Time and Speed - Train and Boat

PrepBank · পাতা ১০ / ১৫ · ৯০১–১,০০০ / ১,৪৩৯

৯০১.

A machine wheel has a circumference of 50 cm and completes 24 rotations in 4 seconds. What is the speed of the wheel in kilometers per hour (km/h)?

ক
25 km/h
খ
10 km/h
গ
10.8 km/h
ঘ
4.5 km/h

ব্যাখ্যা

Question: A machine wheel has a circumference of 50 cm and completes 24 rotations in 4 seconds. What is the speed of the wheel in kilometers per hour (km/h)?

Solution:
Total distance covered = (50 × 24) cm
= 1200 cm
= (1200 ÷ 100) m
= 12 m

We know,
Speed = (Total distance ÷ Time)
= (12 ÷ 4) m/sec
= 3 m/sec

Converting into km/h,
= 3 × (18/5) km/h
= 10.8 km/h

∴ The speed of the wheel is 10.8 km/h.

৯০২.

Walking 3/4 of his normal speed, Rabi is 16 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and office.

ক
48 minutes
খ
36 minutes
গ
56 minutes
ঘ
32 minutes

ব্যাখ্যা

Question: Walking 3/4 of his normal speed, Rabi is 16 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and office.

Solution:
Let,
Total time = x minutes
So, when it is late then required time = x + 16
If actual speed = d metre/min
Then reduced speed = (3d/4) metre/min

ATQ,
dx = 3d(x + 16)/4
⇒ dx = (3dx + 48d)/4
⇒ 4dx = 3dx + 48d
⇒ 4dx - 3dx = 48d
⇒ dx = 48d
∴ x = 48

∴ Total time = 48 minutes

৯০৩.

A 1200 m long train crosses a tree in 120 sec, how much time will it take to pass a platform 600 m long?

ক
ক) 180 sec.
খ
খ) 150 sec.
গ
গ) 160 sec.
ঘ
ঘ) 140 sec.

ব্যাখ্যা

Here
Length of a train is 1200m
Train took 120 sec to cross a tree
Length of a platform is 600m

Speed of the train = 1200/120 = 10 m/sec
Total distance = 1200 +600 = 1800 m

Time = distance/speed
= 1800/10 = 180 sec

∴ Time required to cross a platform is 180 sec.

৯০৪.

A train covers half of his journey at 60 km/h and the remaining half at 40 km/h. It's average speed is-

ক
48 km/h
খ
52 km/h
গ
45 km/h
ঘ
60 km/h

ব্যাখ্যা

Question: A train covers half of his journey at 60 km/h and the remaining half at 40 km/h. It's average speed is-

Solution:
let,
The total distance is 2x
First x distance is covered in 60 km/h
∴ time = x/60 h

Second x distance is covered in 40 km/h
∴ time = x/40 h

∴ Average Speed = Total distance ÷ Total time
= 2x ÷ {(x/60) + (x/40)}
= 2x ÷ (5x/120)
= 2x ÷ (x/24)
= 48

৯০৫.

A man can row at 15 kmph in still water. If the velocity of current is 3 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

ক
ক) 3.6 km
খ
খ) 4.5 km
গ
গ) 7.2 km
ঘ
ঘ) 6.2 km

ব্যাখ্যা

Question: A man can row at 15 kmph in still water. If the velocity of current is 3 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

Solution:
Speed downstream = (15 + 3) kmph = 18 kmph
Speed upstream = (15 - 3) kmph = 12 kmph
Let the required distance be x km
Then,
(x/18) + (x/12) = 1
(2x + 3x)/36 = 1
5x/36 = 1
5x = 36
x = 36/5
x = 7.2 km

৯০৬.

Jahid ran a 2 mile race at an average speed of 8 miles per hour. If Alam ran the same race at an average speed of 6 miles per hour, how many minutes longer than Jahid did Alam take to complete the race?

ক
5 minutes
খ
8 minutes
গ
15 minutes
ঘ
20 minutes
ঙ
None

ব্যাখ্যা

Question: Jahid ran a 2 mile race at an average speed of 8 miles per hour. If Alam ran the same race at an average speed of 6 miles per hour, how many minutes longer than Jahid did Alam take to complete the race?

Solution:
We know,
Time = Distance ÷ Speed

Jahid takes,
2 = Time × 8
⇒ Time = 1/4 hours
∴ Time = 15 minutes

Alam Takes,
2 = Time × 6
⇒ Time = 1/3 hours
∴ Time = 20 minutes

Difference = (20 - 15) = 5 minutes

৯০৭.

A man rows to a place 30 km distant and comes back in 8 hours. He finds that he can row 5 km with the stream in the same time as 3 km against the stream. The rate of the stream is:

ক
2 km/hr
খ
1 km/hr
গ
3.5 km/hr
ঘ
4 km/hr

ব্যাখ্যা

Question: A man rows to a place 30 km distant and comes back in 8 hours. He finds that he can row 5 km with the stream in the same time as 3 km against the stream. The rate of the stream is:

সমাধান:
ধরি,
লোকটি স্রোতের অনুকূলে 5 কিমি এবং স্রোতের প্রতিকূলে 3 কিমি যেতে x ঘন্টা সময় নেয়।

∴ স্রোতের অনুকূলে গতিবেগ = 5/x কিমি/ঘন্টা।
স্রোতের প্রতিকূলে গতিবেগ = 3/x কিমি/ঘন্টা।

এখন,
মোট সময় = স্রোতের অনুকূলে যাওয়ার সময় + স্রোতের প্রতিকূলে আসার সময়
⇒ 8 = {30/(5/x)} + {30/(3/x)} [সময় = দূরত্ব/বেগ]
⇒ 8 = (30x/5) + (30x/3)
⇒ 8 = 6x + 10x
⇒ 8 = 16x
⇒ x = 8/16
⇒ x = 1/2

তাহলে, স্রোতের অনুকূলে গতিবেগ = 5/(1/2) = 10 কিমি/ঘন্টা।
স্রোতের প্রতিকূলে গতিবেগ = 3/(1/2) = 6 কিমি/ঘন্টা।

স্রোতের গতিবেগ = (স্রোতের অনুকূলে গতিবেগ - স্রোতের প্রতিকূলে গতিবেগ)/2
= (10 - 6)/2 কিমি/ঘন্টা
= 4/2 কিমি/ঘন্টা
= 2 কিমি/ঘন্টা

৯০৮.

A car covers four successive 7km distance at speeds of 10km/hr, 20 km/hr, 30 km/hr and 60km/hr respectively. Its average speed over this distance is:

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

ব্যাখ্যা

মোট অতিক্রম করে = 4 × 7 = 28 km
মোট সময় = (7/10) + (7/20) + (7/30) + (7/60)
= 7{(6 + 3 + 2 + 1)/60}
= 7/5

গড় গতিবেগ = 28 × (5/7) = 20 kmph

৯০৯.

In a 120m race, Kamal defeats Jamal by 6 seconds. If the speed of Kamal is 18 kmph, then the speed of Jamal is:

ক
ক) 12.4kmph
খ
খ) 11.4kmph
গ
গ) 10.4kmph
ঘ
ঘ) 14.4 kmph

ব্যাখ্যা

Question: In a 120m race, Kamal defeats Jamal by 6 seconds. If the speed of Kamal is 18 kmph, then the speed of Jamal is:

Solution:
Time taken by Kamal = 120/{18 × (5/18)}
= 24 seconds

Time taken by Jamal = 24 + 6 = 30 second

Jamal's speed=120/30
= 4 m/s
= (4 × 18)/5 kmph
=14.4 kmph

৯১০.

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

ক
5 km/hr
খ
4 km/hr
গ
4.5 km/hr
ঘ
5.6 km/hr

ব্যাখ্যা

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

Solution:
Let, A's speed be = x km/hr
B's speed is = (7 - x) km/hr

ATQ,
24/x + 24/(7 - x) = 14
or, {24(7 - x) + 24x}/{x(7 - x) = 14
or, 24(7 - x) + 24x = 14x(7 - x)
or, 14x² - 98x + 168 = 0
or, x² - 7x + 12 = 0
or, (x - 3)(x - 4) = 0
∴ x = 3 or, x = 4

as A's speed is greater than B.
so, x = 4

৯১১.

A man travels the distance of his journey 3/4 by bus, 1/6 by rickshaw and remaining 2 km on foot. The total distance travelled by the man is:

ক
ক) 24 km
খ
খ) 20 km
গ
গ) 18 km
ঘ
ঘ) 12 km

ব্যাখ্যা

Question: A man travels the distance of his journey 3/4 by bus, 1/6 by rickshaw and remaining 2 km on foot. The total distance travelled by the man is:

Solution:
Let the man travels 1 unit distance
So, remaining distance
= 1 - (1/6 + 3/4)
= 1 - 22/24
=1/12

∵ 1/12 unit = 2 km
So, 1 unit = 24 km.

৯১২.

A train 800 meters long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute , then the length of the tunnel (in metres) is :

ক
480 meters
খ
500 meters
গ
530 meters
ঘ
620 meters

ব্যাখ্যা

Let the length of the tunnel be 'x' meters
Time = (Length of train + Length of tunnel) / speed
Speed = 78 km/h
= 78 × 1000 meter/(60 × 60 sec)
= 78 × 5 / 18
= 65/3 m/sec
Therefore, 60 = (800 + x) / (65/3)
or, 60 × 65 = 2400 + 3x
∴ x = (3900 - 2400) / 3
= 500 meters

৯১৩.

A policeman sighted a robber from a distance of 300 m. The robber also noticed the policeman and started running at 8 km/hr. The policeman also started running after him at the speed of 10 km/hr. Find the distance that the robber would run before being caught.

ক
2.3 km
খ
1.2 km
গ
1.5 km
ঘ
0.5 km
ঙ
None of these

ব্যাখ্যা

Question: A policeman sighted a robber from a distance of 300 m. The robber also noticed the policeman and started running at 8 km/hr. The policeman also started running after him at the speed of 10 km/hr. Find the distance that the robber would run before being caught.

Solution:
Since both are running in the same direction, relative speed = 10 - 8 = 2 km/hr
Now, to catch the robber if he were stagnant, the policeman would have to run 300 m. But since both are moving, the policeman needs to finish off this separation of 300 m.
= 300 m (or 0.3 km)is to be covered at the relative speed of 2 km/hr.

∴ Time taken = 0.3/2 = 0.15 hours

Therefore, distance run by robber before being caught = 8 × 0.15 = 1.2 km

৯১৪.

Two trains of equal length are running on parallel lines in the same direction at 46 km and 36 km per hour. The faster train passes the slower train in 36 seconds. The length of each train is-

ক
50 m
খ
60m
গ
70 m
ঘ
75 m

ব্যাখ্যা

Question: Two trains of equal length are running on parallel lines in the same direction at 46 km and 36 km per hour. The faster train passes the slower train in 36 seconds. The length of each train is-

Solution:
To cross each other, two trains have to cover a distance equal to the sum of the lengths of the train.
Let the length of the trains be = a m each.

So the distance to be covered = 2a
Now the trains are running int he same direction.
∴ Their relative speed = (46 - 36) km/hr.
= 10km/hr. = 10 × (5/18) km/hr. = (25/9) m/sec.

So, the time taken by the trains to cove 2a m distance
= 2a ÷ (25/9) sec

∴ By the given conditions,
2a ÷ (25/9) = 36
⇒ 2a × (9/25) = 36
⇒ 2a = (36 × 25)/9
⇒ 2a = 100
∴ a = 50

So, the length of each train = 50 m.

৯১৫.

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

ক
ক) 20
খ
খ) 28
গ
গ) 42
ঘ
ঘ) 36
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

৯১৬.

A speed of 14 meters per second is the same as -

ক
ক) 50 km/hr
খ
খ) 46.6 km/hr
গ
গ) 28 km/hr
ঘ
ঘ) 70 km/hr

ব্যাখ্যা

Question: A speed of 14 meters per second is the same as

Solution:
1 second speed = 14 meters.
1 hour or 3600 seconds speed = (14 × 3600) meters
= 50400 meters
= 50400/100 km/hr.
= 50.4 km/hr.
≈ 50 km/hr.

[আসন্ন মান হিসেবে অপশন (ক) অধিকগ্রহণযোগ্য]

৯১৭.

The wheel of an engine of 300 cm in circumference makes 10 revolutions in 6 seconds. What is the speed of the wheel (in km/h)?

ক
5
খ
8
গ
12
ঘ
18

ব্যাখ্যা

Question: The wheel of an engine of 300 cm in circumference makes 10 revolutions in 6 seconds. What is the speed of the wheel (in km/h)?

Solution:
total distance = 10 × 300 cm
= 3000 cm
= 30 m

speed = 30/6 ms^-1
= 5 ms^-1
= (5 × 3600)/(1000) kmh^-1
= 18 kmh^-1

৯১৮.

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

ক
9
খ
10
গ
12
ঘ
20
ঙ
25

ব্যাখ্যা

Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

Solution:
Due to stoppages, it covers 9 km less.

Time taken to cover 9 km = (9/54) × 60 min = 10 min.

৯১৯.

A minibus takes 6 hour less to cover 1680 km distance, if its speed is increased by 14 kmph ? What is the usual time of the minibus ?

ক
20
খ
24
গ
30
ঘ
36
ঙ
42

ব্যাখ্যা

Let speed be y km/hour
1680/y - 1680/(y + 14) = 6 or, y = 56 but y ≠ - 76
The usual time of the minibus shall be 1680/56 = 30 hours

৯২০.

Two trains, one from Dhaka to Chittagong and one from Chittagong to Dhaka, started simultaneously. After they meet, the trains reach their destinations after 4 hours and 9 hours respectively. What is the ratio of their speed?

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

ব্যাখ্যা

Question: Two trains, one from Dhaka to Chittagong and one from Chittagong to Dhaka, started simultaneously. After they meet, the trains reach their destinations after 4 hours and 9 hours respectively. What is the ratio of their speed?

Solution:

ধরি,
প্রথম ট্রেনের বেগ S₁ এবং এটি ঢাকা থেকে চট্টগ্রাম যাচ্ছে।
দ্বিতীয় ট্রেনের বেগ S₂ এবং এটি চট্টগ্রাম থেকে ঢাকা যাচ্ছে।
তারা t সময় পর P বিন্দুতে মিলিত হবে।

ঢাকা থেকে P বিন্দুর জন্য
প্রথম ট্রেনের দূরত্ব = S₁t
দ্বিতীয় ট্রেনের দূরত্ব = 9S₂
∴ S₁t = 9S₂. . . . . .(1)

চট্টগ্রাম থেকে P বিন্দুর জন্য
প্রথম ট্রেনের দূরত্ব = 4S₁
দ্বিতীয় ট্রেনের দূরত্ব = S₂t
∴ S₂t = 4S₁. . . . . . (2)

(1) ÷ (2)
S₁t/S₂t = 9S₂/4S₁
S₁²/S₂² = 9/4
S₁/S₂ = 3/2
S₁ : S₂ = 3 : 2

৯২১.

The ratio between the speeds of two trains is 5 : 6. If the second train runs 450 km in 5 hours, then the speed of the first train is:

ক
75 km/hr
খ
90 km/hr
গ
100 km/hr
ঘ
120 km/hr

ব্যাখ্যা

Question: The ratio between the speeds of two trains is 5 : 6. If the second train runs 450 km in 5 hours, then the speed of the first train is:

সমাধান:
দ্বিতীয় ট্রেনের গতিবেগ = দূরত্ব/সময়
= 450 কিমি/5 ঘন্টা
= 90 কিমি/ঘন্টা

এখন, দুটি ট্রেনের গতিবেগের অনুপাত হলো 5 : 6।

ধরি, প্রথম ট্রেনের গতিবেগ 5x এবং দ্বিতীয় ট্রেনের গতিবেগ 6x।
তাহলে, 6x = 90 কিমি/ঘন্টা
⇒ x = 90/6
∴ x = 15

সুতরাং, প্রথম ট্রেনের গতিবেগ = 5x = 5 × 15 = 75 কিমি/ঘন্টা

৯২২.

A train takes 10 sec to pass a signal post and covers a distance of 10 km in 15 min. Find the length of train?

ক
ক) 100.1 m
খ
খ) 223.1 m
গ
গ) 111.1 m
ঘ
ঘ) 120.3 m

ব্যাখ্যা

We know,
Speed =Distance/ Time
Speed =(10/15) 60 = 40×(5/18)m/sec
= 11.1 m/sec
Length of train = (Speed x Time)
= (11.11x10)
= 111.1 m

৯২৩.

A train covers a distance in 30 minutes. If it runs at a speed of 56 km/h on average. The speed at which the train must run to reduce the time of the journey to 20 minutes is-

ক
77 km/h
খ
81 km/h
গ
84 km/h
ঘ
88 km/h
ঙ
92 km/h

ব্যাখ্যা

Question: A train covers a distance in 30 minutes. If it runs at a speed of 56 km/h on average. The speed at which the train must run to reduce the time of the journey to 20 minutes is-

Solution:
Here,
Current speed = 56 km/h
Current time = 30 minutes
= 30/60 h
= 1/2 hour
New time = 20 minutes
= 20/60 h
= 1/3 h

We know,
Distance = Speed × Time
= 56 × (1/2)
= 28 km

∴ New speed = Distance/New time
= 28/(1/3)
= 84 km/h

৯২৪.

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?

ক
ক) 80 km/hr
খ
খ) 91 km/hr
গ
গ) 88 km/hr
ঘ
ঘ) 81 km/hr
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

৯২৫.

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

ক
ক) 9.6 km/hr.
খ
খ) 10.6 km/hr.
গ
গ) 9.8 km/hr.
ঘ
ঘ) 10.8 km/hr.

ব্যাখ্যা

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

Explanation:
Speed = 900m/(5 x 60) sec.
= 3 m/sec.

এখন কিলোমিটারে পরিণত করতে হলে-
= 3 × (18/5) km/hr
= 10.8 km/hr.

৯২৬.

A boat can travel with a speed of 14 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 76 km downstream.

ক
ক) 2 hours
খ
খ) 5 hours
গ
গ) 4 hours
ঘ
ঘ) 9 hours

ব্যাখ্যা

Speed downstream = (14 + 5) km/hr = 19 km/hr.

Time taken to travel 76 km downstream = (76/19) hours
= 4 hours

৯২৭.

A man travels 50 km at speed 25 km/hr and next 40 km at 20 km/hr and there after travel 90 km at 15 km/hr. His average speed is:

ক
ক) 18 km/hr
খ
খ) 16 km/hr
গ
গ) 15 km/hr
ঘ
ঘ) 12 km/hr

ব্যাখ্যা

Question: A man travels 50 km at speed 25 km/hr and next 40 km at 20 km/hr and there after travel 90 km at 15 km/hr. His average speed is:

Solution:
We know,
Average speed = Total distance/Total time
= (50 + 40 + 90)/(2 + 2 + 6) km/hr
= 180/10 km/hr
= 18 km/hr.

৯২৮.

A boat can row 180 km upstream , with the speed of still water in 30 kmph and the difference between time taken upstream and downstream is 2.5 hours. Find the speed of the stream.

ক
5 kmph
খ
7 kmph
গ
6 kmph
ঘ
4 kmph

ব্যাখ্যা

Question: A boat can row 180 km upstream , with the speed of still water in 30 kmph and the difference between time taken upstream and downstream is 2.5 hours. Find the speed of the stream.

Solution:
Speed of boat in still water = 30 kmph.
Speed of stream = x kmph

ATQ,
180/(30 - x) - 180/(30 + x) = 2.5
⇒ {180(30 + x) - 180(30 - x)}/(900 - x²) = 2.5
⇒ 5400 + 180x - 5400 + 180x = 2.5 × (900 - x²)
⇒ 360x = 2250 - 2.5x²
⇒ 2.5x² + 360x - 2250 = 0
⇒ x² + 144x - 900 = 0
⇒ x² + 150x - 6x - 900 = 0
⇒ x(x + 150) - 6(x + 150)
⇒ (x + 150)(x - 6) = 0
∴ x = 6, - 150
Speed cannot be negative so the speed of the stream is 6 kmph.

৯২৯.

A man on tour travels 160 km by car at 64 km/hr and another 160 km by bus at 80 km/hr. The average speed for the whole journey is

ক
36.12 km/hr
খ
50 km/hr
গ
71.11 km/hr
ঘ
82.6 km/hr

ব্যাখ্যা

Question: A man on tour travels 160 km by car at 64 km/hr and another 160 km by bus at 80 km/hr. The average speed for the whole journey is

Solution:
The total distance traveled is the sum of distances traveled by car and bus, which is 160 km + 160 km = 320 km.

Time taken for the car journey = Distance ÷ Speed = 160 km ÷ 64 km/hr = 2.5 hours
Time taken for the bus journey = Distance ÷ Speed = 160 km ÷ 80 km/hr = 2 hours

The total time taken for the entire journey is 2.5 hours (car) + 2 hours (bus) = 4.5 hours.

Average speed = Total distance traveled ÷ Total time taken
⇒ 320 km ÷ 4.5 hours ≈ 71.11 km/hr

৯৩০.

An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of:

ক
ক) 720 km/hr
খ
খ) 620 km/hr
গ
গ) 360 km/hr
ঘ
ঘ) 420 km/hr

ব্যাখ্যা

Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of:

Solution:
Distance = (240 x 5) = 1200 km.

Speed = Distance/Time
Or, Speed = 1200/(5/3) km/hr.

∴ Required speed = 1200/(5/3) km/hr
= 720 km/hr.

৯৩১.

A boat travels 18 km downstream in 45 minutes. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?

ক
12 km/h
খ
24 km/h
গ
21 km/h
ঘ
19 km/h

ব্যাখ্যা

Question: A boat travels 18 km downstream in 45 minutes. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?

Solution:
স্রোতের অনুকূলে 45 মিনিটে যায় 18 কিমি
স্রোতের অনুকূলে 1 মিনিটে যায় 18/45 কিমি
স্রোতের অনুকূলে 1 ঘণ্টা বা 60 মিনিটে যায় (18 × 60)/45 কিমি
= 24 কিমি

∴ স্রোতের অনুকূলে বেগ = 24 কিমি/ঘণ্টা

দেওয়া আছে,
স্রোতের বেগ = 5 কিমি/ঘণ্টা।

∴ স্থির পানিতে নৌকার বেগ = স্রোতের অনুকূলে বেগ - স্রোতের বেগ
= 24 - 5 = 19 কিমি/ঘণ্টা।

৯৩২.

A car moves 550 meters in a minute, and a train travels 72 km in 45 minutes. How much faster is one than the other?

ক
45 km/h
খ
54 km/h
গ
63 km/h
ঘ
74 km/h

ব্যাখ্যা

Question: A car moves 550 meters in a minute, and a train travels 72 km in 45 minutes. How much faster is one than the other?

Solution:
Speed of the car = Distance/Time
= (550/1) meters/minute
= (550/1000)/(1/60) km/h
= (550 × 60)/1000 km/h
= 33 km/h

Speed of the train = Distance/Time
= (72/45) km/minute
= 72/(45/60) km/h
= (72 × 60)/45 km/h
= 96 km/h

∴ Difference in speed between the train and the bus = (96 - 33) km/h = 63 km/h

৯৩৩.

A motorboat can travel at 5 km/hr in still water. It travelled 45 km downstream in a river and then returned, taking altogether 50 hours. Find the rate of flow of the river.

ক
ক) 2 km/hr
খ
খ) 3 km/hr
গ
গ) 3.5 km/hr
ঘ
ঘ) 4 km/hr

ব্যাখ্যা

Question: A motorboat can travel at 5 km/hr in still water. It travelled 45 km downstream in a river and then returned, taking altogether 50 hours. Find the rate of flow of the river.

Solution:
Speed of boat in still water, x = 5 km/hr.
Let,
rate of flow of river = y km/hr.
∴ Speed of upstream = 5 - y
speed of downstream = 5 + y

∴ 45/(5 + y) + 45/(5 - y) = 50
⇒ (225 - 45y + 225 + 45y)/(25 - y²) = 50
⇒ 450 = 1250 - 50y²
⇒ 50y² = 800
⇒ y² = 16
∴ y = 4 km/hr.

৯৩৪.

A car travelling with 5/6 of its actual speed covers 35 km in 150 minutes. Find the actual speed of the car.

ক
ক) 16.8 km/hr.
খ
খ) 17.8 km/hr.
গ
গ) 18.8 km/hr.
ঘ
ঘ) 16.9 km/hr.

ব্যাখ্যা

Question: A car travelling with 5/6 of its actual speed covers 35 km in 150 minutes. Find the actual speed of the car.

Solution:
Let,
the actual speed be x km/hr.
Time taken:
= 150 minutes
= (150/60) hrs.
= 2.5 hrs

ATQ,
Or, (5x/6) × 2.5 = 35
Or, (5x/6) × (25/10) = 35
Or, (5x/6) = (35 × 10)/25
Or, x = (35 × 6 ×10)/( 25 × 5)
Or, x = 16.8 km/hr.

∴ the actual speed of the car16.8 km/hr.

৯৩৫.

A boat can cover 'r' km upstream in 6 hours. It can cover 'r + 18' km downstream in 4 hours. Find the time taken by boat to cover 81 km upstream and 90 km downstream if the speed of boat in still water and speed of stream are in the ratio 4 : 1, respectively.

ক
8 hours
খ
6 hours
গ
7 hours
ঘ
5 hours

ব্যাখ্যা

Question: A boat can cover 'r' km upstream in 6 hours. It can cover 'r + 18' km downstream in 4 hours. Find the time taken by boat to cover 81 km upstream and 90 km downstream if the speed of boat in still water and speed of stream are in the ratio 4 : 1, respectively.

Solution:
Given that,
Boat covers r km upstream in 6 hours
Boat covers (r + 18) km downstream in 4 hours
Ratio of speed of boat in still water : speed of stream = 4 : 1

Let speed of boat in still water = 4k km/hr
Let speed of stream = 1k km/hr

∴ Upstream speed = 4k − 1k = 3k
∴ Downstream speed = 4k + 1k = 5k

Now,
r/6 = 3k
∴ r = 18k …… (1)

And, (r + 18)/4 = 5k
(18k + 18)/4 = 5k ; [From 1]
⇒ 18k + 18 = 20k
⇒ 20k - 18k = 18
⇒ 2k = 18
⇒ k = 18/2 = 9
∴ k = 9

Now, upstream speed = 3k = 27 km/hr
Downstream speed = 5k = 45 km/hr

Required Time,
Time for 81 km upstream = 81/27 = 3 hours
Time for 90 km downstream = 90/45 = 2 hours

∴ Total time = 3 + 2 = 5 hours

∴ The boat takes 5 hours to cover 81 km upstream and 90 km downstream.

৯৩৬.

Rupa and Puja started from the opposite direction of a 12km racing track. Their speed is 10kmph and 8kmph respectively. After which point they will meet if they start simultaneously?

ক
7226m from Rupa
খ
6667m from puja
গ
6667m from Rupa
ঘ
5333m from Rupa

ব্যাখ্যা

Question: Rupa and Puja started from the opposite direction of a 12km racing track. Their speed is 10kmph and 8kmph respectively. After which point they will meet if they start simultaneously?

Solution:
let, they will meet after t hour at point X.
in t hour,
Rupa will cross = 10t km
Puja will cross = 8t km

ATQ,
10t + 8t = 12
18t = 12
t = 12/18 hour

in 12/18 hours,
Rupa will cross = (12/18)10 km = 6667m
puja will cross = (12/18)8 km = 5333m

৯৩৭.

Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h?

ক
90 km/h
খ
160 km/h
গ
67.5 km/h
ঘ
120 km/h
ঙ
None of these

ব্যাখ্যা

Question: Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h?

Solution:
After meeting with each other the 1st train travels 120 × 16 km=1920km.

If the speed of the 2nd train be X km/h, it travels 1920/X hour before meeting.

After meeting, the 2nd train travels 9X km.

Before meeting, the first train covered this distance in 9X/120 hour.

As the two trains started simultaneously, before meeting their journey time was same.
So,
1920/X = 9X/120
⇒ 9X² = 1920 × 120
⇒ X² = (1920 × 120)/9
⇒ X = √[640 × 40]
∴ X=160.

∴ The train B travels at 160km/h.

৯৩৮.

A boat travels 18 km downstream in 45 minutes. If the speed of the stream is 3 km/h, what is the speed of the boat in still water?

ক
20 km/h
খ
21 km/h
গ
22 km/h
ঘ
23 km/h

ব্যাখ্যা

Question: A boat travels 18 km downstream in 45 minutes. If the speed of the stream is 3 km/h, what is the speed of the boat in still water?

Solution:
স্রোতের অনুকূলে 45 মিনিটে যায় 18 কিমি
স্রোতের অনুকূলে 1 মিনিটে যায় 18/45 কিমি
স্রোতের অনুকূলে 1 ঘণ্টা বা 60 মিনিটে যায় (18 × 60)/45 কিমি
= 24 কিমি

∴ স্রোতের অনুকূলে বেগ = 24 কিমি/ঘণ্টা

দেওয়া আছে,
স্রোতের বেগ = 3 কিমি/ঘণ্টা।

∴ স্থির পানিতে নৌকার বেগ = স্রোতের অনুকূলে বেগ - স্রোতের বেগ
= 24 - 3 = 21 কিমি/ঘণ্টা।

৯৩৯.

An F‑7 BGI fighter jet covers a certain distance at a speed of 1200 km/h in 5 hours. What speed must it maintain to cover the same distance in 250 minutes?

ক
440 km/h
খ
1440 km/h
গ
1240 km/h
ঘ
140 km/h

ব্যাখ্যা

Question: An F‑7 BGI fighter jet covers a certain distance at a speed of 1200 km/h in 5 hours. What speed must it maintain to cover the same distance in 250 minutes?

Solution:
Total distance = Speed × Time
= (1200 × 5) km
= 6000 km

Given time = 250 minutes = (250/60) hours
= 25/6 hours

∴ Required speed = Distance/Time
= {6000/(25/6)} km/h
= {6000 × (6/25)} km/h
= (240 × 6) km/h
= 1440 km/h

৯৪০.

A man travels from his home to office at 4 km/hr and reaches his office 20 min late. If the Speed had been 6 km/hr he would have reached 10 min early. Find the distance from his home to office.

ক
8 km
খ
12 km
গ
6 km
ঘ
9 km

ব্যাখ্যা

Question: A man travels from his home to office at 4 km/hr and reaches his office 20 min late. If the Speed had been 6 km/hr he would have reached 10 min early. Find the distance from his home to office.

Solution:
Let the Distance between home and office = d.
Suppose he reaches the office on Time, the Time taken = x minutes

Case 1: When he reaches office 20 minutes late,
Time taken = x + 20 minutes

Case 2: when he reaches office 10 minutes early,
Time taken = x - 10 minutes

As the Distance traveled is the same, the ratio of Speed in case 1 to the Speed in case 2 will be the inverse of the Time taken in both cases
Ratio of Speed in both cases = 4 : 6 = 2 : 3

Ratio of Time in both cases = 3 : 2

∴ (x + 20)/(x - 10) = 3/2
⇒ 2x + 40 = 3x -30
∴ x = 70

minutes Taking case 1,
70 + 20 minutes
= 90 minutes

In 60 minutes he reached 4000 m
∴ In 1 minutes he reached 4000/60 m
∴ In 90 minutes he reached (4000 × 90)/60 m
= 6000 m
= 6 km

৯৪১.

Joy travelled from his town to city. He went to the city by bicycle at the speed of 25 km/h and came back at the speed of 4 km/h. If he took 5 hours and 48 min to complete his journey, what is the distance between town and city?

ক
ক) 15 km
খ
খ) 22 km
গ
গ) 20 km
ঘ
ঘ) 25 km

ব্যাখ্যা

Average speed of Joy = 2xy/(x + y)
= (2 × 25 × 4)/(25 + 4)
= 200/29 km/h

Distance traveled = Speed × Time
= 200/29 × 29/5
= 40 Km

Distance between city and town = 40/2 = 20 km.

৯৪২.

A man rows downstream at 35 km/h and rows upstream at 25 km/h. At what speed can he row in still water?

ক
10 km/h
খ
30 km/h
গ
60 km/h
ঘ
40 km/h

ব্যাখ্যা

Qustion: A man rows downstream at 35 km/h and rows upstream at 25 km/h. At what speed can he row in still water?

Solution:
Given,
Man rows downstream = 35 km/h
Man rows upstream = 25 km/h
We know that,
Speed in still water = (Downstream speed + Upstream speed) ÷ 2
= (35 + 25) ÷ 2
= 60 ÷ 2
= 30 km/h

৯৪৩.

The ratio between the speeds of two cars is 5 : 8. If the first car covers 200 km in 2 hours, find the speed of the second car.

ক
140 km/hr
খ
150 km/hr
গ
160 km/hr
ঘ
170 km/hr

ব্যাখ্যা

Question: The ratio between the speeds of two cars is 5 : 8. If the first car covers 200 km in 2 hours, find the speed of the second car.

Solution:
Let the speed of two cars is 5X and 8X.

Speed of the first car = 200/2 = 100 km/hr

Therefore,
5X = 100
⇒ X = 100/5 = 20 km/hr

So the speed of second car will be = 8 × 20 = 160 km/hr

৯৪৪.

A train which is moving at an average speed of 30 km/h reaches its destination on time. When its average speed reduces to 25 km/h, then it reaches its destination 10 minutes late. The distance travelled by the train, is -

ক
ক) 25 km
খ
খ) 30 km
গ
গ) 45 km
ঘ
ঘ) 50 km

ব্যাখ্যা

Question: A train which is moving at an average speed of 30 km/h reaches its destination on time. When its average speed reduces to 25 km/h, then it reaches its destination 10 minutes late. The distance travelled by the train, is -

Solution:
Let the distance = x
ATQ,
(x/25) - (x/30) = 10/60
⇒ (6x - 5x)/150 = 1/6
⇒ x/150 = 1/6
⇒ x = 150/6
∴ x = 25

∴ The distance travellede by the train is 25 km

৯৪৫.

A man goes downstream with a boat to some destination and returns upstream to his original place in 20 hours. If the speed of the boat in still water and the stream is 40 km/hr and 20 km/hr respectively, the distance of the destination from the starting place?

ক
400 km
খ
250 km
গ
450 km
ঘ
300 km
ঙ
None of these

ব্যাখ্যা

Question: A man goes downstream with a boat to some destination and returns upstream to his original place in 20 hours. If the speed of the boat in still water and the stream is 40 km/hr and 20 km/hr respectively, the distance of the destination from the starting place?

Solution:
Let the distance of the destination from the starting point = x km.
Rate downstream= (40 + 20) km/hr = 60 km/hr
Rate upstream = (40 - 20) km/hr = 20 km/hr
According to the question,
x/60 + x/20 = 20
⇒ 4x = 20 × 60
⇒ 4x = 1200
∴ x = 300 km

Hence, A distance of the destination from the starting point = 300 km

৯৪৬.

A Tank is normally filled in 8 hours but takes 5 hours longer to fill because of a leak in its bottom. If the tank is full, the leak will empty it in?

ক
ক) 20.8
খ
খ) 19.9
গ
গ) 20.5
ঘ
ঘ) 19.8

ব্যাখ্যা

Question: A Tank is normally filled in 8 hours but takes 5 hours longer to fill because of a leak in its bottom. If the tank is full, the leak will empty it in?

Solution:
Let the leak will empty the tank in x hrs.
Total time = 8 + 5 = 13 hrs.

Then,
Or, 1/8 - 1/x = 1/13
Or, (x − 8)/8x = 1/13
Or, 13x − 104 = 8x
Or, 13x − 8x = 104
Or, 5x = 104
Or, x = 20.8

৯৪৭.

A train running at a speed of 90 km/hr crosses a platform double its length in 36 seconds. What is the length of the platform in meters?

ক
300 m
খ
450 m
গ
600 m
ঘ
700 m

ব্যাখ্যা

Question: A train running at a speed of 90 km/hr crosses a platform double its length in 36 seconds. What is the length of the platform in meters?

Solution:
Let, the length of the train be x metres.
Then, the length of the platform = 2x metres.
Speed of the train = 90 × (1000/3600) m/sec
= 25 m/sec

ATQ,
(x + 2x)/25 = 36
⇒ 3x = 900
⇒ x = 300

Hence, the length of platform = 2x = (2 × 300) m
= 600 m

৯৪৮.

The ratio of speed of a motor-boat to that of the current of water is 17 : 5. The boat goes along with the current in 4 hours. It will come back in-

ক
7 hour
খ
7 hour 20 minute
গ
7 hour 30 minute
ঘ
7 hour 40 minute

ব্যাখ্যা

Question: The ratio of speed of a motor-boat to that of the current of water is 17 : 5. The boat goes along with the current in 4 hours. It will come back in-

Solution:
Since the ratio 17 : 5 is given.
Let the speed of boat in still water = 17 km/hr
and speed of stream = 5 km/hr

Downstream speed = 17 + 5 = 22 km/hr
Upstream speed = 17 - 5 = 12 km/hr

Distance = Downstream speed × downstream time
= 22 × 4 = 88 km

Upstream time = Distance/upstream speed
= 88/12
∴ Come back time = 7 hour 20 minute

৯৪৯.

A boat can travel with a speed of 11 km/hr in still water. If the speed of the stream is 5 km/hr. find the time taken by the boat to go 112 km downstream.

ক
3 hrs.
খ
6 hrs.
গ
7 hrs.
ঘ
11 hrs.

ব্যাখ্যা

Question: A boat can travel with a speed of 11 km/hr in still water. If the speed of the stream is 5 km/hr. find the time taken by the boat to go 112 km downstream.

Solution:
Speed downstream = Speed of Boat in still water + Speed of the stream =
(11 + 5)km/hr. = 16km/hr.

Time taken to travel 112 km downstream = Distance/Speed=(112/16)hrs = 7 hrs.

৯৫০.

The time taken by a train 180 m long, travelling at 42 kmph, in passing a person walking in the same direction at 6 kmph, will be -

ক
17 sec
খ
18 sec
গ
19 sec
ঘ
21 sec

ব্যাখ্যা

Question: The time taken by a train 180 m long, travelling at 42 kmph, in passing a person walking in the same direction at 6 kmph, will be -

Solution:
Speed of train relative to man
= (44 - 8) kmph
= 36 kmph
= (36 × 5)/18m/sec
= 10 m/sec

∴ Time taken to pass the man
= 180/10 sec
= 18 sec

৯৫১.

Two trains of equal length take 8 seconds and 12 seconds respectively to cross a lamp post. If the length of each train is 160 meters, in how many seconds will they cross each other when traveling in opposite directions?

ক
9.2 seconds
খ
9.6 seconds
গ
10.2 seconds
ঘ
10.6 seconds

ব্যাখ্যা

Question: Two trains of equal length take 8 seconds and 12 seconds respectively to cross a lamp post. If the length of each train is 160 meters, in how many seconds will they cross each other when traveling in opposite directions?

Solution:
Speed of the first train = 160/8 m/sec
= 20 m/sec

Speed of the second train = 160/12 m/sec
= 40/3 m/sec

∴ Relative speed = 20 + 40/3
= (60 + 40)/3
= 100/3 m/sec

∴ Required time = (160 + 160)/(100/3) sec
= 320 × 3/100
= 960/100
= 9.6 seconds

৯৫২.

An outlet pipe can empty a cistern in 30 min, then what part of the cistern will it empty in 1 min?

ক
ক) 1/20
খ
খ) 1/15
গ
গ) 1/25
ঘ
ঘ) 1/30
ঙ
ঙ) 1/18

ব্যাখ্যা

We know that, when a pipe empties a cistern in 'n' min, then the part emptied by the pipe in 1 min = 1/n
Here, n = 30
Therefore, Required part of the tank emptied in 1 min = 1/30part

৯৫৩.

Two trains of length 140 meters and 166 meters are moving towards each other on parallel tracks at a speed of 50 km/hr and 60 km/hr respectively. In what time the trains will cross each other from the moment they meet?

ক
8 seconds
খ
12 seconds
গ
9 seconds
ঘ
11 seconds
ঙ
None of these

ব্যাখ্যা

Question: Two trains of length 140 meters and 166 meters are moving towards each other on parallel tracks at a speed of 50 km/hr and 60 km/hr respectively. In what time the trains will cross each other from the moment they meet?

Solution:
In this problem, both the trains are moving so we will find the relative speed of the train. They are moving in the opposite direction, so the relative speed will be sum of their individual speeds.

Relative speed: (50 + 60) = 110 km/hr

Relative speed in m/s = 110 × (5/18) m/s = 550/18 m/s = 275/9 m/s

Distance covered is equal to the sum of the length of trains: 140 + 166= 306 meters

Time = 306 × (9/275) sec
= 10.01 sec
≈ 10 sec

৯৫৪.

In a boat race, a person rows a boat 8 km upstream and returns to the starting point in 3 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.

ক
4 km/hr
খ
6 km/hr
গ
5.5 km/hr
ঘ
4.5 km/hr

ব্যাখ্যা

Question: In a boat race, a person rows a boat 8 km upstream and returns to the starting point in 3 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.

সমাধান:
ধরি, স্থির পানিতে নৌকার গতিবেগ = x কিমি/ঘন্টা।
স্রোতের গতিবেগ = 2 কিমি/ঘন্টা।

স্রোতের প্রতিকূলে (Upstream) নৌকার গতিবেগ = (x - 2) কিমি/ঘন্টা।
স্রোতের অনুকূলে (Downstream) নৌকার গতিবেগ = (x + 2) কিমি/ঘন্টা।

মোট সময় = স্রোতের প্রতিকূলে যেতে সময় + স্রোতের অনুকূলে যেতে সময়
⇒ 3 = 8/(x - 2) + 8/(x + 2)
⇒ 3 = 8{1/(x - 2) + 1/(x + 2)}
⇒ 3/8 = (x + 2 + x - 2)/(x - 2)(x + 2)
⇒ 3/8 = 2x/(x² - 4)
⇒ 3(x² - 4) = 8(2x)
⇒ 3x² - 12 = 16x
⇒ 3x² - 16x - 12 = 0
⇒ 3x² - 18x + 2x - 12 = 0
⇒ 3x(x - 6) + 2(x - 6) = 0
⇒ (3x + 2)(x - 6) = 0

সুতরাং, x এর সম্ভাব্য মান হলো 6 অথবা - 2/3
যেহেতু গতিবেগ ঋণাত্মক হতে পারে না, তাই x = 6 কিমি/ঘন্টা।

সুতরাং, স্থির পানিতে নৌকার গতিবেগ হলো 6 কিমি/ঘন্টা।

৯৫৫.

A thief steals a scooter at 10:00 a.m. and drives away at 30 km/h. The theft is discovered at 11:00 a.m. and the owner immediately starts chasing the thief in a car at 50 km/h. At what time will the owner catch the thief?

ক
12 : 30 p.m.
খ
1 : 00 p.m.
গ
2 : 00 p.m.
ঘ
2 : 30 p.m.

ব্যাখ্যা

Question: A thief steals a scooter at 10:00 a.m. and drives away at 30 km/h. The theft is discovered at 11:00 a.m. and the owner immediately starts chasing the thief in a car at 50 km/h. At what time will the owner catch the thief?

Solution:
চোর কর্তৃক অতিক্রান্ত প্রারম্ভিক দূরত্ব (Head Start):
সময় পার্থক্য = 11:00 a.m. - 10:00 a.m. = 1 ঘন্টা।
চোর কর্তৃক অতিক্রান্ত দূরত্ব = 30 × 1 কিমি = 30 কিমি।

আপেক্ষিক গতিবেগ = (মালিকের গতিবেগ - চোরের গতিবেগ)
= (50 - 30) কিমি/ঘন্টা = 20 কিমি/ঘন্টা।

চোরকে ধরতে প্রয়োজনীয় সময় = দূরত্ব/আপেক্ষিক গতিবেগ
= 30/20 ঘন্টা
= 3/2 ঘন্টা
= 1 ঘন্টা 30 মিনিট।

ধাওয়া শুরু হয়েছিল 11 : 00 a.m. এ।
∴ চোরকে ধরার সময়সময় = 11 : 00 a.m. + 1 ঘন্টা 30 মিনিট
= 12 : 30 p.m.
∴ মালিক চোরটিকে 12 : 30 p.m. এ ধরে ফেলবে।

৯৫৬.

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

ক
ক) 1 : 3
খ
খ) 3 : 4
গ
গ) 5 : 3
ঘ
ঘ) 3 : 2

ব্যাখ্যা

প্রশ্ন: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

সমাধান:
Let,
The speeds of first train be x m/sec
The speeds of second train be y m/sec

Then,
length of the first train = 27x metres,
length of the second train = 17y metres.

ATQ,
(27x + 17y)/(x+ y) = 23
⇒ 27x + 17y = 23x + 23y
⇒ 4x = 6y
⇒ x/y = 6/4
⇒ x/y = 3/2
∴ x : y = 3 : 2

৯৫৭.

A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. His average speed is-

ক
9 km/h
খ
3 km/h
গ
4 km/h
ঘ
3.5 km/h

ব্যাখ্যা

Question: A man covers half of his journey at 6 km/h and the remaining half at 3 km/h. His average speed is-

Solution:
Let the total distance be 2d km.
First half at 6 km/h.
Second half at 3 km/h.

Now,
Time for first half, t₁ = d/6 hours
Time for second half, t₂ = d/3 hours

∴ Total Time = (d/6) + (d/3) = 3d/6 = d/2

∴ Average speed = Total distance/Total time = 2d/(d/2) = 4 km/h

∴ Average speed = 4 km/h

৯৫৮.

A 125-meter-long train overtakes a person moving at 5 km/h in 10 seconds, while both are moving in the same direction. What is the speed of the train?

ক
12.5 km/h
খ
24 km/h
গ
40 km/h
ঘ
50 km/h

ব্যাখ্যা

Question: A 125-meter-long train overtakes a person moving at 5 km/h in 10 seconds, while both are moving in the same direction. What is the speed of the train?

Solution:
ট্রেনটি ব্যক্তিকে অতিক্রম করতে ট্রেনের নিজের দৈর্ঘ্যের সমান দূরত্ব অতিক্রম করে।

∴ আপেক্ষিক গতিবেগ = 125m/10s
= 12.5 m/s
= (12.5/1000)/(1/3600) km/h
= (12.5 × 3600)/1000 km/h
= 45 km/h

ধরি,
ট্রেনের গতিবেগ = x km/h

দেওয়া আছে,
ব্যক্তির গতিবেগ = 5 km/h

আমরা জানি,
আপেক্ষিক গতিবেগ = ট্রেনের গতিবেগ - ব্যক্তির গতিবেগ
⇒ ট্রেনের গতিবেগ = আপেক্ষিক গতিবেগ + ব্যক্তির গতিবেগ
⇒ x = (45 + 5) km/h
⇒ x = 50 km/h

৯৫৯.

A person at 5km/h crosses a platform in 12 minutes. A train 1/4 length of the platform crosses the platform at 50km/h. How much time is required to cross the platform by the train?

ক
ক) 1.2 min
খ
খ) 1 min
গ
গ) 1.5 min
ঘ
ঘ) 2 min

ব্যাখ্যা

Question: A person at 5km/h crosses a platform in 12 minutes. A train 1/4 length of the platform crosses the platform at 50km/h. How much time is required to cross the platform by the train?

Solution:
The speed of the person is = 5km/h
time required to cross the platform is = 12min = 12/60 = 1/5 hour

so, the length of the platform is = 5 × 1/5 = 1km

the length of the train is = 1/4 = 0.25km

the speed of the train is = 50km/h

so, time required to cross the platform by the train is = {(1 + 0.25) km}/(50km/h)
= 1.25/50
= 0.025hour
= 0.025 × 60 min
= 1.5 min

৯৬০.

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

ব্যাখ্যা

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

৯৬১.

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)?

ক
ক) 430 metre
খ
খ) 440 metre
গ
গ) 260 metre
ঘ
ঘ) 450 metre
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

৯৬২.

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

ক
4 : 1
খ
3 : 1
গ
2 : 1
ঘ
4 : 3

ব্যাখ্যা

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

Solution:
Let the original speed be S₁ and time t₁ and distance be D.
Now,
(D/2)/2t₁=S₂
S₂ = D/4t₁ and, S₁ = D/t₁

Thus,
S1_/S₂ = 4/1
= 4 : 1

৯৬৩.

A train 108 metre long is moving at a speed of 50 km/hr. It crosses a train 112metre long coming from the opposite direction in 6seconds. What is the speed of the second train?

ক
82 kmph
খ
58 kmph
গ
44 kmph
ঘ
76 kmph

ব্যাখ্যা

Distance covered = (108 + 112)
= 220 meter.
Time = 6 seconds.
Relative speed = 220/6 = 110/3 m/s.
= (110/3) × (18/5) km/hr
= 132 km/hr.
50 + Speed of second train = 132 km/hr.
Speed of second train = (132 - 50)
= 82 km/hr.

৯৬৪.

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
70 s
খ
60 s
গ
50 s
ঘ
12 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

৯৬৫.

A boat takes half time in moving a certain distance downstream than upstream. The ratio of the speed of the boat in still water and that of the current is?

ক
ক) 2 : 1
খ
খ) 3 : 2
গ
গ) 5 : 3
ঘ
ঘ) 3 : 1

ব্যাখ্যা

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

৯৬৬.

Sayed covers 20 miles in 40 minutes. What is his speed in km/hr?

ক
48.3 km/hr
খ
48 km/hr
গ
37.6 km/hr
ঘ
51.2 km/hr

ব্যাখ্যা

Question: Sayed covers 20 miles in 40 minutes. What is his speed in km/hr?

Solution:
We know that,
1 mile = 1.61km
20 miles = (20 × 1.61)km
= 32.2 km

time = 40 minutes = 40/60 = 2/3 hour

speed = 32.2/(2/3) km/hr
= 48.3 km/hr

৯৬৭.

A train travels 15 miles at a speed of 90 miles per hour. If the total time taken for the train's journey to and from the destination is 35 minutes, what is the speed of the train on its return trip?

ক
30 miles/hour
খ
40 miles/hour
গ
36 miles/hour
ঘ
46 miles/hour

ব্যাখ্যা

Question: A train travels 15 miles at a speed of 90 miles per hour. If the total time taken for the train's journey to and from the destination is 35 minutes, what is the speed of the train on its return trip?

Solution:
Time taken to travel 15 miles at 90 miles per hour = 15/90 hours = 1/6 hour = 10 minutes
So, the time taken to return = 35 - 10 minutes = 25 minutes

Distance covered in 25 minutes = 15 miles
Distance covered in 1 minute = 15/25 miles
∴ the speed during the return trip (for 60 minutes) = (15 × 60)/25 = 36 miles per hour

৯৬৮.

A car covers a distance of 15 km in 15 minutes. If its speed is decreased by 10 km/h, then the time taken by it to cover the distance of 20 km will be-

ক
26 minutes
খ
30 minutes
গ
24 minutes
ঘ
20 minutes

ব্যাখ্যা

Question: A car covers a distance of 15 km in 15 minutes. If its speed is decreased by 10 km/h, then the time taken by it to cover the distance of 20 km will be-

Solution:
Given,
15 minutes covers 15 km
∴ 1 minutes = 15/15 km
= 1 km
∴ 60 minutes or 1 hours = (1 × 60) km
= 60 km

If its speed is decreased by 10 km/h
Then new speed = (60 - 10) km
= 50 km/h

∴ 1 km cover in (60 ÷ 50) minutes
= 6/5 minutes
∴ 20 km cover in = (6/5 × 20) minutes
= 24 minutes

৯৬৯.

Jashim and Imran start walking from A to B at 5 and 3 km per hour respectively. Jashim reaches B and starts back for A. How far from B will he meet Imran if the distance between A and B is 32 km?

ক
ক) 6
খ
খ) 8
গ
গ) 9
ঘ
ঘ) 12

ব্যাখ্যা

Question: Jashim and Imran start walking from A to B at 5 and 3 km per hour respectively. Jashim reaches B and starts back for A. How far from B will he meet Imran if the distance between A and B is 32 km?

Solution:
A থেকে B এর দূরত্ব = 32 কি.মি
Jashim এবং Imran B থেকে x কি.মি দূরে পরস্পর সাক্ষাৎ করে।

প্রশ্নমতে
(32 + x)/5 = (32 - x)/3 [তাদের ভ্রমণের সময় সমান]
⇒ 3x + 96 = 160 - 5x
⇒ 3x + 5x = 160 - 96
⇒ 8x = 64
⇒ x = 64/8
x = 8 কি.মি

৯৭০.

The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream at the same time, the speed of the stream is-

ক
5 km/hr
খ
2.5 km/hr
গ
6 km/hr
ঘ
3 km/hr

ব্যাখ্যা

Question: The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream at the same time, the speed of the stream is-

Solution:
Let the speed of the stream be x km/hr
Then speed downstream = (10 + x) km/hr
Speed upstream = (10 − x)km/hr

∴26/(10 + x) = 14/(10 − x)
⇒ 260 − 26x = 140 + 14x
⇒ 40x = 120
⇒ x = 3 km/hr

৯৭১.

In a 600-meter race, C starts 60 meters ahead of D, yet D defeats C by a margin of 30 meters. What distance did C cover when D reached the finish line?

ক
480 meters
খ
520 meters
গ
510 meters
ঘ
500 meters

ব্যাখ্যা

Question: In a 600 meter race, C starts 60 meters ahead of D, yet D defeats C by a margin of 30 meters. What distance did C cover when D reached the finish line?

Solution:
In a 600 meter race,
C starts 60 meters ahead.
so C needs to cover = 600 - 60 = 540 meters
D covers the full distance = 600 meters

D defeats C by 30 meters

∴ When D finishes,
C’s distance = 540 - 30 = 510 meters.

৯৭২.

A train running at a speed of 72 km/hr crosses a platform double its length in 1 minute. What is the length of the platform in metres?

ক
600 metres
খ
800 metres
গ
700 metres
ঘ
680 metres

ব্যাখ্যা

Question: A train running at a speed of 72 km/hr crosses a platform double its length in 1 minute. What is the length of the platform in metres?

Solution:
Speed of the train = 72 km/h
The platform is double the length of the train
Time to cross the platform = 1 minute = 60 seconds

∴ Speed = (72 × 1000)/(60 × 60) = 20 m/s

Let, the length of the train is x
Then, the length of the platform = 2x

∴ Total distance to cross the platform = x + 2x = 3x

We know,
Distance = Speed × Time
⇒ 3x = 20 × 60 =1200
⇒ 3x = 1200
⇒ x = 1200/3
∴ x = 400

So, length of the platform = 2x = 2 × 400 = 800 metres.

৯৭৩.

A man travels from his home to the office at 4km/hr and reaches his office 20 min late. If the Speed had been 6 km/hr he would have reached 10 min early. Find the distance from his home to office?

ক
ক) 8 km
খ
খ) 12 km
গ
গ) 9 km
ঘ
ঘ) 6 km

ব্যাখ্যা

Let,
The distance between home and office =d
Suppose he reaches the office on Time,
the Time taken = a minutes
Case 1: When he reaches office 20 minutes late,
Time taken = a + 20
Case 2: When he reaches office 10 minutes early,
Time taken = a - 10
As the distance traveled is the same,
The ratio of Speed in case 1 to the Speed in case 2 will be the inverse of the Time taken in both cases.
Ratio of Speed in both cases = 4:6
= 2:3
Ratio of Time in both cases = 3:2
Therefore,
(a + 20)/(a -10)= 3/2
⇒ 2a + 40 = 3a -30
⇒ 3a - 2a = 40 + 30
⇒ a = 70 minutes.
Taking case 1,
4= d/(90/60)
⇒ d= 360/60
= 6 km.

৯৭৪.

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
35
খ
37
গ
37.5
ঘ
40

ব্যাখ্যা

Question: 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:

Solution:
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

৯৭৫.

একটি ট্রেনের গতিবেগ ৬০কি.মি./ঘণ্টা। ট্রেনটির দৈর্ঘ্য ১০০ মিটার। ১৪০ মিটার দৈর্ঘ্যের একটি ব্রিজ অতিক্রম করতে ট্রেনটির কত সময় লাগবে?

ক
ক) ১০.৪ সেকেন্ড
খ
খ) ১২.৪ সেকেন্ড
গ
গ) ১৬.৪ সেকেন্ড
ঘ
ঘ) ১৪.৪ সেকেন্ড

ব্যাখ্যা

ট্রেনটির মোট অতিক্রম করতে হবে = (১০০ + ১৪০) মিটার = ২৪০ মিটার

ট্রেনের গতিবেগ = ৬০কি.মি./ঘণ্টা
= (৬০ × ১০০০)/৩৬০০ মিটার/সেকেন্ড
= ৫০/৩ মিটার/সেকেন্ড
মোট সময় লাগবে = ২৪০/(৫০/৩)
= ৭২/৫
= ১৪.৪ সেকেন্ড

৯৭৬.

A train travelling at a speed of 75 mph enters a tunnel 3.5 miles long. The train is 0.25 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

ক
ক) 3 min
খ
খ) 3.5 min
গ
গ) 3.2 min
ঘ
ঘ) 2.5 min

ব্যাখ্যা

Question: A train travelling at a speed of 75 mph enters a tunnel 3.5 miles long. The train is 0.25 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

Solution:
Total distance covered = 3.5 + 0.25 mile = 3.75 miles
Train traveles 75 miles in 60 min
∴ Train traveles 3.75 mile in (60 × 3.75)/75 min
= 3 min

৯৭৭.

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

ক
10
খ
12
গ
14
ঘ
16

ব্যাখ্যা

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

Now
⇒ 4x + 9(9 - x) = 61
⇒ 4x + 81 - 9x = 61
⇒ 5x = 20
⇒ x = 4

∴ Distance travelled on foot = 4x
⇒ 4 × 4
= 16 km

∴ The distance travelled on foot is 16 Km.

৯৭৮.

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
ক) 10 km
খ
খ) 16 km
গ
গ) 21 km
ঘ
ঘ) 23 km

ব্যাখ্যা

Let the time in which he traveled on foot = x hour
Time for travelling on bicycle = (9-x) hr
Distance = Speed×Time, and Total distance = 61 km
So,
4x + 9(9-x) = 61
=> 5x = 20
=> x = 4
So distance traveled on foot = 4x4 = 16 km

৯৭৯.

Two trains of equal length are running on parallel lines in the same direction at 12.78 m/s and 10 m/s. The faster train passes the slower train in 72 seconds. The length of each train is:

ক
200 meters
খ
150 meters
গ
120 meters
ঘ
100 meters

ব্যাখ্যা

Question: Two trains of equal length are running on parallel lines in the same direction at 12.78 m/s and 10 m/s. 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 = (12.78 - 10) m/s
= 2.78 m/s

Now
2x/72 = 2.78
⇒ 2x = 72 × 2.78
⇒ 2x = 200.16
⇒ x = 200.16/2
∴ x = 100.08 ≅ 100

∴ The length of each train is 100 meters.

৯৮০.

A man goes downstream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of the boat in still water and the stream are 10 kmph and 4 kmph respectively, the distance of the destination from the starting place is:

ক
14 km
খ
21 km
গ
24 km
ঘ
28 km

ব্যাখ্যা

Question: A man goes downstream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of the boat in still water and the stream are 10 kmph and 4 kmph respectively, the distance of the destination from the starting place is:

Let,
the distance of the destination from the starting point = x km.
Speed downstream = (10 + 4) = 14 kmph
Speed upstream = (10 - 4) = 6 kmph

∴ Total time taken = 5 hours

ATQ,
(x/14) + (x/6) = 5
⇒ (3x + 7x)/42 = 5
⇒ 10x = 42 × 5
⇒ x = (42 × 5)/10
∴ x = 21 km

৯৮১.

A train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 16 seconds. The speed of the train is:

ক
48 km/hr
খ
50 km/hr
গ
55 km/hr
ঘ
60 km/hr

ব্যাখ্যা

Question: A train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 16 seconds. The speed of the train is:

Solution:
Speed of the train relative to man = 200/16 m/sec
= 12.5 m/sec
= (12.5 × 3600)/1000 km/hr
= 45 km/hr

Let,
The speed of the train be x km/hr.
∴ Relative speed = (x - 5) km/hr.
⇒ x - 5 = 45
∴ x = 50 km/hr.

৯৮২.

A train of length 180 meters crosses a man running at 10 km/hr in the same direction in 10 seconds. What is the speed of the train?

ক
68.8 km/hr
খ
70.4 km/hr
গ
72.8 km/hr
ঘ
74.8 km/hr

ব্যাখ্যা

Question: A train of length 180 meters crosses a man running at 10 km/hr in the same direction in 10 seconds. What is the speed of the train?

Solution:
When the train and man are moving in same direction then relative speed will be the difference between their individual speeds. In this problem the other way to find the relative speed is to divide the distance covered (length of train) by the time taken by the train to cross the man.

Relative Speed = 180/10 m/s

We will convert it into Km/hr
(180/10) × (18/5) = 64.8 km/hr

Now, let the speed of the train is X km/hr.
So, the relative speed, 64.8 km/hr = X km/hr - 10 km/hr
⇒ X - 10 = 64.8
⇒ X = 64.8 + 10
∴ X = 74.8 km/hr

৯৮৩.

Titumir Express leave Rajshahi Central Station every day at 07.50 am and goes to Dinajpur Railway station. This train is very popular among the travelers. On 25th July 2012 number of passengers traveling by I class and II class was in the ratio 1 : 4. The fare for this travel is in the ratio 3 : 1. The total fare collected was 224000 taka. What was the fare collected from I class passengers on that day?

ক
24000 taka
খ
48000 taka
গ
72000 taka
ঘ
96000 taka

ব্যাখ্যা

Let the number of passenger traveling by first class be x
Then, number of passenger traveling by second class will be 4x
But the fare is in the ratio 3 : 1
If 3y fare is collected per I class passenger, y would be collected per II class passenger
Fares of I class passengers : Fares of II class passengers
= x × 3y : 4x × y
= 3 : 4
If total fare is 3 + 4 = 7,
then I class passengers should pay 3 taka
Similarly,
we can calculate the fare of I class passengers when total was 224000 taka
Now, 7/3 = 224000/z(say)
or, z = 224000×3/7
or, z= 96000 taka

৯৮৪.

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
10:40 a.m.
গ
11 a.m.
ঘ
11: 20 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.

৯৮৫.

Two bike riders ride in opposite directions around a circular track, starting at the same time from the same point. Biker A rides at a speed of 16 kmph and biker B rides at a speed of 14 kmph. If the track has a diameter of 40 km, after how much time (in hours) will the two bikers meet?

ক
ক) 6.52
খ
খ) 8.14
গ
গ) 4.18
ঘ
ঘ) 5.02

ব্যাখ্যা

Distance to be covered = πD = 40π km
Relative speed of bikers = 16 + 14 = 30 kmph.
Now, time = distance/speed = 40π/30
= 4.18 hrs.

৯৮৬.

A train 150m long passes a pole in 15 seconds and crosses another train of the same length travelling in opposite direction in 8 seconds. The speed of the second train in (km/h) is -

ক
ক) 60 km/hr
খ
খ) 66 km/hr
গ
গ) 72 km/hr
ঘ
ঘ) 99 km/hr

ব্যাখ্যা

Speed of the first train :
= 150/15 = 10 m/s
Time taken by trains to cross each other = 8 s
And, relative speed of two trains :
= (150+150)/8 = 37.5
∴ Speed of the second train :
= (37.5 - 10) × 18/5
= 99 km/h

৯৮৭.

A train, having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train -

ক
ক) 8 seconds
খ
খ) 4 seconds
গ
গ) 10 seconds
ঘ
ঘ) 6 seconds

ব্যাখ্যা

Distance = 110 meter.
Since the train and man move in opposite directions, the relative speed
= (60 + 6) km/hr.
= 66 km/hr.
= 66 × (5/18) m/s.
= 110/6 m/s.
Time = 110/(110/6)
= 6 seconds.

৯৮৮.

A man travels a certain distance at a rate of 20 miles an hour and returns at the rate of 30 miles an hour. What is his average speed?

ক
ক) 24
খ
খ) 25.5
গ
গ) 25
ঘ
ঘ) None

ব্যাখ্যা

Question: A man travels a certain distance at a rate of 20 miles an hour and returns at the rate of 30 miles an hour. What is his average speed?

Solution:
ধরি, x মিটার দূরত্ব অতিক্রম করে।
x মিটার যেতে সময় লাগে x/20 ঘণ্টা
x মিটার ফিরে আসতে সময় লাগে x/30 ঘণ্টা

∴ গড় গতিবেগ = মোট দূরত্ব / মোট সময়
= x + x / (x/20) + (x/30)
= 2x/(3x + 2x)/60
= 2x/5x/60
= 24 km/hr

৯৮৯.

Kawser travelled 4/7 as many miles on foot as by water and 2/5 as many miles on horseback as by water. If he covered total of 3036 miles, how many miles did he travel on foot?

ক
860 miles
খ
880 miles
গ
840 miles
ঘ
820 miles

ব্যাখ্যা

Question: Kawser travelled 4/7 as many miles on foot as by water and 2/5 as many miles on horseback as by water. If he covered total of 3036 miles, how many miles did he travel on foot?

Solution:
Suppose Kawser travelled x miles by water, 4x/7 miles on foot and 2x/5 miles on horseback.

ATQ,
x + 4x/7 + 2x/5 = 3036
⇒ 69x/35 = 3036
⇒ x = (3036 × 35)/69
∴ x = 1540

∴ Distance travelled on foot :
=(4 ×1540)/7 miles
= 880 miles

৯৯০.

A 180 metre long train crosses a platform thrice its length in 40 seconds. What is the speed of the train in km/hr?

ক
ক) 54.8 km/hr
খ
খ) 58.8 km/hr
গ
গ) 62.8 km/hr
ঘ
ঘ) 64.8 km/hr

ব্যাখ্যা

Length of train = 180 m
Length of platform = (3 ×180)m = 540m

∴Speed of train (180 + 540)/40 m/sec
= 720/40 m/sec
= 18 × (18/5) km/hr
= 64.8 km/hr

৯৯১.

A train running at the speed of 60 kmph crosses a 200m long platform in 27 seconds. What is the length of the train?

ক
ক) 220 metres
খ
খ) 250 metres
গ
গ) 180 metres
ঘ
ঘ) 350 metres

ব্যাখ্যা

Speed = 60 × (1000/3600)m/sec
= 50/3m/sec

Time = 27 sec

Let the length of the train be x metres
Now
(x + 200)/27 = 50/3
3(x + 200) = (27 × 50)
3x + 600 = 1350
3x = 1350 - 600
3x = 750
x = 250

৯৯২.

Rina and Trina walk from same point in opposite directions at the rate 3 km/hr and 2 km/hr respectively. How far will they be from each other after 3 hrs?

ক
ক) 9 km
খ
খ) 12 km
গ
গ) 15 km
ঘ
ঘ) 18 km

ব্যাখ্যা

Question: Rina and Trina walk from same point in opposite directions at the rate 3 km/hr and 2 km/hr respectively. How far will they be from each other after 3 hrs?

Solution:
Since Rina and Trina walk in opposite directions.
Distance covered per hour = Relative speed × Time
= (3 + 2) × 1 = 5 km [opposite direction]

∴ Distance covered in 3 hours = 5 × 3 = 15 km.

৯৯৩.

A train running at the speed of 90 km/hr crosses a pole in 15 seconds. What is the length of the train?

ক
300 meters
খ
400 meters
গ
375 meters
ঘ
425 meters

ব্যাখ্যা

Question: A train running at the speed of 90 km/hr crosses a pole in 15 seconds. What is the length of the train?

Solution:
Speed = 90 km/h = (90 × 1000)/3600 = 25 m/s

We know,
Length = speed × time = 25 × 15 = 375 meters

So the length of the train is 375 meters.

৯৯৪.

Two boats A and B start towards each other from two places, 108 km apart. Speed of the boats A and B in still water are 12 km/h and 15 km/h respectively. If A proceeds down and B up the stream, they will meet after:

ক
3 hours
খ
4 hours
গ
5 hours
ঘ
6 hours

ব্যাখ্যা

Let the speed of the stream be x kmph and both the boats meet after y hour.
According to the question,
(12 + x) × y + (15 - x) × y = 108
Or, 12y + 15y = 108
Or, 27y = 108
∴ y = 108/27 = 4 hours

৯৯৫.

A train 108 meter long is moving at a speed of 50 km/hr. It crosses a train 112 meter long coming from the opposite direction in 6 seconds. What is the speed of the second train?

ক
ক) 82 kmph
খ
খ) 58 kmph
গ
গ) 44 kmph
ঘ
ঘ) 76 kmph

ব্যাখ্যা

৯৯৬.

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. What is the downstream speed in km/hr?

ক
5 km/hr
খ
15 km/hr
গ
20 km/hr
ঘ
25 km/hr

ব্যাখ্যা

Question: 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. What is the downstream speed in km/hr?

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

ATQ,
30/(15 + x) + 30/(15 - x) = 4(1/2)
Or, 900/(225 - x²) = 9/2
Or, 9x² = 225
Or, x² = 25
∴ x = 5 km/hr

∴ The downstream speed = (15 + 5) km/hr = 20 km/hr

৯৯৭.

৩০ কিলোমিটার/ঘণ্টা গতিবেগে চলে ৮০ মিটার লম্বা একটি ট্রেন একটি ব্রিজ অতিক্রম করে। যদি ব্রিজটি অতিক্রম করতে ট্রেনটির ৩৬ সেকেন্ড সময় লাগে তবে ব্রিজের দৈর্ঘ্য কত?

ক
ক) ১৮০ মিটার
খ
খ) ২২০ মিটার
গ
গ) ২০০ মিটার
ঘ
ঘ) ২৪০ মিটার

ব্যাখ্যা

ধরি
ব্রিজের দৈর্ঘ্য = ক মিটার

ট্রেনের গতিবেগ = ৩০ কিলোমিটার/ঘণ্টা
= (৩০ × ১০০০)/৩৬০০
= ৫০/৬ মিটার/সেকেন্ড

প্রশ্নমতে,
(৮০ + ক)/(৫০/৬) = ৩৬
৮০ + ক = ৩৬ × (৫০/৬)
৮০ + ক = ৩০০
ক = ৩০০ - ৮০
ক = ২২০ মিটার

৯৯৮.

In one hour, a boat goes 17 km/hr along the stream and 9 km/hr against the stream. The speed of the boat in still water (in km/h) is-

ক
17 km/h
খ
13 km/h
গ
8 km/h
ঘ
4 km/h

ব্যাখ্যা

Question: In one hour, a boat goes 17 km/hr along the stream and 9 km/hr against the stream. The speed of the boat in still water (in km/h) is-

Solution:
Let x be the boat speed.
And, y be the stream speed.

Down stream speed = x + y = 17 km/h
Upper stream speed = x - y = 9 km/h

Now, x + y + x - y = 17 + 9
⇒ 2x = 26
⇒ x = 13

∴ The speed of the boat in still water is 13 km/h

৯৯৯.

Ratul covers half of his journey at 3 km/h and the remaining half at 6 km/h. His average speed is-

ক
ক) 4 kmph
খ
খ) 4.5 kmph
গ
গ) 5 kmph
ঘ
ঘ) 5.5 kmph

ব্যাখ্যা

Question: Ratul covers half of his journey at 3 km/h and the remaining half at 6 km/h. His average speed is-

Solution:
ধরি, 3 km/h বেগে অতিক্রম করে x কিমি ও 6 km/h বেগে অতিক্রম করে x কিমি।

গড় বেগ = (2x)/{(x/3) + (x/6)}
= (2x)/(3x/6)
= 2x × (6/3x)
= 4 kmph

১,০০০.

In a race of 1200 m, X can beat Y by 120 m. In a 600 m, Y beats Z by 60 m. In a race of 600 m. X will beat Z by-

ক
95 m
খ
104 m
গ
114 m
ঘ
125 m

ব্যাখ্যা

Question: In a race of 1200 m, X can beat Y by 120 m. In a 600 m, Y beats Z by 60 m. In a race of 600 m. X will beat Z by-

Solution:
While X covers 1200 Y covers 1080
while X covers 600 Y covers 540m

While Y covers 600, Z covers 540m
While Y covers 540, Z covers (540 × 540)/600
= 486 m

∴ in a 600 m race X will beat Z by = (600 - 486) m
= 114 m