's say the distance from M to La is x km
First cyclist's total distance = 150 + x (to M and back to L)
Second cyclist's distance = 150 - x (from P to L)

As distance is proportional to speed:
(150 + x) : (150 - x) :: 3:2
⇒ 2(150 + x) = 3(150 - x)
⇒ 300 + 2x = 450 - 3x
⇒ 2x + 3x = 450 - 300
⇒ 5x = 150
∴ x = 30
Therefore, L is 30 km away from M.

২৭৪.

A train 300 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 300 m long?

ক
ক) 40 sec
খ
খ) 43 sec
গ
গ) 45 sec
ঘ
ঘ) 48 sec

ব্যাখ্যা

Question: A train 300 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 300 m long?

Solution:
Speed = (45 ×1000)/3600 m/s
= 12.5 m/s

Total distance to be covered = (300 + 300) m = 600 m.

∴ Required time = 600/12.5 = 48 sec

২৭৫.

Pritom travels a distance of 9 km from his house to the school by auto-rickshaw at 18 km/hr and returns on rickshaw at 15 km/hr. Find the average speed for the whole journey.

ক
12 km/hr
খ
16.3 km/hr
গ
19.5 km/hr
ঘ
20.4 km/hr

ব্যাখ্যা

Question: Pritom travels a distance of 9 km from his house to the school by auto-rickshaw at 18 km/hr and returns on rickshaw at 15 km/hr. Find the average speed for the whole journey.

Solution:
total distance = 9 + 9 = 18 km

time taken by auto rickshaw = 9/18 hr
= 1/2 hr

time taken by auto rickshaw = 9/15 hr
= 3/5 hr

total time = 1/2 hr + 3/5 hr
= 11/10 hr

average speed = 18/11/10
= 180/11 km/hr
= 16.3 km/hr

২৭৬.

In a race, the speeds of A and B are in the ratio 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is:

ক
ক) 2 hours
খ
খ) 2.5 hours
গ
গ) 3 hours
ঘ
ঘ) 4 hours

ব্যাখ্যা

Ratio of speeds = 3:4
Distance remaining constant, the ratio of time taken = 4:3
A takes 0.5 hours more than B
Hence time taken by A = 4 times 0.5 = 2 hours

২৭৭.

A motorcyclist completes a certain journey in 5 hours. He covers one-third of the distance at 60 km/hr and the rest at 80km/hr. the length of the trip is -

ক
300 km
খ
240 km
গ
360 km
ঘ
420 km

ব্যাখ্যা

Question: A motorcyclist completes a certain journey in 5 hours. He covers one-third of the distance at 60 km/hr and the rest at 80km/hr. the length of the trip is -

Solution:
Let the total length of the trip be = x km
one-third or x/3 distance covered at 60km/hr.
time = (x/3)/60 hr

Two-thirds of the distance covered at 80km/hr
time = (2x/3)/80 hr

ATQ,
(x/3)/60 + (2x/3)/80 = 5
or, (2x + 3x)/360 = 5
or, 5x/360 = 5
∴ x = 360 km

২৭৮.

Luke drives the first 300 miles of a trip at 60 miles an hour. How fast does he have to drive, in miles per hour, on the final 200 miles of the trip if the total time of the trip is equal to 7 hours?

ক
ক) 100
খ
খ) 110
গ
গ) 115
ঘ
ঘ) 120

ব্যাখ্যা

Let the required speed be x mph
ATQ,
300/60 + 200/x = 7
Or, 200/x = 7 - 5
Or, 200/x = 2
So, x = 100

২৭৯.

The speed of A and B are in the ratio 3 : 5. A takes 30 minutes more than B to reach a destination. Time in which A reaches the destination?

ক
1 hour 30 minutes
খ
1 hour
গ
1 hour 15 minutes
ঘ
2 hour

ব্যাখ্যা

Question: The speed of A and B are in the ratio 3 : 5. A takes 30 minutes more than B to reach a destination. Time in which A reaches the destination?

Solution:
speed ratio = 3 : 5
time ratio = 5 : 3
∴ 5x - 3x = 30
x = 15

time of A = 5 × 15 = 75 minutes
= 1 hour 15 minutes.

২৮০.

Two trains are running in opposite directions. They cross a man standing on a platform in 28 seconds and 10 seconds respectively. They cross each other in 24 seconds. What is the ratio of their speeds?

ক
7 : 5
খ
7 : 2
গ
3 : 5
ঘ
5 : 7

ব্যাখ্যা

Question: Two trains are running in opposite directions. They cross a man standing on a platform in 28 seconds and 10 seconds respectively. They cross each other in 24 seconds. What is the ratio of their speeds?

Solution:
Given that,
Train one crosses a man in 28 seconds
Train two crosses the man in 10 seconds
They both cross each other in 24 seconds

We know,
Time = Distance/speed
As the trains travel in opposite directions, the speed of the trains added

Now,
Let the speed of the first train & second train be x m/s and y m/s respectively.
Length of the first train is 28x metres
Length of the second train is 10y meters

According to the question,
⇒ 24 = (28x + 10y)/(x + y)
⇒ 24x + 24y = 28x + 10y
⇒ 14y = 4x
⇒ x/y = 7/2

∴ The ratio of the speed of the train is 7 : 2

২৮১.

The distance between two places A and B is 570 km. A train starts from A at 50 km/h at 6 am and another starts from B at 80 km/h at 7 am towards each other. At what time will they meet?

ক
9 am
খ
10 am
গ
11 am
ঘ
12 am

ব্যাখ্যা

Question: The distance between two places A and B is 570 km. A train starts from A at 50 km/h at 6 am and another starts from B at 80 km/h at 7 am towards each other. At what time will they meet?

Solution:
Let the two trains meet at a distance d km from place A.
Time required by the train starting from A to cover p = p/50 hr
Time taken by the other train starting from B to cover (570 - p) km = (570 - p)/80

But the first train has started 1 hr early. So, it has traveled 50 km in this 1 hr.
Therefore,
(p/50) - 1= (570 - p)/80
⇒ (p - 50)/50 = (570 - p)/80
⇒ 28500 - 50p = 80p - 4000
⇒ 130p = 32500
∴ p = 250

So, they will meet at a distance of 250 km from Place A.
So the time at which they will meet will be (250/50) = 5 hrs [after 6 am]
Hence, they will meet at 11 am.

২৮২.

A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?

ক
4.95 kmph
খ
5 kmph
গ
4.75 kmph
ঘ
4.65 kmph

ব্যাখ্যা

Speed downstream = 22/4 = 5.5 kmph
Speed upstream = 22/5 = 4.4 kmph
Speed of the boat in still water = (5.5 + 4.4)/2
= 4.95 kmph.

২৮৩.

A man complete a journey in 10 hours. He travels first half of the journey at the rate of 16 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

ক
ক) 148 km
খ
খ) 192km
গ
গ) 184 km
ঘ
ঘ) 232 km

ব্যাখ্যা

Let
The total journey x km
Now
{(1/2)x/16} + {(1/2)x/24} = 10
(x/16) + (x/24) = 20
(3x + 2x)/48 = 20
5x/48 = 20
x = (20 × 48)/5
x = 192km

২৮৪.

Two buses start from a bus terminal with a speed of 20 km/h at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at interval of 8 minutes?

ক
ক) 3 km/h
খ
খ) 4 km/h
গ
গ) 5 km/h
ঘ
ঘ) 7 km/h

ব্যাখ্যা

Let Speed of the man is x kmph.
Distance covered in 10 minutes at 20 kmph = distance covered in 8 minutes at (20 + x) kmph.
Or, 20×(10/60) = 8/(60(20 + x))
Or, 200 = 160 + 8x
Or, 8x = 40
Hence, x = 5kmph.

২৮৫.

Speed of a boat in standing water is 18 kmph and the speed of the stream is 3 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is-

ক
12 hour
খ
18 hour
গ
20 hour
ঘ
8 hour

ব্যাখ্যা

Question: Speed of a boat in standing water is 18 kmph and the speed of the stream is 3 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is-

Solution:
Given,
Speed of a boat in standing water = 18 kmph
The speed of the stream = 3 kmph

∴ Speed upstream = (18 - 3) kmph
= 15 kmph.

∴ Speed downstream = (18 + 3) kmph
= 21 kmph.

So, Total time taken = (105/15 ) + (105/21) hours
= (7 + 5) hours
= 12 hour

২৮৬.

Speed of the boat and current are 12 and 4 km/h respectively. How much time will it take for the boat to travel 64 km downstream and then return the same distance upstream?

ক
12 hours
খ
10 hours
গ
8 hours
ঘ
16 hours

ব্যাখ্যা

Question: Speed of the boat and current are 12 and 4 km/h respectively. How much time will it take for the boat to travel 64 km downstream and then return the same distance upstream?

Solution:
We know,
Effective speed with the current = Actual speed + speed of stream
= (12 + 4) km/h
= 16 km/h

∴ Time taken to cover 64 km = (64 ÷ 16) hours
= 4 hours

Effective speed against the current = Actual speed - speed of stream
= (12 - 4) km/h
= 8 km/h

∴ Time taken to return 64 km = (64 ÷ 8) hours
= 8 hours

∴ Total time taken = (4 + 8) hours
= 12 hours

২৮৭.

Two trains of equal length travelling in opposite directions at 72 km/h and 108 km/h cross each other in 10 seconds. In how much time (in seconds) does the slower train cross a platform of length 350 m?

ক
15 sec
খ
20 sec
গ
40 sec
ঘ
30 sec
ঙ
None of these

ব্যাখ্যা

Question: Two trains of equal length travelling in opposite directions at 72 km/h and 108 km/h cross each other in 10 seconds. In how much time (in seconds) does the slower train cross a platform of length 350 m?

Solution:
Given that,
Speed of Train₁ = 72km/h
Speed of Train₂ = 108km/h
Time taken to cross each other = 10sec

Now,
Relative speed = 72 + 108 = 180 km/hr
= (180) × (5/18) ;[1 km/h = (5/18)m/s]
= 50 m/s

Since both trains are of equal length and cross each other in 10 seconds with relative speed, we get,
∴ Distance = 2x (because both trains together cover each other’s lengths)
∴ Time = distance/speed
⇒ 10 = 2x/50
⇒ x = 250 m
So, length of the first train = 250 meters.

Therefore, the time taken to cross the platform by the first train,
⇒ t = (250 + 350)/[72 × (5/18)]
∴ t = 600/20 = 30 sec.

The time taken to cross the platform is 30 sec.

২৮৮.

Fahim is travelling to City B. He calculated that if he travels at 20 km/h, he will reach there at 3 : 00 p.m., but if he travels at 30 km/h, he will reach there at 1 : 00 p.m. At what speed must he travel to reach City B exactly at 2 : 00 p.m.?

ক
20 km/h
খ
24 km/h
গ
30 km/h
ঘ
18 km/h

ব্যাখ্যা

Question: Fahim is travelling to City B. He calculated that if he travels at 20 km/h, he will reach there at 3 : 00 p.m., but if he travels at 30 km/h, he will reach there at 1 : 00 p.m. At what speed must he travel to reach City B exactly at 2 : 00 p.m.?

সমাধান:
ধরি,
ফাহিমের অতিক্রান্ত মোট দূরত্ব হলো x কিমি।

20 কিমি/ঘন্টা গতিতে এবং 30 কিমি/ঘন্টা গতিতে পৌঁছানোর সময়ের পার্থক্য = 3 : 00 p.m. - 1 : 00 p.m. = 2 ঘন্টা।

প্রশ্নমতে,
x/20 - x/30 = 2
⇒ (3x - 2x)/60 = 2
⇒ x/60 = 2
⇒ x = 120 কিমি।

20 কিমি/ঘন্টা গতিতে 120 কিমি যেতে সময় লাগে = 120/20 = 6 ঘন্টা।

যেহেতু এই গতিতে সে 3 : 00 p.m. এ পৌঁছায়, তাই যাত্রা শুরুর সময় ছিল:
3 : 00 p.m. - 6 ঘন্টা = 9 : 00 a.m.

9:00 a.m. এ শুরু করে 2:00 p.m. এ পৌঁছানোর জন্য প্রয়োজনীয় সময় = 5 ঘন্টা।

∴ প্রয়োজনীয় গতিবেগ = দূরত্ব/প্রয়োজনীয় সময়
= 120 কিমি 5 ঘন্টা
= 24 কিমি/ঘন্টা।
∴ ফাহিমকে গড়ে 24 কিমি/ঘন্টা গতিতে যেতে হবে।

২৮৯.

A train travels between X and Y in 3 hours. When the speed of train is increased by 6 km/hr, then it covers the same distance in 2 hours. What is the original speed of train?

ক
12 km/hr
খ
18 km/hr
গ
24 km/hr
ঘ
30 km/hr

ব্যাখ্যা

Question: A train travels between X and Y in 3 hours. When the speed of train is increased by 6 km/hr, then it covers the same distance in 2 hours. What is the original speed of train?

Solution:
Let the original speed of the train be a km/hr.
The distance between X and Y is the same in both cases.

Now, given that,
Speed = a km/hr
Time = 3 hours
∴ Distance = a × 3 = 3a km

And,
Speed = (a + 6) km/hr
Time = 2 hours
∴ Distance = (a + 6) × 2 = 2(a + 6) km

Since distance is the same. Then we get,
⇒ 3a = 2(a + 6)
⇒ 3a = 2a + 12
⇒ 3a - 2a = 12
∴ a = 12

So the original speed of the train is 12 km/hr

২৯০.

A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.

ক
8 km/h
খ
10 km/h
গ
6 km/h
ঘ
7 km/h

ব্যাখ্যা

Question: A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.

Solution:
Let,
Upstream speed = U km/h
Downstream speed = D km/h

Then we get speed of boat = (U + D)/2

Now,
According to the question,
20/U + 44/D = 8 ....… (i)
15/U + 22/D = 5 ....… (ii)

Now, multiply by 2 the equation (ii) then subtract from equation (i) we get
20/U + 44/D = 8
30/U + 44/D = 10
⇒ - 10/U = - 2
⇒ 2U = 10
⇒ U = 10/2 = 5
∴ U = 5 km/hr

Putting the value in equation (i), we get
20/5 + 44/D = 8
⇒ 44/D = 8 - 4
⇒ 4D = 44
⇒ D = 44/4
∴ D = 11

So, the speed of boat = (U + D)/2 = (5 + 11)/2 = 8 km/hr

So the speed of the boat in still water is 8 km/h.

২৯১.

Two trains of equals length, running in opposite direction, pass a pole in 48 and 24 seconds. The trains will cross each other in-

ক
32 sec
খ
34 sec
গ
36 sec
ঘ
40 sec

ব্যাখ্যা

Question: Two trains of equals length, running in opposite direction, pass a pole in 48 and 24 seconds. The trains will cross each other in-

Solution:
Let,
the length of both train be = a meters
Speed of the first train = (a/48) m/s
and speed of the second train = (a/24) m/s

When running in opposite directions, relative speed = (a/48) + (a/24)
= (a + 2a)/48
= 3a/48
= a/16

Now,
to cross each other, distance to be covered = (a + a) = 2a meters

∴ the two train will cross each other = (2a)/(a/16)
= 32 sec

২৯২.

Speed of motorboat in still water is 35 kmph. If the motorboat travels 100 km along the stream in 2 hour 30 min, then the time taken by it to cover the same distance against the stream is-

ক
2 hour 20 min
খ
3 hour 20 min
গ
4 hour 20 min
ঘ
5 hour 20 min

ব্যাখ্যা

Question: Speed of motorboat in still water is 35 kmph. If the motorboat travels 100 km along the stream in 2 hour 30 min, then the time taken by it to cover the same distance against the stream is-

Solution:
The speed of the motorboat in still water is 35 km/hr.
let the speed of the stream = x km/hr
Downstream speed = Distance/time
= 100/2.5
= 40 km/hr

Speed of stream = 35 + x = 40
∴ x = 5 km/hr

Upstream speed = 35 - 5 = 30 km/hr
Time taken in upstream = 100/30 = 3 hour 20 min

২৯৩.

A person crosses a 900 m long street in 5 minutes. What is his speed in km per hour?

ক
ক) 12.8 km/hr.
খ
খ) 9.8 km/hr.
গ
গ) 10.8 km/hr.
ঘ
ঘ) 6.8 km/hr.

ব্যাখ্যা

Speed = 900/(5× 60) m/sec
= 3 m/sec
= (3 × 18)/5 km/hr.
= 10.8 km/hr.

২৯৪.

Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?

ক
6 km/hr, 7 km/hr
খ
8 km/hr, 5 km/hr
গ
8 km/hr, 7 km/hr
ঘ
8 km/hr, 6 km/hr

ব্যাখ্যা

Question: Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?

Solution:
Let the speed of the second lady be x km/hr
Then, speed of first lady = (x + 2) km/hr

ATQ,
24/x - 24/(x + 2) = 1
⇒ x(x + 2) = 48
⇒ x² + 2x - 48 = 0
⇒ x² + 8x - 6x - 48 = 0
⇒ x(x + 8) - 6(x + 8) = 0
⇒ (x + 8)(x - 6) = 0
⇒ x = 6

Hence, speed of first lady = 8 km/hr
The speed of the second lady = 6 km/hr

২৯৫.

The speed of a boat in still water is 9 km/h. The time it takes to travel downstream is half the time it takes to travel upstream. What is the speed of the stream?

ক
3 km/h
খ
2.5 km/h
গ
4 km/h
ঘ
3.5 km/h

ব্যাখ্যা

Question: The speed of a boat in still water is 9 km/h. The time it takes to travel downstream is half the time it takes to travel upstream. What is the speed of the stream?

Solution:
Let the speed of the current be = x km/h

Then,
Downstream speed = (9 + x) km/h
Upstream speed = (9 - x) km/h

According to the question:
(9 + x) = 2(9 - x)
⇒ 9 + x = 18 - 2x
⇒ 2x + x = 18 - 9
⇒ 3x = 9
⇒ x = 9/3
⇒ x = 3

∴ Speed of the stream = 3 km/h

২৯৬.

A train 300 metres long is running at a speed of 90 km/hr. How many seconds will it take cross a 200 metres long train running in the same direction at a speed of 60 km/hr?

ক
48 s
খ
60 s
গ
72 s
ঘ
90 s

ব্যাখ্যা

Question: A train 300 metres long is running at a speed of 90 km/hr. How many seconds will it take cross a 200 metres long train running in the same direction at a speed of 60 km/hr?

Solution:
Length of 1st train 300 metres
Length of 2nd train 200 metres

∴ Total distance to cross each other = 300 + 200 metres
= 500 metres

Relative speed for travelling same direction = 90 - 60 km/hr
= 30 km/hr
= (30 × 1000)/3600 m/s
= 300/36 m/s

Required time to cross = 500/(300/36) s
= (500 × 36)/300 s
= 60 s

২৯৭.

A car covers a distance of 450 m in 1 minute whereas a train covers 69 km in 45 minutes. Find the difference of their speeds.

ক
ক) 45 km/hr
খ
খ) 55 km/hr
গ
গ) 65 km/hr
ঘ
ঘ) 75 km/hr

ব্যাখ্যা

Question: A car covers a distance of 450 m in 1 minute whereas a train covers 69 km in 45 minutes. Find the difference of their speeds.
Solution:
Speed of car = Distance covered/Time taken = 450/60 m/sec = 15/2
= 15/2 × 3600/1000 km/hr
= 27 km/hr

Distance covered by train = 69 km

Time taken = 45 min = 45/60 hr = 3/4 hr

Therefore, speed of trains = 69/(3/4) km/hr
= 69/1 × 4/3 km/hr
= 92 km/hr

∴ the difference of their speeds = 92 - 27 km/hr
= 65 km/hr

২৯৮.

A man can row 12 km/h in still water. He finds that it takes him twice as long to row upstream as to row downstream. What is the speed of the stream?

ক
2 km/h
খ
3 km/h
গ
4 km/h
ঘ
5 km/h

ব্যাখ্যা

Question: A man can row 12 km/h in still water. He finds that it takes him twice as long to row upstream as to row downstream. What is the speed of the stream?

Solution:
Speed in still water = 12 km/h
Speed of the stream = x km/h

Let the distance travelled is = D km
Time taken upstream = 2 × (Time taken downstream)
D/(12-x) = 2 × {D/(12+x)}
⇒ 1/(12-x) = 2/(12+x)
⇒ 12 + x = 24 - 2x
⇒ 3x = 12
∴ x = 4

So, Speed of the stream = 4 km/h

২৯৯.

Two trains of equal length are running on parallel lines in different direction at 40 km/h and 32 km/h. The faster train passes the slower train in 36 seconds. The length of each train is-

ক
380 meters
খ
370 meters
গ
350 meters
ঘ
360 meters

ব্যাখ্যা

Question: Two trains of equal length are running on parallel lines in different direction at 40 km/h and 32 km/h. The faster train passes the slower train in 36 seconds. The length of each train is-

Solution:
Let
The length of each train = x metres.
Then, distance covered = 2x metres.
Relative speed = (40 + 32)km/hr
= 72 km/h
= 72 × (5/18) m/sec
= 20 m/sec

ATQ,
2x = 20 × 36
⇒ 2x = 720
∴ x = 360

৩০০.

The speed of a boat in still water is 25 kmph. If it can travel 10 km upstream in 1 hr, what time it would take to travel the same distance downstream?

ক
ক) 40 minutes
খ
খ) 22 minutes
গ
গ) 15 minutes
ঘ
ঘ) 30 minutes

ব্যাখ্যা

Speed of boat in still water = 25 km/hr
Speed upstream
= 10/1
= 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 hours
= (10×60)/40
= 15 minutes