Time and Speed - Train and Boat

PrepBank · পাতা ১২ / ১৫ · ১,১০১–১,২০০ / ১,৪৩৯

১,১০১.

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

ক
6 km/hr
খ
2.5 km/hr
গ
3.5 km/hr
ঘ
4 km/hr

সঠিক উত্তর: ঘ

4 km/hr

উত্তর

সঠিক উত্তর: ঘ

4 km/hr

ঘ

ব্যাখ্যা

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

Solution:
ধরি, আমানের বেগ x km/hr এবং বিজয়ের বেগ y km/hr.
6(x + y) = 60
⇒ x + y = 10
⇒ 2x + 2y = 20

5 (2x/3 + 2y) = 60
⇒ 2x/3 + 2y = 12
⇒ 2x + 6y = 36

2x + 6y - 2x - 2y = 36 - 20
⇒ 4y = 16
∴ y = 16/4
= 4 km/hr

১,১০২.

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

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

সঠিক উত্তর: ঘ

ঘ) 2.5 km/hr

উত্তর

সঠিক উত্তর: ঘ

ঘ) 2.5 km/hr

ঘ

ব্যাখ্যা

Given that, time is taken to travel upstream = 2 × times taken to travel downstream
When the distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream = x
Then speed downstream 2x
we have,
1/2(x + 2x) = speed in still water
⇒ 1/2(3x)=7.5
⇒ 3x = 15
⇒ x = 5
i.e., speed upstream = 5 km/hr
Rate of stream = 1/2(2x - x)
= x/2
= 5/2
= 2.5 km/hr.

১,১০৩.

If Titu walks at 14 km/hr instead of 10 km/hr, he can cover 20 km more. The actual distance travelled by him is -

ক
80 km
খ
70 km
গ
56 km
ঘ
50 km

সঠিক উত্তর: ঘ

50 km

উত্তর

সঠিক উত্তর: ঘ

50 km

ঘ

ব্যাখ্যা

Question: If Titu walks at 14 km/hr instead of 10 km/hr, he can cover 20 km more. The actual distance travelled by him is -

Solution:
টিটুর বেগ বৃদ্ধি পায় = ১৪ - ১০ কি.মি./ঘণ্টা
= ৪ কি.মি./ঘণ্টা

সে মোট হাটে = ২০/৪ ঘণ্টা = ৫ ঘণ্টা

প্রকৃত বেগে ১ ঘণ্টায় যায় ১০ কি.মি.
∴ প্রকৃত বেগে ৫ ঘণ্টায় যায় (১০ × ৫) কি.মি.
= ৫০ কি.মি.

প্রকৃতপক্ষে দূরত্ব হলো ৫০ কি.মি.

১,১০৪.

The total time taken by a motorboat to go 40 km downstream and return upstream is 4.5 hours. If the boat's speed in still water is 20 km/h, find the speed of the stream.

ক
6.67 km/hours
খ
5.67 km/hours
গ
4.99 km/hours
ঘ
8.22 km/hours
ঙ
None of the above

সঠিক উত্তর: ক

6.67 km/hours

উত্তর

সঠিক উত্তর: ক

6.67 km/hours

ক

ব্যাখ্যা

Question: The total time taken by a motorboat to go 40 km downstream and return upstream is 4.5 hours. If the boat's speed in still water is 20 km/h, find the speed of the stream.
(একটি মোটরবোটকে ৪০ কিলোমিটার প্রবাহের দিকে যেতে এবং ফেরত আসতে ৪.৫ ঘণ্টা সময় লাগে। যদি নৌকার গতির পরিমাণ স্থির পানিতে ২০ কিলোমিটার প্রতি ঘণ্টা হয়, তাহলে স্রোতের বেগ কত হবে?)

Solution:
ধরা যাক, স্রোতের বেগ = x km/h
তাহলে,
স্রোতের অনুকূলে বেগ = (20 + x) km/h
স্রোতের প্রতিকূলে বেগ = (20 - x) km/h

প্রশ্নমতে
40/(20 + x) + 40/(20 - x) = 4.5
⇒ 1600/(400 - x²) = 9/2
⇒ 9(400 - x²) = 2 × 1600
⇒ 3600 - 3200 = 9x²
⇒ (3x)² = 20²
⇒ 3x = 20
⇒ x = 20/3
∴ x = 6.67

∴ স্রোতের বেগ হল 6.67 km/h

১,১০৫.

The average speed of a car is one-third the speed of an express train. The train covers 1800 km in 15 hours. How much distance will the car cover in 36 minutes?

ক
14 km
খ
18 km
গ
20 km
ঘ
24 km

সঠিক উত্তর: ঘ

24 km

উত্তর

সঠিক উত্তর: ঘ

24 km

ঘ

ব্যাখ্যা

Question: The average speed of a car is one-third the speed of an express train. The train covers 1800 km in 15 hours. How much distance will the car cover in 36 minutes?

Solution:
ট্রেনের গতিবেগ = অতিক্রান্ত দূরত্ব/সময়
= 1800 কিমি/15 ঘন্টা
= 120 কিমি/ঘন্টা

এখন, গাড়ির গতিবেগ ট্রেনের গতিবেগের এক-তৃতীয়াংশ।

∴ গাড়ির গতিবেগ = ট্রেনের গতিবেগ × 1/3
= 120 কিমি/ঘন্টা × 1/3
= 40 কিমি/ঘন্টা

∴ গাড়ির অতিক্রান্ত দূরত্ব = গাড়ির গতিবেগ × সময়
= 40 কিমি/ঘন্টা × 36 মিনিট
= 40 কিমি/ঘন্টা × (36/60) ঘন্টা
= 40 কিমি/ঘন্টা × 0.6 ঘন্টা
= 24 কিমি

সুতরাং, গাড়িটি 36 মিনিটে 24 কিমি দূরত্ব অতিক্রম করবে।

১,১০৬.

The speed of a boat in still water in 17 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:

ক
ক) 3 km
খ
খ) 3.6 km
গ
গ) 4 km
ঘ
ঘ) 4.2 km

সঠিক উত্তর: গ

গ) 4 km

উত্তর

সঠিক উত্তর: গ

গ) 4 km

গ

ব্যাখ্যা

Question: The speed of a boat in still water in 17 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:

Solution:
Speed downstream = (17 + 3) kmph = 20 kmph.
Distance travelled = 20 × (12/60) km = 4 km

১,১০৭.

A train of length 200 meters crosses a man running at 10 km/hr in the same direction in 10 seconds. What is the speed of the train?

ক
72 km/hr
খ
62 km/hr
গ
80 km/hr
ঘ
85 km/hr
ঙ
82 km/hr

সঠিক উত্তর: ঙ

82 km/hr

উত্তর

সঠিক উত্তর: ঙ

82 km/hr

ঙ

ব্যাখ্যা

Question: A train of length 200 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 = 200/10

We will convert it into Km/hr
(200/10) × (18/5) = 72 km/hr

Now, let the speed of the train is X km/hr.
So, the relative speed, 72 km/hr = X km/hr - 10 km/hr
⇒ X - 10 = 72
⇒ X = 72 + 10
∴ X = 82 km/hr

১,১০৮.

Saiful traveled 2/3 as km on foot as by water and 1/3 as km on bus as by water. If he covered a total of 48 km, how many km did he travel on foot?

ক
8 km
খ
16 km
গ
12 km
ঘ
24 km

সঠিক উত্তর: খ

16 km

উত্তর

সঠিক উত্তর: খ

16 km

খ

ব্যাখ্যা

Question: Saiful traveled 2/3 as km on foot as by water and 1/3 as km on bus as by water. If he covered a total of 48 km, how many km did he travel on foot?

Solution:
Let, he traveled x km by water, 2x/3 km on foot and x/3 km bus

ATQ,
x + (2x/3) + (x/3) = 48
⇒ (3x + 2x + x)/3 = 48
⇒ 6x = 144
⇒ x = 24

So, traveled (2 × 24)/3 = 16 km on foot.

১,১০৯.

How many seconds will a 800 meter long train take to cross a man walking with a speed of 6 km/h in the direction of the moving train if the speed of the train is 78 km/h?

ক
36 sec
খ
35 sec
গ
40 sec
ঘ
48 sec

সঠিক উত্তর: গ

40 sec

উত্তর

সঠিক উত্তর: গ

40 sec

গ

ব্যাখ্যা

Question: How many seconds will a 800 meter long train take to cross a man walking with a speed of 6 km/h in the direction of the moving train if the speed of the train is 78 km/h?

Solution:
Speed of the train relative to man = (78 - 6) km/h
= 72 km/h
= (72 × 5/18) m/sec
= 20 m/sec

Time taken to pass the man = 800/20 sec
= 40 sec

১,১১০.

A man covers the journey from station A to station B at a uniform speed of 36 kmph and returns to A with a uniform speed of 45 kmph, his average speed for the whole journey is:

ক
40 kmph
খ
42 kmph
গ
44 kmph
ঘ
28 kmph
ঙ
None of the above

সঠিক উত্তর: ক

40 kmph

উত্তর

সঠিক উত্তর: ক

40 kmph

ক

ব্যাখ্যা

Question: A man covers the journey from station A to station B at a uniform speed of 36 kmph and returns to A with a uniform speed of 45 kmph, his average speed for the whole journey is:

Solution:
The average speed for this case is given by, 2xy/(x + y)

Here x and y are two different speeds.

∴ Average speed = 2xy/(x + y)
= (2 × 36 × 45)/(36 + 45)
= (36 × 90)/81
= 40 kmph

Hence, his average speed for the whole journey is 40 kmph

১,১১১.

In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is:

ক
ক) 86 sec
খ
খ) 80 sec
গ
গ) 76 sec
ঘ
ঘ) None of these

সঠিক উত্তর: খ

খ) 80 sec

উত্তর

সঠিক উত্তর: খ

খ) 80 sec

খ

ব্যাখ্যা

B runs 45/2 m in 6 sec.
B covers 300 m in (6x2)/45 x300 sec
= 80 sec

১,১১২.

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

ক
ক) 8 km/hr.
খ
খ) 10 km/hr.
গ
গ) 12 km/hr.
ঘ
ঘ) 14 km/hr.

সঠিক উত্তর: গ

গ) 12 km/hr.

উত্তর

সঠিক উত্তর: গ

গ) 12 km/hr.

গ

ব্যাখ্যা

Distance = 6 Km.
Time = 45 minutes.
He covers half of the distance (3 km) in 2/3 of the time

i.e. (2 × 45)/3 = 30 minutes = 1/2 hour.
Now, Time = 15 minutes = 15/60 = 1/4 hours.

Distance = 3 km.
Speed = 3/(1/4) = 12 Kmph.

১,১১৩.

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

ক
ক) 1.5 km/hr
খ
খ) 1 km/hr
গ
গ) 2.5 km/hr
ঘ
ঘ) 2 km/hr
ঙ
ঙ) 5.2 km/hr

সঠিক উত্তর: খ

খ) 1 km/hr

উত্তর

সঠিক উত্তর: খ

খ) 1 km/hr

খ

ব্যাখ্যা

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

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

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

১,১১৪.

A man can reach a certain place in 40 hours. If he reduces his speed by 1/15th, he goes 5 km less in that time. Find the total distance covered by him.

ক
ক) 60 km
খ
খ) 85 km
গ
গ) 75 km
ঘ
ঘ) 52 km

সঠিক উত্তর: গ

গ) 75 km

উত্তর

সঠিক উত্তর: গ

গ) 75 km

গ

ব্যাখ্যা

Let,
Speed = x km/h
So,
40x - 40x × (14/15) = 5
Or, 40x - 112x/3 = 5
Or, 120x - 112x = 15
Or, x = 15/8
∴ distance covered = (15 × 40)/8 = 75 km

১,১১৫.

A boatman can row 96 km downstream in 8 hour. If the speed of the current is 4 km/hr, then find the time required to cover 8 km upstream?

ক
ক) 1 hr
খ
খ) 4 hrs
গ
গ) 2 hrs
ঘ
ঘ) 6 hrs
ঙ
ঙ) 3 hrs

সঠিক উত্তর: গ

গ) 2 hrs

উত্তর

সঠিক উত্তর: গ

গ) 2 hrs

গ

ব্যাখ্যা

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

১,১১৬.

A boat has a crack in its hull which is leaking water into the boat and could sink the boat in 6 hours. The boat has a pump which can pump the water out in 8 hours. If the boat is 168 km away from the shore and the pump is running what is the minimum speed the boat should run at so that it can reach the shore before sinking?

ক
5 km/hour
খ
6 km/hour
গ
7 km/hour
ঘ
8 km/hour
ঙ
None of these

সঠিক উত্তর: গ

7 km/hour

উত্তর

সঠিক উত্তর: গ

7 km/hour

গ

ব্যাখ্যা

Question: A boat has a crack in its hull which is leaking water into the boat and could sink the boat in 6 hours. The boat has a pump which can pump the water out in 8 hours. If the boat is 168 km away from the shore and the pump is running what is the minimum speed the boat should run at so that it can reach the shore before sinking?

Solution:
ছিদ্রপথে জাহজে ১ ঘণ্টায় পানি প্রবেশ করে = ১/৬ অংশ
পাম্প দ্বারা ১ ঘণ্টায় পানি বের হয় = ১/৮ অংশ
∴ ছিদ্রপথ ও পাম্প দ্বারা ১ মিনিটে পূর্ণ হয় = (১/৬) - (১/৮) অংশ
= (৪ - ৩)/২৪ অংশ
= ১/২৪ অংশ

∴ সম্পূর্ণ জাহাজ পূর্ণ হবে ২৪ ঘণ্টায়। তাই জাহাজটিকে ২৪ ঘণ্টায় ১৬৮ কিলোমিটার অতিক্রম করতে হবে।
অতএব, বেগ = ১৬৮/ ২৪ কি.মি./ঘণ্টা
= ৭ কি.মি./ঘণ্টা

১,১১৭.

A train 130 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

ক
42.8 km/hr
খ
48.8 km/hr
গ
51.8 km/hr
ঘ
55.8 km/hr

সঠিক উত্তর: গ

51.8 km/hr

উত্তর

সঠিক উত্তর: গ

51.8 km/hr

গ

ব্যাখ্যা

Question: A train 130 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

Solution:
Speed of the train relative to man = 130/10 m/sec
= 13 m/sec
= (13 × 3600)/1000 km/hr
= 46.8 km/hr

Let,
The speed of the train be x km/hr.
∴ Relative speed = (x - 5) km/hr.
⇒ x - 5 = 46.8
∴ x = 51.8 km/hr.

১,১১৮.

Rina goes to school walking at 3 km/h and comes back home at 2 km/h. If she takes 5 hours in total for the round trip, how far is her school from her house?

ক
6 km
খ
7 km
গ
8 km
ঘ
9 km

সঠিক উত্তর: ক

6 km

উত্তর

সঠিক উত্তর: ক

6 km

ক

ব্যাখ্যা

Question: Rina goes to school walking at 3 km/h and comes back home at 2 km/h. If she takes 5 hours in total for the round trip, how far is her school from her house?

Solution:
মনে করি,
স্কুল থেকে বাসার দূরত্ব = x কি. মি.

∴ স্কুলে যাওয়ার পথে প্রয়োজনীয় সময় = দূরত্ব/সময় = x/3 ঘণ্টা
এবং
বাসায় ফেরার পথে প্রয়োজনীয় সময় = দূরত্ব/সময় = x/2 ঘণ্টা

প্রশ্নমতে,
(x/3) + (x/2) = 5
⇒ (2x + 3x)/6 = 5
⇒ 5x/6 = 5
⇒ 5x = 6 × 5
⇒ 5x = 30
⇒ x = 30/5
⇒ x = 6

∴ স্কুল থেকে বাসার দূরত্ব = 6 কি. মি.

১,১১৯.

A train running at the speed of 120 km/h crosses a pole in 12 seconds. What is the length of the train?

ক
350 meter
খ
380 meter
গ
400 meter
ঘ
450 meter

সঠিক উত্তর: গ

400 meter

উত্তর

সঠিক উত্তর: গ

400 meter

গ

ব্যাখ্যা

Question: A train running at the speed of 120 km/h crosses a pole in 12 seconds. What is the length of the train?

Solution:
Speed = 120 km/h
= (120 × 5/18) m/sec
= 100/3 m/sec

∴ Length of the train = (100/3 × 12) m
= 400 m

১,১২০.

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

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

সঠিক উত্তর: গ

গ) 4 km/hr

উত্তর

সঠিক উত্তর: গ

গ) 4 km/hr

গ

ব্যাখ্যা

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

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

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

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

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

১,১২১.

A boat goes 8 km upstream in 24 minutes. The speed of the stream is 4 km/hr. The speed of boat in still water is -

ক
ক) 24 km/hr
খ
খ) 25 km/hr
গ
গ) 26 km/hr
ঘ
ঘ) 22 km/hr

সঠিক উত্তর: ক

ক) 24 km/hr

উত্তর

সঠিক উত্তর: ক

ক) 24 km/hr

ক

ব্যাখ্যা

Speed upstream = 8/(24/60)
= 20 km/hr.
Speed of the stream = 4 km/hr.
Speed of boat in still water = (20 + 4)
= 24 km/hr.

১,১২২.

A clock slows down by one minute every 24 hours. How long will it take to slow down by one hour?

ক
ক) 60 days
খ
খ) 45 days
গ
গ) 30 days
ঘ
ঘ) 75 days

সঠিক উত্তর: ক

ক) 60 days

উত্তর

সঠিক উত্তর: ক

ক) 60 days

ক

ব্যাখ্যা

Since the clock takes 24 hours or 1 day to slow down by 1 minute.
So, it will take 60 days to slow down 60 minutes or 1 hour.

১,১২৩.

A man can swim in still water at 8 km/hr. If the river is flowing at 2km/hr he takes 80 minutes to reach a place and return back, how far is the place?

ক
4 km
খ
3 km
গ
4.5 km
ঘ
5 km

সঠিক উত্তর: ঘ

5 km

উত্তর

সঠিক উত্তর: ঘ

5 km

ঘ

ব্যাখ্যা

Question: A man can swim in still water at 8 km/hr. If the river is flowing at 2km/hr he takes 80 minutes to reach a place and return back, how far is the place?

Solution:
Let the place is x km far.

Speed downstream = 8 + 2 = 10 km/hr
Speed upstream = 8 - 2 = 6 km/hr

Time = Distance/Speed

So, as per question;
x/6 + x/10 = 80/60
⇒ (5x + 3x)/30 = 4/3
⇒ 8x/30 = 4/3
⇒ 24x = 120
∴ x = 120/24 = 5 km

১,১২৪.

A train crosses a bridge and a bike standing on the bridge in 40 seconds, 25 seconds respectively. What is the length of the bridge if the speed of the train is 50.4km/hr?

ক
180
খ
210
গ
183
ঘ
255

সঠিক উত্তর: খ

210

উত্তর

সঠিক উত্তর: খ

210

খ

ব্যাখ্যা

Given that,
The speed of the train = 50.4km/hr
= 50.4 x 5/18 m/sec
= 14 m/sec
The train crosses a bike(standing object) in 25 seconds.
Then,
Length of the train = (14 x 25)m
= 350 m.
Now,
let, the length of the bridge is X m.
the train crosses the bridge in 40 seconds.
Then, (X + 350)/40 = 14
⇒ X + 350 = 14 x 40
⇒ X = 560 - 350
⇒ X = 210
Hence the bridge is 210m long.

১,১২৫.

A man can row upstream at 24km/hr and downstream at 16km/hr. The man rowing speed in still water is?

ক
20 km/hr
খ
18 km/hr
গ
15 km/hr
ঘ
10 km/hr

সঠিক উত্তর: ক

20 km/hr

উত্তর

সঠিক উত্তর: ক

20 km/hr

ক

ব্যাখ্যা

Question: A man can row upstream at 24km/hr and downstream at 16km/hr. The man rowing speed in still water is?

Solution:
Let, x = downstream speed and y = upstream speed
We know,
Speed of boat in still water = (x + y)/2
∴ Boat's speed = (24 + 16)/2 = 40/2 = 20 km/hr.

১,১২৬.

In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr?

ক
2.5 second
খ
4.25 second
গ
5 second
ঘ
12.5 second

সঠিক উত্তর: ক

2.5 second

উত্তর

সঠিক উত্তর: ক

2.5 second

ক

ব্যাখ্যা

Question: In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr?

Solution:
Speed = 144 km/hr
= (144 × 1000)/3600 m/sec
= 40 m/sec

∴Required Time = (Distance/speed) sec
= (100/40) sec
= 2.5 sec.

১,১২৭.

A man takes 50 minutes to cover a certain distance at a speed of 6 km/hr. If he walks with a speed of 10 km/hr, he covers the same distance in-

ক
ক) 10 min
খ
খ) 20 min
গ
গ) 30 min
ঘ
ঘ) 40 min

সঠিক উত্তর: গ

গ) 30 min

উত্তর

সঠিক উত্তর: গ

গ) 30 min

গ

ব্যাখ্যা

Distance = Speed×Time
Distance = (6× 50)/60)km
Distance = 5 km
∴ Required time
= Distance/ Speed
= 5/10 hrs
= 1/2 hrs
= 30 min

১,১২৮.

A, B and C are the three contestants in one km race. If A can give B a start of 40 metres and A can give C a start of 64 metres, how many metres start can B give C?

ক
35 m
খ
25 m
গ
20 m
ঘ
22 m

সঠিক উত্তর: খ

25 m

উত্তর

সঠিক উত্তর: খ

25 m

খ

ব্যাখ্যা

While A covers 1000 m, B covers (1000 - 40) m = 960 m
And C covers (1000 - 64) m = 936 m.

When B covers 960 m, C covers 936 m.
When B covers 1000 m, C covers
= (936/960) × 1000 = 975 m

∴ B can give C a start of
(1000 - 975) = 25 m.

১,১২৯.

The ratio between the speeds of a bus and bike is 5 : 8. If the bus travels 120 km in 2 hours, find the speed of the bike.

ক
88 km/h
খ
86 km/h
গ
96 km/h
ঘ
98 km/h

সঠিক উত্তর: গ

96 km/h

উত্তর

সঠিক উত্তর: গ

96 km/h

গ

ব্যাখ্যা

Question: The ratio between the speeds of a bus and bike is 5 : 8. If the bus travels 120 km in 2 hours, find the speed of the bike.

Solution:
Let,
the speed of bus and bike is 5x and 8x.

Speed of bus = 120/2
= 60 km/h

ATQ,
5x = 60
⇒ x= 60/5
∴ x = 12

Speed of bike = 8x = (8 × 12) = 96 km/h

১,১৩০.

A man walking at a speed of 3 km/hr. crosses a square field diagonally in 5 minutes. What is the area of the field (in m²) ?

ক
ক) 32550 m²
খ
খ) 32150 m²
গ
গ) 31520 m²
ঘ
ঘ) 31250 m²

সঠিক উত্তর: ঘ

ঘ) 31250 m²

উত্তর

সঠিক উত্তর: ঘ

ঘ) 31250 m²

ঘ

ব্যাখ্যা

Question:
A man walking at a speed of 3 km/hr. crosses a square field diagonally in 5 minutes. What is the area of the field (in m²) ?

Solution:
Man walks in 5 mins = 3 × (5/60) = 1/4 km = 250m

So, the length of the diagonal of the square field = 250m
Let the measure of each side of the square field be X.

According to the question,
X√2 = 250
⇒ X = 250√2
⇒ X² = 31250

∴ The area of the square field is 31250 m².

১,১৩১.

A train crossed a platform in 45 seconds travelling with a speed of 36 km/h. If the length of train is 200 meters, then what will be the length (in meters) of the platform?

ক
250
খ
200
গ
300
ঘ
350

সঠিক উত্তর: ক

250

উত্তর

সঠিক উত্তর: ক

250

ক

ব্যাখ্যা

Question: A train crossed a platform in 45 seconds travelling with a speed of 36 km/h. If the length of train is 200 meters, then what will be the length (in meters) of the platform?

Solution:
Speed = 36 km/hr
= (36 × 1000)/3600 m/s
= 10 m/s

In 45 seconds, the train travelled = 45 × 10 m
= 450 m

length (in meters) of the platform = 450 - 200
= 250 m

১,১৩২.

If the clock in the mirror shows 5:25, what is the time on the real clock?

ক
8:35
খ
5:35
গ
7:35
ঘ
6:35

সঠিক উত্তর: ঘ

6:35

উত্তর

সঠিক উত্তর: ঘ

6:35

ঘ

ব্যাখ্যা

Question: If the clock in the mirror shows 5:25, what is the time on the real clock?

Solution:
∴ Actual time = 11:60 - time in the mirror
= 11:60 - 5:25
= 6:35

১,১৩৩.

ক : খ = ৪ : ৫, খ : গ = ৬ : ৭ হলে ক : খ : গ = কত?

ক
ক) ২৪ : ৩৫ : ৪৫
খ
খ) ২৪ : ৩০ : ৩৫
গ
গ) ২৪ : ৩০ : ৪০
ঘ
ঘ) ২১ : ৩০ : ৩৫

সঠিক উত্তর: খ

খ) ২৪ : ৩০ : ৩৫

উত্তর

সঠিক উত্তর: খ

খ) ২৪ : ৩০ : ৩৫

খ

ব্যাখ্যা

দেয়া আছে,
ক : খ = ৪ : ৫ = ৪ × ৬ : ৫ × ৬ = ২৪ : ৩০
খ : গ = ৬ : ৭ = ৬ × ৫ : ৭ × ৫ = ৩০ : ৩৫
ক : খ : গ = ২৪ : ৩০ : ৩৫

১,১৩৪.

A man complete a journey in 5 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) 48km
খ
খ) 72km
গ
গ) 96km
ঘ
ঘ) 108km

সঠিক উত্তর: গ

গ) 96km

উত্তর

সঠিক উত্তর: গ

গ) 96km

গ

ব্যাখ্যা

Question: A man complete a journey in 5 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.

Solution:
Let
The total journey x km
Now
{(1/2)x/16} + {(1/2)x/24} = 5
⇒ (x/16) + (x/24) = 10
⇒ (3x + 2x)/48 = 10
⇒ 5x/48 = 10
⇒ x = (10 × 48)/5
x = 96km

১,১৩৫.

Hasan rides his bike at a speed of 24 km/h and arrives at his office 5 minutes late. If he had traveled 25% faster, he would have arrived 4 minutes before the scheduled time. What is the distance between his house and his office (in km)?

ক
18 km
খ
24 km
গ
36 km
ঘ
40 km
ঙ
none of these

সঠিক উত্তর: ক

18 km

উত্তর

সঠিক উত্তর: ক

18 km

ক

ব্যাখ্যা

Question: Hasan rides his bike at a speed of 24 km/h and arrives at his office 5 minutes late. If he had traveled 25% faster, he would have arrived 4 minutes before the scheduled time. What is the distance between his house and his office (in km)?

Solution:
দেওয়া আছে, হাসানের প্রাথমিক গতিবেগ = 24 কিমি/ঘন্টা

25% গতিবেগ বৃদ্ধি পেলে নতুন গতিবেগ হবে = 24 + (24 × 25%)
= 24 + 6 = 30 কিমি/ঘন্টা

মনে করি, বাড়ি থেকে অফিসের দূরত্ব x কিমি।
∴ প্রথম ক্ষেত্রে সময় লাগে = x/24 ঘন্টা
দ্বিতীয় ক্ষেত্রে সময় লাগে = x/30 ঘন্টা

সময়ের পার্থক্য = 5 মিনিট (দেরি) + 4 মিনিট (আগে) = 9 মিনিট
= 9/60 ঘণ্টা

প্রশ্নমতে,
(x/24) - (x/30) = 9/60
⇒ (5x - 4x) /120 = 3/20
⇒ x/120 = 3/20
⇒ x = (3 × 120)/20
⇒ x = 3 × 6
∴ x = 18

সুতরাং, তার বাড়ি থেকে অফিসের দূরত্ব 18 কিমি।

১,১৩৬.

Two trains, each 100 meters long, are running on parallel tracks in opposite directions. If their speeds are 72 km/h and 54 km/h, how long will it take them to cross each other completely?

ক
5 seconds
খ
5.2 seconds
গ
5.5 seconds
ঘ
5.7 seconds

সঠিক উত্তর: ঘ

5.7 seconds

উত্তর

সঠিক উত্তর: ঘ

5.7 seconds

ঘ

ব্যাখ্যা

Question: Two trains, each 100 meters long, are running on parallel tracks in opposite directions. If their speeds are 72 km/h and 54 km/h, how long will it take them to cross each other completely?

Solution:
Train 1 length = 100 meters
Train 2 length = 100 meters
Total distance = (100 + 100) = 200 meters

Speed of Train 1 = 72 km/h = 72 × (5/18) m/s = 20 m/s
Speed of Train 2 = 54 km/h = 54 × (5/18) m/s = 15 m/s

Relative speed = (20 + 15) = 35 m/s

Time = (200/35) = 5.71 seconds
= 5.7 seconds

১,১৩৭.

A train moving at 54 km/hr crosses a bridge in 40 seconds. The length of train is 150 meters. Find the length of the bridge.

ক
425 m
খ
445 m
গ
475 m
ঘ
450 m

সঠিক উত্তর: ঘ

450 m

উত্তর

সঠিক উত্তর: ঘ

450 m

ঘ

ব্যাখ্যা

Question: A train moving at 54 km/hr crosses a bridge in 40 seconds. The length of train is 150 meters. Find the length of the bridge.

Solution:
Speed of train= 54 km/h= 54 × (5/18) = 3 × 5 = 15m/second
Time taken = 40 seconds
Distance covered= speed × Time
Distance = 15× 40= 600 m

Distance covered = Length of Train + Length of Bridge
600 = 150 + Length of Bridge
Length of Bridge = 600 - 150 = 450 m

১,১৩৮.

A 207m long train running at the speed of 62 km/hour crosses another train running in opposite direction at the speed of 38 km/hour in 18 seconds. The length of the other train -

ক
230
খ
267
গ
279
ঘ
293
ঙ
300

সঠিক উত্তর: ঘ

293

উত্তর

সঠিক উত্তর: ঘ

293

ঘ

ব্যাখ্যা

Let the length of the other train be x meter.
We have,
t = ( s₁ + s₂ ) / ( v₁ + v₂ )
or, 18 = 18 ( 207 + x ) / { 5 ( 62 + 38 ) }
or, 207 + x = ( 100 × 5 × 18 ) 18
or, x = 500 - 207 = 293

১,১৩৯.

If a man goes 32 km downstream in 4 hours and returns against the stream in 16 hours, then the speed of the stream in km/h is -

ক
6 km/h
খ
5 km/h
গ
4 km/h
ঘ
3 km/h

সঠিক উত্তর: ঘ

3 km/h

উত্তর

সঠিক উত্তর: ঘ

3 km/h

ঘ

ব্যাখ্যা

Question: If a man goes 32 km downstream in 4 hours and returns against the stream in 16 hours, then the speed of the stream in km/h is -

Solution:
Downstream speed = 32/4 = 8 km/h
Upstream speed = 32/16 = 2 km/h

∴ Speed of the stream = (8 - 2)/2 = 3 km/h

১,১৪০.

A 100 m long train is going at a speed of 108 km/h. It will cross a 140 m long tunnel in-

ক
15 sec
খ
12 sec
গ
8 sec
ঘ
18 sec

সঠিক উত্তর: গ

8 sec

উত্তর

সঠিক উত্তর: গ

8 sec

গ

ব্যাখ্যা

Question: A 100 m long train is going at a speed of 108 km/h. It will cross a 140 m long tunnel in-

Solution:
Given,
Speed of the train = 108 km/h
= (108 × 5/18) m/sec
= 30 m/sec

∴ Total distance covered = (100 + 140) m
= 240 m

∴ Required time = (240 ÷ 30) sec
= 8 sec

১,১৪১.

A train running at a speed of 72 km/hr crosses a platform double its length in 45 seconds. What is the length of the platform in metres?

ক
400m
খ
650m
গ
600m
ঘ
800m

সঠিক উত্তর: গ

600m

উত্তর

সঠিক উত্তর: গ

600m

গ

ব্যাখ্যা

Question: A train running at a speed of 72 km/hr crosses a platform double its length in 45 seconds. What is the length of the platform in metres?

Solution:
72 কি.মি = 72 × 1000 = 72000 মিটার
1 ঘণ্টা = 60 × 60 = 3600 সেকেন্ড

∴ 3600 সেকেন্ড যায় = 72000 মিটার
3600 সেকেন্ড যায় = 72000/3600 মিটার
45 সেকেন্ড যায় = {(72000 × 45)/3600} = 900 মিটার

ধরি, ট্রেনের দৈর্ঘ্য = x
প্লাটফর্মের দৈর্ঘ্য = 2x

প্রশ্নমতে,
⇒ x + 2x = 900
⇒ 3x = 900
⇒ x = 900/3
∴ x = 300

∴ প্লাটফর্মের দৈর্ঘ্য = 2x = 2 × 300 = 600 মিটার

১,১৪২.

৭ + ২ [- ৮ - {- ৩ - (- ২ - ৩)} - ৪] = কত?

ক
ক) - ২১
খ
খ) - ২০
গ
গ) - ১৪
ঘ
ঘ) - ১৬

সঠিক উত্তর: ক

ক) - ২১

উত্তর

সঠিক উত্তর: ক

ক) - ২১

ক

ব্যাখ্যা

৭ + ২ [- ৮ - {- ৩ - (- ২ - ৩)} - ৪]
= ৭ + ২ [- ৮ - {- ৩ - (- ৫)} - ৪]
= ৭ + ২ [- ৮ - {- ৩ + ৫} - ৪]
= ৭ + ২ [- ৮ - { + ২} - ৪]
= ৭ + ২ [- ৮ - ২ - ৪]
= ৭ + ২ [- ১ ৪]
= ৭ - ২৮
= - ২১

১,১৪৩.

A takes 3 hours more than B to walk d km, but if A doubles his speed, then he can make it in 1 hour less than B. How much time does A require for walking d km?

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

সঠিক উত্তর: ঘ

8 hours

উত্তর

সঠিক উত্তর: ঘ

8 hours

ঘ

ব্যাখ্যা

Question: A takes 3 hours more than B to walk d km, but if A doubles his speed, then he can make it in 1 hour less than B. How much time does A require for walking d km?

Solution:
Let,
B takes "t" hours to walk "d" km.

Then, A takes (t + 3) hours to walk d km.
With double speed, A will take = (1/2)(t + 3) hours.

ATQ,
t - (1/2)(t + 3) = 1
⇒ {2t - (t + 3)}/2 = 1
⇒ 2t - t - 3 = 2
∴ t = 5

∴ B takes 5 hours to walk d km.

∴ A takes (5 + 3) = 8 hours to walk d km.

১,১৪৪.

Four people are running around a circular ground from a point on the circumference at 9.00 am. For one round, these four persons take respectively 40, 50, 60 and 30 minutes. At what time will they meet together again?

ক
ক) 6.00 pm
খ
খ) 7.00 pm
গ
গ) 5.30 pm
ঘ
ঘ) 7.30 pm

সঠিক উত্তর: খ

খ) 7.00 pm

উত্তর

সঠিক উত্তর: খ

খ) 7.00 pm

খ

ব্যাখ্যা

Question: Four people are running around a circular ground from a point on the circumference at 9.00 am. For one round, these four persons take respectively 40, 50, 60 and 30 minutes. At what time will they meet together again?

Solution:
L.C.M. of 40, 50, 60 and 30
= 600 minutes
= 10 hours
So, they meet again 10 hours after they start.
They meet together again = 9.00 am + 10 hours
= 7.00 pm

১,১৪৫.

A boat's speed with the current is 17 km/hr and the speed of the current is 3.5 km/hr. What is the boat's speed against the current?

ক
10 km/h
খ
7 km/h
গ
13.5 km/h
ঘ
17 km/h

সঠিক উত্তর: ক

10 km/h

উত্তর

সঠিক উত্তর: ক

10 km/h

ক

ব্যাখ্যা

Question: A boat's speed with the current is 17 km/hr and the speed of the current is 3.5 km/hr. What is the boat's speed against the current?

Solution:
Given that,
Boat's speed with the current = 17 km/hr
Speed of the current = 3.5 km/hr

∴ Boat's speed in still water = speed with the current - speed of the current
= (17 - 3.5) km/hr
= 13.5 km/hr

∴ Boat's speed against the current = speed in still water - speed of the current
= (13.5 - 3.5) km/hr
= 10 km/hr

Therefore, the boat's speed against the current is 10 km/hr.

১,১৪৬.

Two trains are running in the same direction at 90 km/h and 60 km/h. The faster train crosses a man in the slower train in 18 seconds. What is the length of the faster train?

ক
120 meters
খ
135 meters
গ
150 meters
ঘ
180 meters

সঠিক উত্তর: গ

150 meters

উত্তর

সঠিক উত্তর: গ

150 meters

গ

ব্যাখ্যা

Question: Two trains are running in the same direction at 90 km/h and 60 km/h. The faster train crosses a man in the slower train in 18 seconds. What is the length of the faster train?

Solution:
Relative speed of train = (90 - 60) km/h
= 30 km/h
= (30 × 1000)/3600
= 25/3 m/s

∴ Distance covered = Speed × Time
= (25/3) × 18
= 150 meters

To overtake the person, the train has to travel a distance equal only to its own length.

So, Length of faster train = Distance covered = 150 meters.

১,১৪৭.

A train running at the speed of 72 km/h crosses a pole in 20 seconds. What is the length of the train?

ক
400 m
খ
360 m
গ
380 m
ঘ
420 m

সঠিক উত্তর: ক

400 m

উত্তর

সঠিক উত্তর: ক

400 m

ক

ব্যাখ্যা

Question: A train running at the speed of 72 km/h crosses a pole in 20 seconds. What is the length of the train?

Solution:
Given,
Speed = 72 km/h
= (72 × 5/18) m/sec
= 20 m/sec

Length of the train = Speed × Time
= 20 × 20 m
= 400 m

∴ Length of the train = 400 m

১,১৪৮.

A man’s speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man’s speed against the current is -

ক
ক) 8.5 km/hr
খ
খ) 9 km/hr
গ
গ) 10 km/hr
ঘ
ঘ) 12.5 km/hr

সঠিক উত্তর: গ

গ) 10 km/hr

উত্তর

সঠিক উত্তর: গ

গ) 10 km/hr

গ

ব্যাখ্যা

Man's speed with the current = 15 km/hr
Speed of the man + Speed of the current = 15 km/hr
Speed of the current is 2.5 km/hr
Hence, Speed of the man = 15 - 2.5 = 12.5 km/hr
Man's speed against the current = (Speed of the man - Speed of the current)
= 12.5 - 2.5
= 10 km/hr.

১,১৪৯.

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

ক
10 km/hr
খ
14 km/hr
গ
16 km/hr
ঘ
20 km/hr

সঠিক উত্তর: গ

16 km/hr

উত্তর

সঠিক উত্তর: গ

16 km/hr

গ

ব্যাখ্যা

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

Solution:
Speed of the boat in downstream = 55/2.5
= (55×10)/25
=22km/hr

Then,
speed of the boat in upstream = 22/2.2
= (22×10)/22
= 10km/hr

∴ Speed of the boat in still water = (22 + 10)/2
= 16km/hr

১,১৫০.

A person crosses an 800m long street in 5 minutes. What is his speed in km per hour?

ক
8.6
খ
9.6
গ
7.6
ঘ
8.2

সঠিক উত্তর: খ

9.6

উত্তর

সঠিক উত্তর: খ

9.6

খ

ব্যাখ্যা

Question: A person crosses an 800m long street in 5 minutes. What is his speed in km per hour?

Solution:
distance = 800m = 0.8km
time = 5 minutes = 5/60 = 1/12 hour

speed = distance/time
= 0.8/(1/12) km per hour
= 9.6 km per hour.

১,১৫১.

In covering a distance of 36 km, Hasan takes 4 hours more than Imran. If Hasan doubles his speed, he would take 2 hours less than Imran. What is Hasan’s speed?

ক
2 km/h
খ
3 km/h
গ
5 km/h
ঘ
6 km/h

সঠিক উত্তর: খ

3 km/h

উত্তর

সঠিক উত্তর: খ

3 km/h

খ

ব্যাখ্যা

Question: In covering a distance of 36 km, Hasan takes 4 hours more than Imran. If Hasan doubles his speed, he would take 2 hours less than Imran. What is Hasan’s speed?

Solution:
Let
Hasan's speed be x km/h

ATQ,
36/x - 36/2x = (4 + 2)
⇒ (72 - 36)/2x = 6
⇒ 36/2x = 6
⇒ 12x = 36
∴ x = 3

∴ Hasan's speed be 3 km/h

১,১৫২.

A train travelling at 60 kmph crosses a man in 6 seconds. What is the length of the train?

ক
ক) 180 metres
খ
খ) 120 metres
গ
গ) 150 metres
ঘ
ঘ) 100 meters
ঙ
ঙ) 324 metres

সঠিক উত্তর: ঘ

ঘ) 100 meters

উত্তর

সঠিক উত্তর: ঘ

ঘ) 100 meters

ঘ

ব্যাখ্যা

Speed in m/sec = 60×(5/18) = (50/3) m/sec
Time taken to cross the man = 6 secs
Therefore, Length of the train = (Speed×Time)
= (50/3)×6 = 100 metres

১,১৫৩.

A man can reach a certain place in 40 hours. If he reduces his speed by 1/15th, he goes 5 km less in that time. Find the total distance covered by him.

ক
ক) 60km
খ
খ) 85km
গ
গ) 75km
ঘ
ঘ) 52km

সঠিক উত্তর: গ

গ) 75km

উত্তর

সঠিক উত্তর: গ

গ) 75km

গ

ব্যাখ্যা

Let,
Speed = x km/h
So,
40x - 40x × (14/15) = 5
Or, 40x - 112x/3 = 5
Or, 120x - 112x = 15
Or, x = 15/8
∴ distance covered = (15 × 40)/8 = 75 km

১,১৫৪.

Nahid riding his bicycle covers 165 meters in 15 seconds. What is his speed in km per hour?

ক
ক) 36.9 km/hr
খ
খ) 38.6 km/hr
গ
গ) 39.6 km/hr
ঘ
ঘ) 36.6 km/hr

সঠিক উত্তর: গ

গ) 39.6 km/hr

উত্তর

সঠিক উত্তর: গ

গ) 39.6 km/hr

গ

ব্যাখ্যা

Question: Nahid riding his bicycle covers 165 meters in 15 seconds. What is his speed in km per hour?

Solution:
Given,
Distance = 165 meters.
TIme = 15 seconds

∴ Speed = Distance/Time
= 165/15 m/s
= (165 × 3600)/(15 × 1000) km/hr.
= 39.6 km/hr.

১,১৫৫.

Each wheel of a car is making 5 revolutions per second. If the diameter of a wheel is 84 cm, then the speed of the car in cm/sec would be:

ক
ক) 1420 cm/sec
খ
খ) 1320 cm/sec
গ
গ) 2640 cm/sec
ঘ
ঘ) 1020 cm/sec

সঠিক উত্তর: খ

খ) 1320 cm/sec

উত্তর

সঠিক উত্তর: খ

খ) 1320 cm/sec

খ

ব্যাখ্যা

Question: Each wheel of a car is making 5 revolutions per second. If the diameter of a wheel is 84 cm, then the speed of the car in cm/sec would be:

Solution:
Given,
the diameter of a wheel is 84 cm
the radius of a wheel is, r = 84/2 = 42

Circumference of the circle = 2πr
= 2 × (22/7)× 42
= 264 cm
Distance cover in 1 sec = 264 × 5
= 1320 cm/sec

১,১৫৬.

Pavel and Rajib started from the opposite direction of a 10km racing track. Their speed is 15kmph and 10kmph respectively. After which time they will meet if they start simultaneously?

ক
10 minutes
খ
25 minutes
গ
24 minutes
ঘ
20 minutes

সঠিক উত্তর: গ

24 minutes

উত্তর

সঠিক উত্তর: গ

24 minutes

গ

ব্যাখ্যা

Question: Pavel and Rajib started from the opposite direction of a 10km racing track. Their speed is 15kmph and 10kmph respectively. After which time they will meet if they start simultaneously?

Solution:

let, they will meet after t hour at point X.
in t hour,
A will cross = (15 × t) = 15t km
B will cross = (10 × t) = 10t km

ATQ,
15t + 10t = 10
25t = 10
t = 0.4 hours
= 24 minutes

১,১৫৭.

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

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

সঠিক উত্তর: গ

গ) 99 km/hr

উত্তর

সঠিক উত্তর: গ

গ) 99 km/hr

গ

ব্যাখ্যা

Speed of the first train :
= 150/15
= 10 m/s

Time taken by trains to cross each other = 8 sec

And, relative speed of two trains :
= (150 + 150)/8
= 37.5 m/s

∴ Speed of the second train :
= (37.5 - 10) × (3600/1000)
= (27.5 ×18)/5
= 99 km/hr

১,১৫৮.

A man reaches his office 20 min late, if he walks from his home at 3 km per hour and reaches 30 min early if he walks 4 km per hour. How far is his office from his house?

ক
20 km
খ
16 km
গ
14 km
ঘ
10 km

সঠিক উত্তর: ঘ

10 km

উত্তর

সঠিক উত্তর: ঘ

10 km

ঘ

ব্যাখ্যা

Question: A man reaches his office 20 min late, if he walks from his home at 3 km per hour and reaches 30 min early if he walks 4 km per hour. How far is his office from his house?

Solution:
Let distance = x km.
Time taken at 3 kmph = dist/speed = x/3 which is 20 min late.
Time taken at 4 kmph = x/4 which is 30 min earlier
Difference between time taken : 30 - (- 20) = 50 mins = 50/60 hours.
ATQ,
x/3 - x/4 = 50/60
⇒ x/12 = 5/6
∴ x = 10 km.

১,১৫৯.

A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 54 km downstream

ক
ক) 3 hours
খ
খ) 2 hours
গ
গ) 4 hours
ঘ
ঘ) 5 hours

সঠিক উত্তর: খ

খ) 2 hours

উত্তর

সঠিক উত্তর: খ

খ) 2 hours

খ

ব্যাখ্যা

Speed of the boat in still water = 22 km/hr
speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 54 km
Time taken = distance/ speed
= 54/27
= 2 hours

১,১৬০.

A Boat takes a total 10 hours for traveling downstream from point A to point B and coming back point C which is somewhere between A and B. The speed of the Boat in still water is 9 km/hr and rate of stream is 3 km/hr, then what is the distance between A and B if the ratio of distance between A to C and distance between B to C is 2 : 1?

ক
48 km
খ
56 km
গ
68 km
ঘ
72 km

সঠিক উত্তর: ঘ

72 km

উত্তর

সঠিক উত্তর: ঘ

72 km

ঘ

ব্যাখ্যা

Question: A Boat takes a total 10 hours for traveling downstream from point A to point B and coming back point C which is somewhere between A and B. The speed of the Boat in still water is 9 km/hr and rate of stream is 3 km/hr, then what is the distance between A and B if the ratio of distance between A to C and distance between B to C is 2 : 1?

Solution:

Let, the distance between B to C = x
the distance between A to C = 2x
the distance between A to B = 3x

ATQ,
3x/12 + x/6 = 10
⇒ (3x + 2x)/12 = 10
⇒ 5x = 120
∴ x = 24

∴ The distance between A to B = 3 × 24 = 72 km

১,১৬১.

Two trains start from stations A and B and travel towards each other at a speed of 50 kmph and 60 kmph respectively. A the time of their meeting, the second train had travelled 120 km more then the first. The distance between A and B is :

ক
720 km
খ
1020 km
গ
1220 km
ঘ
1320 km

সঠিক উত্তর: ঘ

1320 km

উত্তর

সঠিক উত্তর: ঘ

1320 km

ঘ

ব্যাখ্যা

Question: Two trains start from stations A and B and travel towards each other at a speed of 50 kmph and 60 kmph respectively. A the time of their meeting, the second train had travelled 120 km more then the first. The distance between A and B is :

Solution:
At the time of meeting, let the distance travelled by the first train be x km.
Then, discount covered by the second train = (x + 120) km

ATQ,
x/50 = (x + 120)/60
⇒ 60x = 50(x + 120)
⇒ 60x - 50x = 6000
⇒ 10x = 6000
∴ x = 600

So, distance between A and B = (x + x + 120) km
= (600 + 600 + 120) km
= 1320 km

১,১৬২.

A person crosses a 600 meters long street in 5 minutes. What is his speed in kilometers per hour?

ক
ক) 3.6
খ
খ) 7.2
গ
গ) 8.4
ঘ
ঘ) 10

সঠিক উত্তর: খ

খ) 7.2

উত্তর

সঠিক উত্তর: খ

খ) 7.2

খ

ব্যাখ্যা

Speed = 600 meters / 5 minutes
= (600 × 60)/(5 × 1000) km/hr
= 7.2 km/hr

১,১৬৩.

P, Q and R are in a cycle race of 4500 meters. P cycles twice as fast as Q. R cycles 1/3 as fast as Q. R completes the race in 45 minutes. Then where was Q from the finishing line when P finished the race?

ক
2250 m
খ
300 m
গ
1500 m
ঘ
3000 m

সঠিক উত্তর: ক

2250 m

উত্তর

সঠিক উত্তর: ক

2250 m

ক

ব্যাখ্যা

Question: P, Q and R are in a cycle race of 4500 meters. P cycles twice as fast as Q. R cycles 1/3 as fast as Q. R completes the race in 45 minutes. Then where was Q from the finishing line when P finished the race?

Solution:
Given that,
Race = 4500 m
R finishes in 45 min
∴ speed of R = 4500/45 = 100 m/min

R’s speed = (1/3) Q’s speed
∴ Q’s speed = 300 m/min

And, P’s speed = 2 × Q’s speed = 600 m/min

∴ Time for P to finish 4500 m = 4500/600 = 7.5 min
In 7.5 min, Q covers = 300 × 7.5 = 2250 m

∴ Distance left for Q = 4500 - 2250 = 2250 m

So Q was 2250 meters from the finishing line when P finished.

১,১৬৪.

A person can swim at a speed of 4 km/h in still water. If the speed of the current is 2 km/h, then the time taken to swim 12 km downstream and return to the starting point is -

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

সঠিক উত্তর: গ

8 hours

উত্তর

সঠিক উত্তর: গ

8 hours

গ

ব্যাখ্যা

Question: A person can swim at a speed of 4 km/h in still water. If the speed of the current is 2 km/h, then the time taken to swim 12 km downstream and return to the starting point is -

Solution:
Speed of the swimmer in still water = 4 km/h
Speed of the current = 2 km/h
Distance one way = 12 km

Downstream Speed = 4 + 2 = 6 km/h
Upstream Speed = 4 - 2 = 2 km/h

Time taken downstream = 12/6 = 2 hours
Time taken upstream = 12/2 = 6 hours

Total time = 6 + 2 = 8 hours

১,১৬৫.

Jamil can run 1 km in 4 minutes. He has a car that has a top speed of 75 km/hour. Jamil's speed is what percentage of his car's top speed?

ক
ক) 10%
খ
খ) 20%
গ
গ) 25%
ঘ
ঘ) 30%

সঠিক উত্তর: খ

খ) 20%

উত্তর

সঠিক উত্তর: খ

খ) 20%

খ

ব্যাখ্যা

Question: Jamil can run 1 km in 4 minutes. He has a car that has a top speed of 75 km/hour. Jamil's speed is what percentage of his car's top speed?

Solution:
4 মিনিট= 4/60 ঘণ্টা
= 1/15 ঘণ্টা

জামিলের গতিবেগ = 1/(1/15) কি.মি./ঘণ্টা
= 15 কি.মি./ঘণ্টা

গাড়ির গতিবেগ = 75 কি.মি./ঘণ্টা

জামিলের গতিবেগ তার গাড়ির গতিবেগের = {(15/75) × 100}%
= 20%

১,১৬৬.

With an average speed of 50 km/hr, a train reaches its destination in time. If it goes with an average speed of 40 km/hr, it is late by 24 min. The total journey is:

ক
60 km
খ
75 km
গ
80 km
ঘ
85 km

সঠিক উত্তর: গ

80 km

উত্তর

সঠিক উত্তর: গ

80 km

গ

ব্যাখ্যা

Question: With an average speed of 50 km/hr, a train reaches its destination in time. If it goes with an average speed of 40 km/hr, it is late by 24 min. The total journey is:

Solution:
Difference between timings = 24 min = 24/60 hr = 2/5 hr.
Let the length of the journey be x km.

Then,
(x/40) - (x/50) = 2/5
Or, (5x - 4x)/200 = 2/5
Or, x/200 = 2/5
Or, x = (25 × 200)
∴ x = 80 km.

∴ The total journey is 80 km.

১,১৬৭.

A train 200 m long passed a pole in 20 seconds. How long will it take to pass a platform 610 m long?

ক
64 sec
খ
81 sec
গ
73 sec
ঘ
89 sec

সঠিক উত্তর: খ

81 sec

উত্তর

সঠিক উত্তর: খ

81 sec

খ

ব্যাখ্যা

Question: A train 200 m long passed a pole in 20 seconds. How long will it take to pass a platform 610 m long?

Solution:
Speed = 200/20 = 10 m/s
∴ Required time = (200 + 610)/10
= 81 sec

১,১৬৮.

In a 500-meter race, B starts 50 meters ahead of A, yet A defeats B by a margin of 25 meters. What distance did B cover when A reached the finish line?

ক
400 meters
খ
425 meters
গ
450 meters
ঘ
475 meters

সঠিক উত্তর: খ

425 meters

উত্তর

সঠিক উত্তর: খ

425 meters

খ

ব্যাখ্যা

Question: In a 500-meter race, B starts 50 meters ahead of A, yet A defeats B by a margin of 25 meters. What distance did B cover when A reached the finish line?

Solution:
500 মিটার রেসে B 50 মিটার এগিয়ে থেকে দৌড় শুরু করায় B কে দূরত্ব অতিক্রম করতে হবে = (500 - 50) মিটার = 450 মিটার
A এর অতিক্রান্ত দূরত্ব = 500 মিটার

কিন্তু A, B-কে 25 মিটার দূরত্বে পরাজিত করে।
∴ A যখন শেষপ্রান্ত স্পর্শ করে তখন B এর অতিক্রান্ত দূরত্ব = (450 - 25) মিটার = 425 মিটার

১,১৬৯.

If Rahim walks at 14 km/hr instead of 10 km/hr for a certain time, he would have walked 30 km more. if Rahim walks at a speed of 10 km/hr, the distance travelled by him within that time is-

ক
66 km
খ
72 km
গ
75 km
ঘ
84 km

সঠিক উত্তর: গ

75 km

উত্তর

সঠিক উত্তর: গ

75 km

গ

ব্যাখ্যা

Question: If Rahim walks at 14 km/hr instead of 10 km/hr for a certain time, he would have walked 30 km more. if Rahim walks at a speed of 10 km/hr, the distance travelled by him within that time is-

Solution:
Let,
the actual distance travelled be = a km.

Then,
a/10 = (a + 30)/14
⇒ 14a = 10a + 300
⇒ 14a - 10a = 300
⇒ 4a = 300
⇒ a = 300/4
∴ a = 75 km

১,১৭০.

A boat's speed with the current is 17 km/hr and the speed of the current is 3.5 km/hr. What is the boat's speed against the current?

ক
12 km/hr
খ
10 km/hr
গ
13.5 km/hr
ঘ
14.5 km/hr

সঠিক উত্তর: খ

10 km/hr

উত্তর

সঠিক উত্তর: খ

10 km/hr

খ

ব্যাখ্যা

Question: A boat's speed with the current is 17 km/hr and the speed of the current is 3.5 km/hr. What is the boat's speed against the current?

Solution:
নৌকার স্রোতের সাথে গতিবেগ = 17 কিমি/ঘন্টা
স্রোতের গতিবেগ = 3.5 কিমি/ঘন্টা

স্থির পানিতে নৌকার গতিবেগ = স্রোতের সাথে গতিবেগ - স্রোতের গতিবেগ
= (17 - 3.5) কিমি/ঘন্টা
= 13.5 কিমি/ঘন্টা

স্রোতের বিপরীতে নৌকার গতিবেগ = স্থির পানিতে গতিবেগ - স্রোতের গতিবেগ
= (13.5 - 3.5) কিমি/ঘন্টা
= 10 কিমি/ঘন্টা

সুতরাং, স্রোতের বিপরীতে নৌকার গতিবেগ 10 কিমি/ঘন্টা।

১,১৭১.

A high-speed train running at 102 km/hr passes a person walking in the opposite direction at 6 km/hr. If the train takes 8 seconds to pass the person, what is the length of the train (in meter)?

ক
180 m
খ
220 m
গ
240 m
ঘ
260 m

সঠিক উত্তর: গ

240 m

উত্তর

সঠিক উত্তর: গ

240 m

গ

ব্যাখ্যা

Question: A high-speed train running at 102 km/hr passes a person walking in the opposite direction at 6 km/hr. If the train takes 8 seconds to pass the person, what is the length of the train (in meter)?

Solution:
ধরি,
ট্রেনের দৈর্ঘ্য = x মিটার
ট্রেনের গতিবেগ = 102 km/hr
মানুষের গতিবেগ = 6 km/hr

যেহেতু তারা বিপরীত দিক থেকে আসছে, তাই আপেক্ষিক গতিবেগ = (102 + 6) km/hr
= 108 km/hr
= 108 × (5/18) = 30 m/s

আমরা জানি, অতিক্রান্ত দূরত্ব (ট্রেনের দৈর্ঘ্য) = আপেক্ষিক গতিবেগ × সময়

প্রশ্নমতে,
x = 30 × 8
∴ x = 240

সুতরাং, ট্রেনটির দৈর্ঘ্য 240 মিটার।

১,১৭২.

A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is :

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

সঠিক উত্তর: খ

18 km/hr

উত্তর

সঠিক উত্তর: খ

18 km/hr

খ

ব্যাখ্যা

Question: A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is :

Solution:
Let, the distance travelled by a car be x km
First x/3 km distance cover at a speed of 10 km/hr
Second x/3 km distance cover at speed = 20 km/hr
Third x/3 km distance cover at speed = 60 km/hr

According to the question,
Total time = x/(3 × 10) + x/(3 × 20) + x/(3 × 60)
= x/30 + x/60 + x/180
= (6x + 3x + x)/180
= 10x/180
= x/18

Average speed = (x × 18)/x km/hr = 18 km/hr

১,১৭৩.

A train covers a certain distance at a speed of 240 kmph in 6 hours. To cover the same distance in 4 hours, it must travel at a speed of-

ক
260 km/h
খ
360 km/h
গ
160 km/h
ঘ
220 km/h

সঠিক উত্তর: খ

360 km/h

উত্তর

সঠিক উত্তর: খ

360 km/h

খ

ব্যাখ্যা

Question: A train covers a certain distance at a speed of 240 kmph in 6 hours. To cover the same distance in 4 hours, it must travel at a speed of-

Solution:
Given,
Distance = (240 × 6)
= 1440 km

We know,
Speed = (Distance ÷ Time)

∴ Required speed = (1440 ÷ 4) km/h
= 360 km/h

∴ The required speed is 360 km/h.

১,১৭৪.

A train 150 meters long takes 30 seconds to cross a 300-meter-long bridge. How much time will it take to cross a 300-meter-long platform?

ক
18 seconds
খ
24 seconds
গ
30 seconds
ঘ
36 seconds

সঠিক উত্তর: গ

30 seconds

উত্তর

সঠিক উত্তর: গ

30 seconds

গ

ব্যাখ্যা

Question: A train 150 meters long takes 30 seconds to cross a 300-meter-long bridge. How much time will it take to cross a 300-meter-long platform?

Solution:
Length of the train = 150 meters
Length of the bridge = 300 meters
Total distance = 150 + 300 = 450 meters

∴ Speed of the train = 450/30 = 15 m/s

New total distance (train + platform) = 150 + 300 = 450 meters

Time taken to cross the platform = 450/15 = 30 seconds

১,১৭৫.

Q. (36-55) Choose the correct answer.
৩৬) A train which is 1 km long traveling at a speed of 60 km/hour enters a tunnel 1km of length. What time does the train take to come fully out of the tunnel?

ক
ক) 1 min
খ
খ) 2 min
গ
গ) 30 min
ঘ
ঘ) 60 min

সঠিক উত্তর: খ

খ) 2 min

উত্তর

সঠিক উত্তর: খ

খ) 2 min

খ

ব্যাখ্যা

Question: A train which is 1 km long traveling at a speed of 60 km/hour enters a tunnel 1km of length. What time does the train take to come fully out of the tunnel?

Solution:
টানেল থেকে পুরোপুরি বের হলে, অতিক্রান্ত দূরত্ব ১ + ১ কি.মি.
= ২ কি.মি.

৬০ কি.মি. যেতে সময় লাগে ১ ঘণ্টা বা ৬০ মিনিট
১ কি.মি. যেতে সময় লাগে ৬০/৬০ = ১ মিনিট
∴ ২ কি.মি. যেতে সময় লাগে = ২ × ১ মিনিট
= ২ মিনিট

১,১৭৬.

A person takes 8 hours 30 minutes in cycling a distance and walking back to the starting place. He could cycle both ways in 10 hours 40 minutes. What is the time taken by him to walk both ways?

ক
4 hours 45 minutes
খ
6 hours 20 minutes
গ
5 hours 40 minutes
ঘ
7 hours 30 minutes

সঠিক উত্তর: খ

6 hours 20 minutes

উত্তর

সঠিক উত্তর: খ

6 hours 20 minutes

খ

ব্যাখ্যা

Question: A person takes 8 hours 30 minutes in cycling a distance and walking back to the starting place. He could cycle both ways in 10 hours 40 minutes. What is the time taken by him to walk both ways?

Solution:
Time taken in cycling both ways = 10 hours 40 minutes ........... (1)
Time taken in cycling one way and walking back = 8 hours 30 minutes ........... (2)

Using the equation {(2) × 2} - (1), we have:
Time taken by the person to walk both ways = 17 hours - 10 hours 40 minutes
= 6 hours 20 minutes

১,১৭৭.

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
8 am
খ
9 am
গ
10 am
ঘ
11 am
ঙ
12 am

সঠিক উত্তর: ঘ

11 am

উত্তর

সঠিক উত্তর: ঘ

11 am

ঘ

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

১,১৭৮.

A tiger is 50 of its own leaps behind a deer. The tiger takes 5 leaps per minute to the deer's 4. If the tiger and the deer cover 8 m and 5 m per leap respectively, what distance will the tiger have to run before it caches the deer?

ক
800 m
খ
600 m
গ
1200 m
ঘ
1600 m
ঙ
None of the above

সঠিক উত্তর: ক

800 m

উত্তর

সঠিক উত্তর: ক

800 m

ক

ব্যাখ্যা

Question: A tiger is 50 of its own leaps behind a deer. The tiger takes 5 leaps per minute to the deer's 4. If the tiger and the deer cover 8 m and 5 m per leap respectively, what distance will the tiger have to run before it caches the deer?

Solution:
Speed of tiger = 40 m/min
Speed of deer = 20 m/min.

Relative speed = 40 - 20 = 20 m/min.
Initial difference in distance = 50 × 8 = 400 m

Time taken to catch = 400/20
= 20 min.

Distance travelled in 20 min,
= 20 × 40
= 800 m

১,১৭৯.

A boy traveled from the home to the college at the rate or 25 km/hr and walked back at the rate of 4 km/ hr. If the whole journey took 5 hours 48 minutes, find the distance of the college from the home.

ক
ক) 5 km
খ
খ) 10 km
গ
গ) 15 km
ঘ
ঘ) 20 km

সঠিক উত্তর: ঘ

ঘ) 20 km

উত্তর

সঠিক উত্তর: ঘ

ঘ) 20 km

ঘ

ব্যাখ্যা

Let the distance is D
While going with the speed of 25kmph
Formula
Speed=Distance/Time
Speed=25kmph
Distance=D
So,Time=D/25
Similarly, for return journey
The distance will be same as he returns from post office to village
Time=D/4
Now,Total time is given and we have time of onward and return Journey
Add this two time and equate with given time
D/25 + D/4=5 hrs 48 Min………….(1)
5hrs 48min can be written as
48min=48/60=4/5hrs
5hrs adding in this makes 5 + 4/5 = 29/5…….(2)
From (1) and (2)
D/25+D/4=29/5
29D/100=29/5
D=(29/5)*(100/29)
D=20
Answer is 20Km

১,১৮০.

A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

ক
ক) 80 kmph
খ
খ) 90 kmph
গ
গ) 120 kmph
ঘ
ঘ) 140 kmph

সঠিক উত্তর: গ

গ) 120 kmph

উত্তর

সঠিক উত্তর: গ

গ) 120 kmph

গ

ব্যাখ্যা

Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

Solution:
Let speed of the car be x kmph.
Then, speed of the train = 150x/100 = 3x/2

Now
(75/x) - {75/(3x/2)} = 125/(10 × 60)
(75/x) - (50/x) = 5/24
(75 - 50)/x = 5/24
25/x = 5/24
5x = 24 × 25
x = ( 24 × 25)/5
x = 120 kmph

১,১৮১.

Find the speed of the stream, if a boat takes 8 hours to travel a distance of 192 km upstream, and the speed of the boat in still water is 32 km/h.

ক
8 km/h
খ
6 km/h
গ
4 km/h
ঘ
10 km/h

সঠিক উত্তর: ক

8 km/h

উত্তর

সঠিক উত্তর: ক

8 km/h

ক

ব্যাখ্যা

Question: Find the speed of the stream, if a boat takes 8 hours to travel a distance of 192 km upstream, and the speed of the boat in still water is 32 km/h.

Solution:
স্থির পানিতে নৌকার বেগ 32 km/h
ধরি,
স্রোতের বেগ x km/h

স্রোতের প্রতিকূলে কার্যকরি বেগ = 192/8 = 24 km/h

∴ 32 - x = 24
⇒ x = 32 - 24
∴ x = 8

∴ স্রোতের বেগ 8 km/h

১,১৮২.

A cyclist moving on a circular track of a radius of 100 meters completes one revolution in 2 minutes. What is the average speed of a cyclist (approx.)?

ক
310 meters/minute
খ
328 meters/minute
গ
336 meters/minute
ঘ
320 meters/minute
ঙ
None of the above

সঠিক উত্তর: ঙ

None of the above

উত্তর

সঠিক উত্তর: ঙ

None of the above

ঙ

ব্যাখ্যা

Question: A cyclist moving on a circular track of a radius of 100 meters completes one revolution in 2 minutes. What is the average speed of a cyclist (approx.)?

Solution:
Distance covered in one complete revolution
= 2πr
= 2 × 100 × (22/7)
= 628.571 meters
≈ 628 meters

Hence,
Average speed
= 628/2
= 314 meters/minute

১,১৮৩.

A boat takes 12 hours to cover 64 km downstream and 8 hours to cover 32 km upstream. Then the speed of the boat in still water is

ক
ক) 14/3 km/hr
খ
খ) 3/2 km/hr
গ
গ) 6/5 km/hr
ঘ
ঘ) 8/7 km/hr

সঠিক উত্তর: ক

ক) 14/3 km/hr

উত্তর

সঠিক উত্তর: ক

ক) 14/3 km/hr

ক

ব্যাখ্যা

Distance covered downstream = 64 km
Time is taken in downstream = 12 hours.
Rate of downstream = distance/time = a = 64 km/12 hours
= 16/3 km/hr.
Distance covered in upstream = 32km
Time is taken upstream = 8 hours.
Rate of upstream = distance/time = b = 32km/8 hours
= 4 km/hr.
Speed in still water = (a + b)/2 = (1/2){(16/3) + 4} km/hr
= (1/2)(28/3)
= 14/3 km/hr.

১,১৮৪.

A motorcycle at a speed of 60km/hr, it covers a certain distance in 3 hours and the train can cover the same distance in 1 and half hours then the speed of the train is -

ক
80km/hr
খ
120km/hr
গ
160km/hr
ঘ
50km/hr

সঠিক উত্তর: খ

120km/hr

উত্তর

সঠিক উত্তর: খ

120km/hr

খ

ব্যাখ্যা

The Distance covered by the motorcycle with speed 60km/hr in 3 hours = (60 x 3)
= 180 km
Now,
Speed = Distance/Time
Since the train covers the same 180 km in 3/2 hours (we can write 1 and half hours as 3/2hours)
Then the speed of the train = 180/ (3/2)
= 180 × (2/3)
= 120 km/hr.
Hence, the train travelled at the speed of 120km/hr to cross 180km in 1 and half hour.

১,১৮৫.

A man takes 3 hours 45 minutes to row a boat 22.5 km downstream of a river and 2 hours 30 minutes to cover a distance of 10 km up stream. Find the speed of the river current in km/hr.

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

সঠিক উত্তর: ক

ক) 1 km/hr

উত্তর

সঠিক উত্তর: ক

ক) 1 km/hr

ক

ব্যাখ্যা

এখানে
3 ঘণ্টা 45 মিনিট = 3(3/4) ঘণ্টা = 15/4 ঘণ্টা
2 ঘণ্টা 30 মিনিট = 2(1/2) ঘণ্টা = 5/2 ঘণ্টা
ধরি
নৌকার বেগ = x কি.মি./ঘণ্টা
স্রোতের বেগ= y কি.মি./ঘণ্টা

স্রোতের অনুকূলে নৌকার বেগ = 22.5/(15/4)
x + y = (22.5 × 4)/15
x + y = 6 কি.মি./ঘণ্টা ................(1)

স্রোতের প্রতিকূলে নৌকার বেগ = 10/(5/2) কি.মি./ঘণ্টা
x - y = (10 × 2)/5 কি.মি./ঘণ্টা
x - y = 4 কি.মি./ঘণ্টা ................(2)

(1) থেকে (2 বিয়োগ করে পাই,
x + y - x + y = (6 - 4)কি.মি./ঘণ্টা
2y = 2
y = 1 কি.মি./ঘণ্টা

১,১৮৬.

A man takes 6 hours 15 minutes in walking a distance and riding back to starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride back both ways is:

ক
305 minutes
খ
265 minutes
গ
275 minutes
ঘ
285 minutes
ঙ
None of the above

সঠিক উত্তর: ঘ

285 minutes

উত্তর

সঠিক উত্তর: ঘ

285 minutes

ঘ

ব্যাখ্যা

Question: A man takes 6 hours 15 minutes in walking a distance and riding back to starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride back both ways is:

Solution:
Time taken in walking both the ways = 7 hours 45 minutes - - - - - - - - (1)
Time taken in walking one way and riding back = 6 hours 15 minutes - - - - - (2)

By the equation (2) × 2 - (1), we have,
Time taken by the man in riding both ways = 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45 minutes
= 285 minutes

১,১৮৭.

A train 165 m long is running at a uniform speed of 54 km/hr. How much time will it take to cross a pole?

ক
9 seconds
খ
11 seconds
গ
15 seconds
ঘ
22 seconds

সঠিক উত্তর: খ

11 seconds

উত্তর

সঠিক উত্তর: খ

11 seconds

খ

ব্যাখ্যা

Question: A train 165 m long is running at a uniform speed of 54 km/hr. How much time will it take to cross a pole?

Solution:
Speed of train = 54 km/hr
= 54 × 5/18 m/sec
= 15 m/sec

Length of the train = 165 meters

Therefore, time taken by the train to cross a pole = length of train/speed of train
= 165/15 sec
= 11 sec

Thus, train takes 11 seconds to cross the pole.

১,১৮৮.

A boat covers a certain distance downstream in 1 hour, while it comes back in 1 (1/ 2) hours. If the speed of the stream is 3 kmph, what is the speed of the boat in still water?

ক
ক) 13 kmph
খ
খ) 17 kmph
গ
গ) 19 kmph
ঘ
ঘ) 11 kmph
ঙ
ঙ) 15 kmph

সঠিক উত্তর: ঙ

ঙ) 15 kmph

উত্তর

সঠিক উত্তর: ঙ

ঙ) 15 kmph

ঙ

ব্যাখ্যা

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

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

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

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

১,১৮৯.

A long distance runner runs 8 laps of a 360 meters track everyday. His timings for four consecutive days are 78, 86, 79 and 77 minutes respectively. On an average, how many meters/minute does the runner cover?

ক
28 m/min
খ
32 m/min
গ
36 m/min
ঘ
40 m/min

সঠিক উত্তর: গ

36 m/min

উত্তর

সঠিক উত্তর: গ

36 m/min

গ

ব্যাখ্যা

Question: A long distance runner runs 8 laps of a 360 meters track everyday. His timings for four consecutive days are 78, 86, 79 and 77 minutes respectively. On an average, how many meters/minute does the runner cover?

Solution:
Total distance covered = (4 × 8 × 360) meters
= 11520 meters

Total time taken = (78 + 86 + 79 + 77) = 320 minutes

∴ Average speed = (Total distance ÷ Total time) m/min
= (11520 ÷ 320) m/min
= 36 m/min

১,১৯০.

Palash drives form City A to B at 40km per hour and returns over the same road at 30km per hour and spends 8 hours away from home including a one-hour stop for lunch. What is the distance (in km) between City A and City B?

ক
ক) 100
খ
খ) 120
গ
গ) 140
ঘ
ঘ) 180

সঠিক উত্তর: খ

খ) 120

উত্তর

সঠিক উত্তর: খ

খ) 120

খ

ব্যাখ্যা

Question: Palash drives form City A to B at 40km per hour and returns over the same road at 30km per hour and spends 8 hours away from home including a one-hour stop for lunch. What is the distance (in km) between City A and City B?

Solution:
ধরি
A থেকে B এর দূরত্ব x কি.মি.

প্রশ্নমতে,
(x/40) + (x/30) + 1 = 8
(x/40) + (x/30) = 8 - 1
(3x + 4x)/120 = 7
7x/120 = 7
x/120 = 1
x = 120

A থেকে B এর দূরত্ব 120 কি.মি.

১,১৯১.

Ratio of speed of boat in still water and speed of stream is 4 : 3. Boat covers 20 km upstream in 4 hours and x km in 3 hours downstream. Find the value of x?

ক
60 km
খ
85 km
গ
90 km
ঘ
100 km
ঙ
105 km

সঠিক উত্তর: ঙ

105 km

উত্তর

সঠিক উত্তর: ঙ

105 km

ঙ

ব্যাখ্যা

Question: Ratio of speed of boat in still water and speed of stream is 4 : 3. Boat covers 20 km upstream in 4 hours and x km in 3 hours downstream. Find the value of x?

Solution:
ধরি, স্থির পানিতে নৌকার গতিবেগ = 4k কিমি/ঘন্টা
এবং স্রোতের গতিবেগ = 3k কিমি/ঘন্টা।

স্রোতের প্রতিকূলে (Upstream) নৌকার গতিবেগ = (4k - 3k) কিমি/ঘন্টা
= 1k কিমি/ঘন্টা।
স্রোতের অনুকূলে (Downstream) নৌকার গতিবেগ = (4k + 3k) কিমি/ঘন্টা
= 7k কিমি/ঘন্টা।

প্রশ্ন অনুযায়ী,
স্রোতের প্রতিকূলে 20 কিমি যেতে সময় লাগে 4 ঘন্টা।
অতএব, স্রোতের প্রতিকূলে গতিবেগ = 20 কিমি/4 ঘন্টা
= 5 কিমি/ঘন্টা।
সুতরাং, 1k = 5
⇒ k = 5

এখন, স্রোতের অনুকূলে নৌকার গতিবেগ = 7k = 7 × 5 = 35 কিমি/ঘন্টা।
∴ স্রোতের অনুকূলে 3 ঘন্টায় অতিক্রান্ত দূরত্ব, x = 35 কিমি/ঘন্টা × 3 ঘন্টা
= 105 কিমি।

১,১৯২.

A man takes 6 hours 15 minutes in walking a distance and riding back to starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride back both ways is:

ক
ক) 4 hours
খ
খ) 5 hours 45 minutes
গ
গ) 4 hours 30 minutes
ঘ
ঘ) 4 hours 45 minutes

সঠিক উত্তর: ঘ

ঘ) 4 hours 45 minutes

উত্তর

সঠিক উত্তর: ঘ

ঘ) 4 hours 45 minutes

ঘ

ব্যাখ্যা

Question: A man takes 6 hours 15 minutes in walking a distance and riding back to starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride back both ways is:

Solution:
Time taken in walking both the ways = 7 hours 45 minutes - - - - - - - - (1)
Time taken in walking one way and riding back = 6 hours 15 minutes - - - - - - - - (2)

By the equation (2) × 2 - (1), we have,
Time taken by the man in riding both ways = 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45 minutes.

১,১৯৩.

A man takes 50 minutes to cover a certain distance at a speed of 6km/hr. If he walks with a speed of 10km/hr, he covers the same distance in -

ক
15 minutes
খ
30 minutes
গ
40 minutes
ঘ
25 minutes

সঠিক উত্তর: খ

30 minutes

উত্তর

সঠিক উত্তর: খ

30 minutes

খ

ব্যাখ্যা

Question: A man takes 50 minutes to cover a certain distance at a speed of 6km/hr. If he walks with a speed of 10km/hr, he covers the same distance in -

Solution:
distance = speed × time
= (6 × 50/60)
= 5km

time = distance/ speed
= 5/10
= 1/2 hour
= 30 minutes

১,১৯৪.

A man travels first 150 km of his journey at 80 km/hr. Due to bad weather he travels the next 150 km of his journey at 60 km/hr. What is his average speed for the first 300 km of his journey?

ক
60.6 km/hr
খ
63.6 km/hr
গ
66.6 km/hr
ঘ
68.6 km/hr

সঠিক উত্তর: ঘ

68.6 km/hr

উত্তর

সঠিক উত্তর: ঘ

68.6 km/hr

ঘ

ব্যাখ্যা

Question: A man travels first 150 km of his journey at 80 km/hr. Due to bad weather he travels the next 150 km of his journey at 60 km/hr. What is his average speed for the first 300 km of his journey?

Solution:
Total distance = 300 km
The total time taken to cover the first 300 km is the sum of the time taken to cover the first 150 km and the next 150 km.

Total time = 150/80 + 150/60 hour
= 15/8 + 15/6
= (45 + 60)/24
= 105/24
= 35/8 hour

Average Speed = 300/(35/8) km/hr
= 68.57 km/hr
≈ 68.6 km/hr

১,১৯৫.

A train running at the speed of 60 km/hr crosses a pole in 10 seconds. What is the length of the train?

ক
ক) 160 meter
খ
খ) 165.87 meter
গ
গ) 166.67 meter
ঘ
ঘ) 155.56 meter

সঠিক উত্তর: গ

গ) 166.67 meter

উত্তর

সঠিক উত্তর: গ

গ) 166.67 meter

গ

ব্যাখ্যা

Question: A train running at the speed of 60 km/hr crosses a pole in 10 seconds. What is the length of the train?

Solution:
In 3600 seconds the train covered 60000 meter
∴ In 10 seconds the train covered (60000 × 10)/3600 meter
= 166.67 meter

∴ The length of the train is 166.67 meter.

১,১৯৬.

Anik travels 35 kilometers (km) partly at 4km /h and partly at 5 km/h. If he covers the distance at 5 km/h he could cover 2 km more in the same time. The time taken to cover the whole distance at original rate is-

ক
ক) 4hr 30 min
খ
খ) 5hr 24 min
গ
গ) 7hr 24 min
ঘ
ঘ) 9 hr 24 min
ঙ
ঙ) None

সঠিক উত্তর: গ

গ) 7hr 24 min

উত্তর

সঠিক উত্তর: গ

গ) 7hr 24 min

গ

ব্যাখ্যা

Suppose, he traveled at 4 km/h for p hours and @5 km/h for q hours.
So, 4p+5q = 35 -------- (i)
According to the question,
5(p+q) = 35+2
⇒ 5p + 5q = 37 -------- (ii)
Solving these two equations, we get,
p = 2, q = 27/5
So, total time taken = 2 + 27/5 = 37/5 hr = 7hr + 2×60/5 min = 7 hr 24 min.

১,১৯৭.

Niloy walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 50 miles?

ক
318 minutes
খ
322 minutes
গ
324 minutes
ঘ
328 minutes

সঠিক উত্তর: গ

324 minutes

উত্তর

সঠিক উত্তর: গ

324 minutes

গ

ব্যাখ্যা

Question: Niloy walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 50 miles?

Solution:
Niloy needs time = 50/10 = 5 hours
= (5 × 60)
= 300 minutes

He will also rest 4 times after 10, 20, 30 and 40 miles
Total resting time = 4 × 6 = 24 minutes.

Total time = 300 + 24 = 324 minutes

১,১৯৮.

A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:

ক
ক) 9 km/hr
খ
খ) 12.5 km/hr
গ
গ) 8.5 km/hr
ঘ
ঘ) 10 km/hr

সঠিক উত্তর: ঘ

ঘ) 10 km/hr

উত্তর

সঠিক উত্তর: ঘ

ঘ) 10 km/hr

ঘ

ব্যাখ্যা

Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr
Speed of the current is 2.5 km/hr
Hence, speed of the man
= 15-2.5
= 12.5 km/hr
Man's speed against the current = speed of the man - speed of the current
= 12.5-2.5
= 10 km/hr

১,১৯৯.

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
54 km/hr
খ
50 km/hr
গ
52 km/hr
ঘ
48 km/hr

সঠিক উত্তর: খ

50 km/hr

উত্তর

সঠিক উত্তর: খ

50 km/hr

খ

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.

১,২০০.

In the first hour of a two-hour trip, a car traveled d kilometers, and in the second hour of the trip, the car traveled one-half that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour?

ক
d
খ
d/3
গ
d/2
ঘ
(3d)/4
ঙ
(3d)/2

সঠিক উত্তর: ঘ

(3d)/4

উত্তর

সঠিক উত্তর: ঘ

(3d)/4

ঘ

ব্যাখ্যা

Question: In the first hour of a two-hour trip, a car traveled d kilometers, and in the second hour of the trip, the car traveled one-half that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour?

Solution:
Total time travelled = 2 hrs
Distance travelled first hour = d
Distance travelled second hour = d/2

The question is asking for the avg speed at which the car travels for 2 hrs

We know that avg speed = total distance/total time

Lets place the information given in the question to the formula above = (d + d/2)/2
= {(3d)/2}/2
= (3d)/4