Time and Speed - Train and Boat

PrepBank · পাতা ৪ / ১৫ · ৩০১–৪০০ / ১,৪৩৯

৩০১.

A train 240 meters long passes a pole in 16 seconds. How long will it take to pass a platform that is 360 meters long?

ক
40 seconds
খ
30 seconds
গ
90 seconds
ঘ
20 seconds

ব্যাখ্যা

Question: A train 240 meters long passes a pole in 16 seconds. How long will it take to pass a platform that is 360 meters long?

Solution:
Train's speed = Distance/Time = 240/16 = 15 m/s

Total distance to pass the platform,
= Length of train + Length of platform
= 240 m + 360 m
= 600 m

∴ Required time = Distance/Speed
= 600/15
= 40 seconds

∴ The train will take 40 seconds to pass the platform.

৩০২.

A takes 2 hours 30 minutes more than B to walk 40 km. If A doubles his speed, then he can make it in 1 hour less than B. What is the average time taken by A and B to walk a 40 km distance?

ক
5 hours 15 minutes
খ
5 hours 45 minutes
গ
6 hours
ঘ
7 hours 15 minutes
ঙ
7 hours 45 minutes

ব্যাখ্যা

Question: A takes 2 hours 30 minutes more than B to walk 40 km. If A doubles his speed, then he can make it in 1 hour less than B. What is the average time taken by A and B to walk a 40 km distance?

Solution:
(40/A) - (40/B) = 5/2 . . . . . . . (i)
(40/B) - (40/2A) = 1 . . . . . . . (ii)

Equation (i) + Equation (ii)
(40/A) - (40/2A) = (5/2) - 1
⇒ (40/A) - (40/2A) = 7/2
⇒ 40/2A = 7/2
⇒ A = 40/7

Putting the value of A in equation (i)
7 - (40/B) = 5/2
⇒ 7 - (5/2) = 40/B
⇒ 9/2 = 40/B
⇒ B = 80/9

Now,
Total time = [40/(40/7)] + [40/(80/9)]
= 7 + (9/2)
= 23/2

Required average time = (23/2)/2
= 23/4
= 5 hours 45 minutes.

৩০৩.

Mr. Sohel can do a job in 8 days and his son can do it 24 days. How many days will it take them to complete the job if they worked together?

ক
4 days
খ
6 days
গ
8 days
ঘ
12 days
ঙ
None

ব্যাখ্যা

Question: Mr. Sohel can do a job in 8 days and his son can do it 24 days. How many days will it take them to complete the job if they worked together?

Solution:
Given,
Mr. Sohel can do the job in 8 days
∴ in 1 day Mr. Sohel can do = 1/8 part
and,
His son can do the job in 24 days
∴ in 1 day his son can do = 1/24 part

∴ in 1 day they worked together = (1/8 + 1/24) part
= (3 + 1)/24 part
= 4/24 part
= 1/6 part

Hence, worked together 1/6 part can do in 1 day
∴ They can complete the job in 6 days if they work together

৩০৪.

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/3
খ
d/2
গ
(3d)/4
ঘ
(3d)/2

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:
1st hour , distance travelled by car = d km
2nd hour , distance travelled by car = d/2 km
Total distance = d + d/2
= (2d + d)/2
= (3d)/2

Average speed = Total distance/Time
= (3d/2)/2
= (3d)/4

৩০৫.

Two trains are moving in opposite directions 80 km/h and 100 km/h. Their lengths are 1100 m and 900 m respectively. The time taken by the slower train to cross the faster train in seconds is:

ক
35 sec
খ
40 sec
গ
50 sec
ঘ
55 sec

ব্যাখ্যা

Question: Two trains are moving in opposite directions 80 km/h and 100 km/h. Their lengths are 1100 m and 900 m respectively. The time taken by the slower train to cross the faster train in seconds is:

Solution:
Relative speed= (80 + 100) km/h
= 180 × (5/18) m/sec
= 50 m/sec

Distance covered= (1100 + 900) m
=2000 m

Required time= (2000 ÷ 50) sec
= 40 sec

৩০৬.

Sifat 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 km he travel on foot?

ক
ক) 8 km
খ
খ) 12 km
গ
গ) 16 km
ঘ
ঘ) 24 km

ব্যাখ্যা

Question: Sifat 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 dis 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.

৩০৭.

Rahim is twice as fast as Karim and Karim is three times as fast as Jamal. The distance covered by Jamal in 6 hours will be covered by Rahim in how many hours?

ক
30 minutes
খ
25 minutes
গ
60 minutes
ঘ
48 minutes
ঙ
40 minutes

ব্যাখ্যা

Question: Rahim is twice as fast as Karim and Karim is three times as fast as Jamal. The distance covered by Jamal in 6 hours will be covered by Rahim in how many hours?

Solution:
Let speed of Jamal = x
Then Speed of Karim = 3x
Then Speed of Rahim = 6x

∴ Ratio of the speed of Rahim and Jamal = 6 : 1

So, The greater the speed, the less time is taken for the journey.

Rahim’s speed is 6 times that of Jamal.
So Rahim will take (1/6) of the total time taken by Jamal to cover the same distance.

So, Time taken by Rahim
= 6 × (1/6) hours
= 1 hour
= 60 minutes

৩০৮.

A train is passing a platform at 20m/s and a man is walking at 2m/s in the opposite direction. It took 10 sec for the train to cross the man. What is the length of the train?

ক
220m
খ
200m
গ
110m
ঘ
180m

ব্যাখ্যা

Question: A train is passing a platform at 20m/s and a man is walking at 2m/s in the opposite direction. It took 10 sec for the train to cross the man. What is the length of the train?

Solution:
as they are going opposite,
resultant speed is = (20 + 2) m/s
= 22 m/s

the length of the train is = 22 × 10 = 220m

৩০৯.

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

ক
ক) 240 meters
খ
খ) 260 meters
গ
গ) 140 meters
ঘ
ঘ) 220 meters

ব্যাখ্যা

Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Solution:
Speed = (54 × 1000)/3600
= 15 m/sec

Length of the train = (15 × 20) m = 300 m
Let
the length of the platform be x meters.

Then,
(x + 300)/36 = 15
⇒ x + 300 = 540
∴ x = 240 meters

৩১০.

The speed of a motor-boat is that of the current of water as 36:5. The boat goes along with the current in 5 hours 10 minutes. When will it come back?

ক
5 hours 50 minutes
খ
6 hours 50 minutes
গ
12 hours 10 minutes
ঘ
6 hours 5 minutes
ঙ
10 hours 5 minutes

ব্যাখ্যা

Let the speed of the motor boat = 36x kmph and
speed of current = 5x kmph.

The boat goes along with the current in 5 hours 10 minutes
= 31/6 hour.

Hence, Distance = 31/6 × (36x + 5x)
= 31/6 × 41x

Speed of boat upstream
= 36x - 5x
= 31x
Hence, time taken to come back
= 31/6 × 41x / 31x
= 41/6 hours
= 6 hours 50 minutes

৩১১.

A man sitting in a train is counting the pillars of electricity. The distance between two pillars is 50 meters, and the speed of the train is 45 km/hr. In 4 hours, how many pillars will he count?

ক
3601
খ
3575
গ
3650
ঘ
3500

ব্যাখ্যা

Question: A man sitting in a train is counting the pillars of electricity. The distance between two pillars is 50 meters, and the speed of the train is 45 km/hr. In 4 hours, how many pillars will he count?

Solution:
Distance covered by the train in 4 hours = (Speed × Time)
= (45 × 4) km
= 180 km
= 180000 m

∴ Number of pillars counted by the man = (180000/50) + 1
= (3600 + 1)
= 3601

৩১২.

Jack takes 20 minutes to jog around the race course one time, and 25 minutes to jog around a second time. What is his average speed in miles per hour for the whole jog if the course is 3 miles long?

ক
6
খ
8
গ
9
ঘ
10
ঙ
None of the above

ব্যাখ্যা

Average speed = total distance / total time
Total distance covered = 6 miles; total time = 45 minutes = 0.75 hours
Average speed = 6/ 0.75 = 8 miles/hour

৩১৩.

A boat running downstream covers a distance of 40 km in 4 hours, while covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?

ক
8 km/hr
খ
6.5 km/hr
গ
7 km/hr
ঘ
9 km/hr

ব্যাখ্যা

Question: A boat running downstream covers a distance of 40 km in 4 hours, while covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?

Solution:
স্রোতের অনুকূলে নৌকার গতিবেগ (Downstream Rate):
= অতিক্রান্ত দূরত্ব/সময়
= 40 কিমি/4 ঘন্টা
= 10 কিমি/ঘন্টা

স্রোতের প্রতিকূলে নৌকার গতিবেগ (Upstream Rate):
= অতিক্রান্ত দূরত্ব/সময়
= 40 কিমি/5 ঘন্টা
= 8 কিমি/ঘন্টা

স্থির পানিতে নৌকার গতিবেগ = (স্রোতের অনুকূলে গতিবেগ + স্রোতের প্রতিকূলে গতিবেগ)/2
= (10 + 8)/2 কিমি/ঘন্টা
= 18/2 কিমি/ঘন্টা
= 9 কিমি/ঘন্টা

সুতরাং, স্থির পানিতে নৌকাটির গতিবেগ হলো 9 কিমি/ঘন্টা।

৩১৪.

A man can row 12 km/hr in still water. If the speed of the current is 4 km/hr, he takes 4 hours more upstream than downstream. What is the distance (in km)?

ক
ক) 32 km
খ
খ) 48 km
গ
গ) 50 km
ঘ
ঘ) 64 km

ব্যাখ্যা

Question: A man can row 12 km/hr in still water. If the speed of the current is 4 km/hr, he takes 4 hours more upstream than downstream. What is the distance (in km)?

Solution:
Speed of the man in still water = 12 km/h
Speed of the current = 4 km/h
Speed of the man along the current = (12 + 4) km/h = 16 km/h
Speed of the man against the current = (12 - 4) km/h = 8 km/h

Let, The distance is x km
Now
x/8 - x/16 = 4
⇒ (2x - x)/16 = 4
⇒ x/16 = 4
∴ x = 64 km

৩১৫.

A boat goes 8 km downstream in 16 minutes. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?

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

ব্যাখ্যা

Question: A boat goes 8 km downstream in 16 minutes. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?

Solution:
The speed upstream is = 8/16 km/min
= (8 × 60)/16 km/hr
= 30 km/hr

Let,
The speed of boat in still water is = x km/hr

Now,
x + 4 = 30
⇒ x = 30 - 4
∴ x = 26

৩১৬.

A train of 220 m long is moving at 45 km/h. The time taken by the train to cross a tunnel of 260 m long is-

ক
25 sec
খ
35 sec
গ
38 sec
ঘ
40 sec

ব্যাখ্যা

Question: A train of 220 m long is moving at 45 km/h. The time taken by the train to cross a tunnel of 260 m long is-

Solution:
মোট অতিক্রান্ত দূরত্ব = (220 + 260) মিটার
= 480 মিটার

45 কিমি = (45 × 1000) = 45000 মিটার
1 ঘণ্টা = 3600 সেকেন্ড

45000 মিটার অতিক্রম করে 3600 সেকেন্ডে
1 মিটার অতিক্রম করে 3600/45000 সেকেন্ডে
480 মিটার অতিক্রম করে (3600 × 480)/45000 সেকেন্ডে
= 38.4 সেকেন্ডে

কাছাকাছি উত্তর হিসাবে অপশন গ কে সঠিক উত্তর নেওয়া হয়েছে।

৩১৭.

A train 360 metre long runs with a speed of 45 km/hr. What time will it take to pass a platform 140 metre long?

ক
ক) 44 seconds
খ
খ) 40 seconds
গ
গ) 30 seconds
ঘ
ঘ) 38 seconds
ঙ
ঙ) 25 seconds

ব্যাখ্যা

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

৩১৮.

A train covered first 120 km at a speed of 20 km an hour and then covered the remaining 180 km at a speed of 45 km an hour. Find its average speed.

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

ব্যাখ্যা

Question: A train covered first 120 km at a speed of 20 km an hour and then covered the remaining 180 km at a speed of 45 km an hour. Find its average speed.

Solution:
Total distance = 120 + 180 = 300 km.

Time taken for the first 120 km = 120/20 = 6 hrs.
Time taken for the next 180 km = 180/45 = 4 hrs.
Total time taken = 6 + 4 = 10 hrs.

Average Speed =Total Distance Travelled/Total Time Taken
= 300/10
= 30 km/hr

৩১৯.

A train moves with a speed of 108 km/hr. Its speed in metres per second is-

ক
10.8
খ
18
গ
30
ঘ
30.8
ঙ
None of these

ব্যাখ্যা

Question: A train moves with a speed of 108 km/hr. Its speed in metres per second is-

Solution:
Speed = 108 km/hr
To convert km/hr into m/s multiply the number by 5/18.
speed = 108 × (5/18) m/s = 30 m/s.

৩২০.

A boat went to a place in 7km/h and came back in 8km/h. What is average speed of the boat?

ক
ক) 8 km/h
খ
খ) 7.47 km/h
গ
গ) 8.5 km/h
ঘ
ঘ) 7.37 km/h

ব্যাখ্যা

Question: A boat went to a place in 7km/h and came back in 8km/h. What is average speed of the boat?

Solution:
ধরি,
দূরত্ব = x

তাহলে,
যেতে সময় লাগে x/7 hour
আসতে সময় লাগে x/8 hour

আমরা জানি,
গড় বেগ = (মোট দুরত্ব)/মোট সময়
= 2x/(x/7 + x/8)
= 2x/ (15x/56)
= 112/15
= 7.47km/h

৩২১.

A bus covers a certain distance at 16 h. It covers half the distance at 40 km/h and the rest at 60 km/h. Find the length of the journey.

ক
ক) 520 km
খ
খ) 448 km
গ
গ) 384 km
ঘ
ঘ) 768 km
ঙ
ঙ) 786 km

ব্যাখ্যা

Let the total distance covered = x
= Length of journey
According to the question,
x/2 × 1/40 + x/2 × 1/60 = 16
x/80 + x/120 = 160
(3x + 2x)/240 = 16
5x = 16 × 240
x = (16 × 240)/5
x = 16 × 48
x = 768 km

৩২২.

An ambulance moving at 33 km/h is 45 m behind a school bus. After 15 s, it is 30 m ahead of the bus. Find the speed of the school bus.

ক
4 km/h
খ
8 km/h
গ
10 km/h
ঘ
15 km/h
ঙ
18 km/h

ব্যাখ্যা

Question: An ambulance moving at 33 km/h is 45 m behind a school bus. After 15 s, it is 30 m ahead of the bus. Find the speed of the school bus.

Solution:
Relative Speed = Total distance/Total time
= (30 + 45)/15
= 75/15
= 5 m/s
= 5 × (18/5)
= 18 km/h

Now,
Relative Speed = Speed of ambulance - Speed of school bus
∴ Speed of school bus = Speed of ambulance - Relative speed
= 33 - 18
= 15 km/h

৩২৩.

A train travels 50% faster than a car. Both vehicles start from station P and reach station Q, 180 km away, at the same time. During the journey, the train stopped for 15 minutes at various stations. What is the speed of the car?

ক
120 km/h
খ
180 km/h
গ
200 km/h
ঘ
240 km/h
ঙ
260 km/h

ব্যাখ্যা

Question: A train travels 50% faster than a car. Both vehicles start from station P and reach station Q, 180 km away, at the same time. During the journey, the train stopped for 15 minutes at various stations. What is the speed of the car?

Solution:
Let speed of the car be x kmph.
Then, speed of the train = x + (50x)/100 = x + x/2
= (3x)/2

Now,
(180/x) - [180/{(3x)/2)}] = 15/60
⇒ (180/x) - (360/3x) = 1/4
⇒ (180/x) - (120/x) = 1/4
⇒ 60/x = 1/4
⇒ x = 240 km/h

৩২৪.

A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in:

ক
8 minutes
খ
10 minutes
গ
15 minutes
ঘ
12 minutes
ঙ
7 minutes

ব্যাখ্যা

Ratio of the speed of A, B and C = 6 : 3 : 1
Then, ratio of time taken= 1/6 : 1/3 : 1 = 1 : 2 : 6
Hence, time taken by A = 72/6 = 12 minutes.

৩২৫.

A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to pass a man standing at a crossing.

ক
18 seconds
খ
12 seconds
গ
15 seconds
ঘ
24 seconds

ব্যাখ্যা

Question: A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to pass a man standing at a crossing.

Solution:
Given that,
Length of train, L = 100 meters
Speed of train, v = 30 km/h
= 30 × (1000/3600) m/s
= 30 × (5/18) m/s
= 150/18 m/s
= 25/3 m/s

We know,
Time taken = Distance/Speed
= 100/(25/3) m/s
= 100 × (3/25)
= 300/25
= 12 seconds

So the train takes 12 seconds to pass the man standing at the crossing.

৩২৬.

A person walks at 14 km/h instead of 10 km/h and in the same time covers 20 km more distance. Find the actual distance traveled.

ক
70 km
খ
65 km
গ
80 km
ঘ
50 km

ব্যাখ্যা

Question: A person walks at 14 km/h instead of 10 km/h and in the same time covers 20 km more distance. Find the actual distance traveled.

Solution:
Given that,
Usual speed = 10 km/h
Increased speed = 14 km/h
Extra distance covered = 20 km

Let the actual distance traveled be = d km

Now,
Time = d/10
And, At 14 km/h, distance covered in the same time = d + 20
So,
⇒ d/10 = (d + 20)/14
⇒ 14d = 10d + 200
⇒ 14d - 10d = 200
⇒ 4d = 200
⇒ d = 200/4
∴ d = 50 km

The actual distance traveled is 50 km.

৩২৭.

A man takes 50 minutes to cover a certain distance at a speed of 6 km/hr. If he walks with a speed of 15 km/hr, he covers the same distance in :

ক
ক) 15 min
খ
খ) 18 min
গ
গ) 20 min
ঘ
ঘ) 25 min

ব্যাখ্যা

Distance=Speed × Time
Distance=(6×50)/60 km
Distance=5 km

∴ Required time=Distance/ Speed
=5/15 hrs.
=1/3 hrs
= 20 min

৩২৮.

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
42 km/hr
খ
45 km/hr
গ
50 km/hr
ঘ
52 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.

৩২৯.

A person can swim in still water with a speed of 12 km/h. If the speed of the stream is 3 km/h, what will be the time taken by the person to go 54 km upstream?

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

ব্যাখ্যা

Question: A person can swim in still water with a speed of 12 km/h. If the speed of the stream is 3 km/h, what will be the time taken by the person to go 54 km upstream?

Solution:
Given,
Speed of the person in still water = 12 km/h
Speed of the stream = 3 km/h
Distance to be covered upstream = 54 km
We know,
The effective speed = Speed in still water - Speed of stream
= (12 - 3) km/h
= 9 km/h

Time = (Distance ÷ Effective speed) hours
= (54 ÷ 9) hours
= 6 hours

৩৩০.

In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is-

ক
5 kmph
খ
6 kmph
গ
6.25 kmph
ঘ
7.5 kmph
ঙ
None of these

ব্যাখ্যা

Question: In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is-

Solution:
Let Abhay's speed be x km/hr.
Then,
30/x - 30/2x = 3
⇒ 6x = 30
∴ x = 5 km/hr.

৩৩১.

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

ক
ক) 10
খ
খ) 12
গ
গ) 15
ঘ
ঘ) 20

ব্যাখ্যা

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

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

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

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

৩৩২.

If a man goes 24 km downstream in 4 hours and returns against the stream in 12 hours, then the speed of the stream in km/hr is -

ক
ক) 1.5 km/hr
খ
খ) 2 km/hr
গ
গ) 2.5 km/hr
ঘ
ঘ) 3 km/hr

ব্যাখ্যা

Question: If a man goes 24 km downstream in 4 hours and returns against the stream in 12 hours, then the speed of the stream in km/hr is -

Solution:
Downspeed stream = 24/4 = 6 km/hr
Upstream speed = 24/12 = 2 km/hr

∴ Speed of the stream = (6 - 2)/2 = 2 km/hr

৩৩৩.

A train of length 100 meters is moving at a speed of 70 km/hr. In what time it will cross a man who is walking at 10 km/hr in the same direction?

ক
5 seconds
খ
6 seconds
গ
8 seconds
ঘ
7 seconds
ঙ
None of these

ব্যাখ্যা

Question: A train of length 100 meters is moving at a speed of 70 km/hr. In what time it will cross a man who is walking at 10 km/hr in the same direction?

Solution:
n this problem, both the train and man are moving so we will find the relative speed of the train. They are moving in the same direction, so the relative speed = (speed of train - speed of man)

Relative Speed = (70-10) = 60 km/hr

Relative Speed in m/s = 60 × (5/18) = 50/3 m/s

Distance covered to cross the man = length of the train (100 meters)

Time = 100 × (3/50) sec
= 6 sec

৩৩৪.

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.

ক
120 m
খ
220 m
গ
150 m
ঘ
180 m

ব্যাখ্যা

Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.

Solution:
Given that,
Speed of train, v = 60 km/h
Time to cross a pole, t = 9 seconds

We know,
Length of the train = speed × time
= (50/3) × 9
= (50 × 9)/3
= 450/3
= 150 meters

So the length of the train is 150 meters.

৩৩৫.

Thrice the speed of a boat downstream is equal to four times the speed upstream. The ratio of its speed in still water to its speed in current is-

ক
ক) 5 : 1
খ
খ) 6 : 1
গ
গ) 4 : 1
ঘ
ঘ) 7 : 1

ব্যাখ্যা

Question: Thrice the speed of a boat downstream is equal to four times the speed upstream. The ratio of its speed in still water to its speed in current is-

Solution:
Let,
Speed in still water = x km/hr.
Speed of current = y km/hr.
Speed downstream = (x + y) km/hr.
Speed upstream = (x - y) km/hr.
so,
3 (x + y) = 4 (x - y)
⇒ 3x + 3y = 4x - 4y
⇒ 4x - 3x = 3y + 4y
⇒ x = 7y
⇒ x/y = 7/1
∴ x : y = 7 : 1

৩৩৬.

A plane flying north at 500 mph passes over a city at 12 noon. A plane flying east at the same altitude passes over the same city at 12 : 30 P.M. The plane is flying east to 400 mph. To the nearest hundred miles, how far apart are the two planes at 2 P.M.?

ক
ক) 600 miles
খ
খ) 962 miles
গ
গ) 1020 miles
ঘ
ঘ) 1166 miles

ব্যাখ্যা

Distance covered by the first plane till 2 P.M.
i.e., in 2 hrs = (500 × 2) miles
= 1000 miles.
Distance covered by the second plane till 2 P.M.
i.e., in 1(1/2) hrs = (400 × 3/2) miles
= 600 miles.
∴ Required distance
= AB =√{(1000)² + (600)²}
=√(1000000 + 360000)
=√1360000
= 200√34 miles
= 200 × 5.83
= 1166 miles.

৩৩৭.

একটি গাড়ি যাত্রার প্রথম ৩৯ কিলোমিটার ৪৫ মিনিটে এবং বাকি ২৫ কিলোমিটার ৩৫ মিনিটে অতিক্রম করে। গাড়িটির গড় গতিবেগ কত?

ক
ক) ৩৬ কি.মি./ঘণ্টা
খ
খ) ৪২ কি.মি./ঘণ্টা
গ
গ) ৪৮ কি.মি./ঘণ্টা
ঘ
ঘ) ৫৪ কি.মি./ঘণ্টা

ব্যাখ্যা

মোট দূরত্ব = (৩৯ + ২৫) কিলোমিটার
= ৬৪ কিলোমিটার

সময় = (৪৫ + ৩৫) মিনিট
= ৮০ মিনিট
= ১ ঘণ্টা ২০ মিনিট
= ৪/৩ ঘণ্টা

গাড়িটির গড় গতিবেগ = ৬৪/(৪/৩) কিলোমিটার/ঘণ্টা
= ৪৮ কি.মি./ঘণ্টা

৩৩৮.

An individual is cycling at a speed of 30 km per hour. He catches his predecessor who had started earlier in three hours. What is the speed of his predecessor who had started 3 hours earlier?

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

ব্যাখ্যা

Question: An individual is cycling at a speed of 30 km per hour. He catches his predecessor who had started earlier in three hours. What is the speed of his predecessor who had started 3 hours earlier?

Solution:
The distance covered in three hour = 3 × 30
= 90 km

Time taken by first individual = (3h + 3h) = 6h

Then, the speed of predecessor, = 90/6 kmph
= 15 kmph.

৩৩৯.

A barge, when empty, travels twice as fast as when it is full. If it travel 20 miles north with a cargo, spends 30 minutes for unloading and returns to its original port empty to complete the entire trip taking 8 hours, what is the speeds of the barge when it is empty?

ক
12mph
খ
8mph
গ
10mph
ঘ
15mph
ঙ
.

ব্যাখ্যা

Question: A barge, when empty, travels twice as fast as when it is full. If it travel 20 miles north with a cargo, spends 30 minutes for unloading and returns to its original port empty to complete the entire trip taking 8 hours, what is the speeds of the barge when it is empty?

Solution:
ধরি,
Barge এর মাল বোঝাই অবস্থায় গতি বেগ x মাইল /ঘণ্টা
Barge এর খালি অবস্থায় গতি বেগ 2x মাইল/ঘণ্টা

মাল বোঝাই অবস্থায়
Barge এর 20 মাইল যেতে সময় লাগে = 20/x ঘণ্টা

খালি অবস্থায়
Barge এর 20 মাইল যেতে সময় লাগে =20/2x = 10/x ঘণ্টা

প্রশ্নমতে,
20/x + 10/x + 30/60 = 8
20/x + 10/x + 1/2 = 8
(40 + 20 + x)/2x = 8
16x = 60 + x
16x - x = 60
15x = 60
x = 4

Barge এর খালি অবস্থায় গতি বেগ = 2x মাইল/ঘণ্টা
= 2 × 4 মাইল/ঘণ্টা
= 8 মাইল/ঘণ্টা

৩৪০.

A train 900 meter long is running at a speed of 90 km/h. If it crosses a tunnel in 1 min, then the length of the tunnel is-

ক
500 meter
খ
600 meter
গ
700 meter
ঘ
800 meter

ব্যাখ্যা

Question: A train 900 meter long is running at a speed of 90 km/h. If it crosses a tunnel in 1 min, then the length of the tunnel is-

Solution:
Let
the length of the tunnel = x meter
Then, distance = (900 + x) meter
Time = 1 minute = 60 seconds

∴ Speed = 90 km/h
= {90 × (5/18)} m/s
= 25 m/s

ATQ,
900 + x = 60 × 25
⇒ 900 + x = 1500
∴ x = 600

So, the length of the tunnel is 600 meter

৩৪১.

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) 3:2
গ
গ) 3:4
ঘ
ঘ) None of these

ব্যাখ্যা

Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres
and length of the second train = 17y metres
∴ 27x+17y/(x+y) = 23
⇒ 27x+17y = 23x+23y
⇒ 4x=6y
⇒ x/y= 3/2

৩৪২.

A train of length 150m takes 10 seconds to cross another train 100m long coming from the opposite direction. If the speed of first train is 30 km/hr, what is the speed of second train ?

ক
ক) 48 km/hr
খ
খ) 54 km/hr
গ
গ) 60 km/hr
ঘ
ঘ) 72 km/hr

ব্যাখ্যা

ধরি
২য় ট্রেনের গতিবেগ x

দেয়া আছে,
১ম ট্রেনের দৈর্ঘ্য = 150 মিটার
২য় ট্রেনের দৈর্ঘ্য = 100মিটার

১ম ট্রেনের গতিবেগ = 30 কি.মি./ঘণ্টা
এখন
10 = (150 + 100)/{(30 + x)(5/18)}
⇒18 × 250 = 10(150 + 5x)
⇒ 4500 = 1500 + 50x
⇒ 50x = 4500 - 1500
⇒ 50x = 3000
⇒ x = 60km/hr

৩৪৩.

When the speed is increased to 4 kmph it takes 4 hours less to cover a distance of 32 km. Find the previous speed.

ক
2 kmph
খ
4 kmph
গ
8 kmph
ঘ
2 kmph
ঙ
None of the above

ব্যাখ্যা

Previous speed = x
A/Q,
32/x - 32/(x + 4) = 4
Or, 32x + 128 - 32x/x(x + 4) = 4
Or, (x + 4)x = 32
Or, x² + 4x - 32 = 0
Or, x² + 8x - 4x - 32 = 0
Or, (x + 8) (x - 4) = 0
So, previous speed is 4 kmph.
And, Present speed will be 4 + 4 = 8 kmph.

৩৪৪.

A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and comes back, how far is the place?

ক
ক) 2 km
খ
খ) 2.4 km
গ
গ) 3 km
ঘ
ঘ) 3.6 km

ব্যাখ্যা

Question: A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and comes back, how far is the place?

Solution
Speed downstream = (5 + 1) kmph = 6 kmph
Speed upstream = (5 - 1) kmph = 4 kmph
Let the required distance be x km

Then,
x/6 + x/4 = 1
⇒ (2x + 3x)/12 = 1
⇒ 2x + 3x = 12
⇒ 5x = 12
⇒ x = 2.4 km

৩৪৫.

The speed of a boat along the stream is 18 km/hr and against the stream is 12 km/hr. What is the time taken by the boat to sail 45 km in still water?

ক
1 hours
খ
2 hours
গ
3 hours
ঘ
4 hours
ঙ
4.5 hours

ব্যাখ্যা

Speed of boat in still water = (18 + 12)/2 = 15 km/hr [ speed = distance/time ]
Time taken by the boat in still water = 45/15 = 3 hours

৩৪৬.

In a city, the fare of a cab consists of fixed charge plus the charge for the distance covered. For a journey of 8 km, the charge paid is Tk. 300 and for 15 km, the charge paid is Tk. 335. Determine the charge a person will have to pay for 24 km?

ক
ক) Tk. 236
খ
খ) Tk. 248
গ
গ) Tk. 346
ঘ
ঘ) Tk. 380

ব্যাখ্যা

Question: In a city, the fare of a cab consists of fixed charge plus the charge for the distance covered. For a journey of 8 km, the charge paid is Tk. 300 and for 15 km, the charge paid is Tk. 335. Determine the charge a person will have to pay for 24 km?

A private taxi company charges a fixed charge along with a per kilometre charge based on the distance covered. For a journey of 24 km, the charges paid are Rs. 368 and for a journey of 32 km, the charges paid Rs. 464.

Let, the fixed charge be ‘a’ and charge per km be ‘b’.
According to question: a + 8b = 300 ---- (I)
a + 15b = 335 ---- (II)

(II) - (I),
15b - 8b = 35
7b = 34
b = 5

If we put the value of ‘b’ in equation (I), we get:
a + 8 × 5 = 300
a = 260

For travelling a distance of 24 km, a person will have to pay Rs. (a + 24b)
= 260 + 24 × 5
= 260 + 120
= 380

৩৪৭.

A man completes a journey in 10 hours. He travels the first half of the journey at the rate of 30 km/hr and the second half at the rate of 50 km/hr. Find the total journey in km.

ক
375 km
খ
384 km
গ
405 km
ঘ
280 km

ব্যাখ্যা

Question: A man completes a journey in 10 hours. He travels the first half of the journey at the rate of 30 km/hr and the second half at the rate of 50 km/hr. Find the total journey in km.

Solution:
ধরা যাক, মোট যাত্রার দূরত্ব হলো d কিমি।
তাহলে, যাত্রার প্রথম অর্ধেকের দূরত্ব হবে d/2 কিমি
এবং দ্বিতীয় অর্ধেকের দূরত্বও হবে d/2 কিমি।

প্রথম অর্ধেক যাত্রায়,
সময় = দূরত্ব/গতিবেগ
= (d/2)/30 ঘন্টা
= d/60 ঘন্টা

দ্বিতীয় অর্ধেক যাত্রায়,
সময় = দূরত্ব/গতিবেগ
= (d/2)/50 ঘন্টা
= d/100 ঘন্টা

প্রশ্নমতে,
(d/60) + (d/100) = 10
⇒ (5d + 3d)/300 = 10
⇒ 8d/300 = 10
⇒ 8d = 10 × 300
⇒ 8d = 3000
⇒ d = 3000/8
⇒ d = 375 কিমি

∴ মোট যাত্রার দূরত্ব 375 কিলোমিটার।

৩৪৮.

Two trains 150 m and 180 m long run at the speed of 72 km/hr and 36 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is:

ক
8 sec
খ
9.8 sec
গ
10 sec
ঘ
11 sec

ব্যাখ্যা

Question: Two trains 150 m and 180 m long run at the speed of 72 km/hr and 36 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is:

Solution:
Relative speed = (72 + 36) km/hr
= 108 × (5/18) m/sec
= 30 m/sec

Distance covered in crossing each other = (150 + 180) m
= 330 m.

Required time = 330/30 sec
= 11 sec

৩৪৯.

A train covers a distance between two stations A and B in 45 minutes. If the speed of the train is reduced by 5 km/hr, then it covers the distance in 48 minutes. The distance between the stations A and B is :

ক
ক) 40 km
খ
খ) 50 km
গ
গ) 55 km
ঘ
ঘ) 60 km

ব্যাখ্যা

Question: A train covers a distance between two stations A and B in 45 minutes. If the speed of the train is reduced by 5 km/hr, then it covers the distance in 48 minutes. The distance between the stations A and B is :

Solution:
Let
the distance between the stations A and B be x km
Time taken = 45 min = 45/60 = 3/4 hour

∴ Original speed =(x × 4/3)km/hr = 4x/3 km/hr

New speed = {(4x/3) - 5} km/hr.
= (4x - 15)/3 km/hr.

Now
x/{(4x - 15/3} =48/60
3x/(4x - 15) = 4/5
16x - 60 = 15x
16x - 15x = 60
x = 60 km

৩৫০.

A train 125 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
ক) 45 km/hr
খ
খ) 50 km/hr
গ
গ) 54 km/hr
ঘ
ঘ) 55 km/hr

ব্যাখ্যা

Speed of the train relative to man
= 125/10 m/sec
= 25/2 m/sec
= (25/2)×(18/5) km/hr
= 45km/hr
Let the speed of the train be x km/hr. Then, relative speed=(x−5)km/hr
∴x−5= 45
⇒x = 50km/hr

৩৫১.

A motorboat in still water travels at speed of 26 kmph. It goes 42 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be:

ক
1 hr
খ
1 hr 30 min
গ
1 hr 45 min
ঘ
2 hr

ব্যাখ্যা

Question: A motorboat in still water travels at speed of 26 kmph. It goes 42 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be:

Solution:
মোটরযানের বেগ ২৬ কিমি/ঘণ্টা

স্রোতের বিপরীতে ১ঘণ্টা ৪৫ মিনিট বা ৭/৪ ঘণ্টায় যায় ৪২ কিমি
১ ঘণ্টায় যায় ৪২/৭/৪ কিমি
= ২৪ কিমি
স্রোতের বেগ = ২৬ - ২৪ কিমি/ঘণ্টা
= ২ কিমি/ঘণ্টা

স্রোতের অনুকূলে বেগ = ২৬ +২
= ২৮ কিমি/ঘণ্টা

৪২ কিমি যেতে সময় লাগে ৪২/২৮
= ৩/২
= ১.৫ ঘণ্টা
= ১ ঘণ্টা ৩০ মিনিট

৩৫২.

An employee may claim Tk. 7.00 for each km when he travels by taxi and Tk. 6.00 for each km if he drives his own car. If in one week he claimed Tk. 595 for traveling 90 km. How many kms did he travel by taxi?

ক
55 kms
খ
35 kms
গ
25 kms
ঘ
65 kms

ব্যাখ্যা

Question: An employee may claim Tk. 7.00 for each km when he travels by taxi and Tk. 6.00 for each km if he drives his own car. If in one week he claimed Tk. 595 for traveling 90 km. How many kms did he travel by taxi?

Solution:
Let x and y be the respective km's travelled by man via taxi and by his own car.
Given x + y = 90
⇒ x = 90 - y
But according to the question,
7x + 6y = 595
⇒ 7(90 - y) + 6y = 595
⇒ 630 - 7y + 6y = 595
⇒ y = 630 - 595
∴ y = 35

∴ x = 90 - 35 = 55

Therefore, the distance travelled by taxi is 55 kms.

৩৫৩.

A train 150m long, takes 30 seconds to cross a bridge 500m long. How much time will the train to cross a platform 370 m long?

ক
ক) 28 sec
খ
খ) 27 sec
গ
গ) 24 sec
ঘ
ঘ) 25 sec

ব্যাখ্যা

Length of the train = 150 m
Length of the bridge = 500 m
∴ Total length = (500 + 150)m
= 650m

∴ Speed of the train =650/30 m/sec
= 65/3 m/sec

Now total length of the train and new bridge = (370 + 150)m
= 520m

∴ Time taken = (520 × 3)/65 sec
= 24 sec

৩৫৪.

In 24 seconds, an athlete covers 200 meters. What is his speed in kilometres per hour?

ক
15
খ
20
গ
30
ঘ
40

ব্যাখ্যা

Question: In 24 seconds, an athlete covers 200 meters. What is his speed in kilometres per hour?

Solution:
Speed of athlete
= 200 m/24 sec
= (200 × 18)/(5 × 24)
= 30 km/hour

৩৫৫.

A 1300 m long train crosses a tree in 130 sec, how much time will it take to pass a platform 800 m long?

ক
ক) 150 sec.
খ
খ) 160 sec.
গ
গ) 170 sec.
ঘ
ঘ) 210 sec.

ব্যাখ্যা

Here
Length of a train is 1300m
Train took 130 sec to cross a tree
Length of a platform is 800m

Speed of the train = 1300/130 = 10 m/sec
Total distance = 1300 + 800 = 2100 m

Time = distance/speed
= 2100/10 = 210 sec

∴ Time required to cross a platform is 210 sec.

৩৫৬.

A man can row three-quarters of a kilometre against the stream in 11.25 minutes and down the stream in 7.5 minutes. The speed (in km/hr) of the man in still water is:

ক
2 km/hr
খ
3 km/hr
গ
4 km/hr
ঘ
5 km/hr

ব্যাখ্যা

Question: A man can row three-quarters of a kilometre against the stream in 11.25 minutes and down the stream in 7.5 minutes. The speed (in km/hr) of the man in still water is:

Solution:
Three - quarters of a kilometer = (3 × 1000)/4 meters = 750 meters

11.25 minutes = 11.25 × 60 = 675 sec
7.5 minutes = 7.5 × 60 = 450sec

Rate upstream = 750/ 675 m/sec
= 10/9 m/sec

Rate downstream =750/450 m/sec
= 5/3 m/sec

∴Rate in still water = (1/2){(10/9) + (5/3)} m/sec
= (1/2){(10 + 15)/9}
= (1/2)(25/9)
= 25/18
= (25/18)(18/5) km/hr.
= 5 km/hr

৩৫৭.

A 120 m long train passed a pole in 12 seconds. How long will it take to pass a 450 m long platform?

ক
ক) 89 sec
খ
খ) 57 sec
গ
গ) 59 sec
ঘ
ঘ) 61 sec

ব্যাখ্যা

Train’s speed = 120/12 = 10 m/s
The train has to cover = (120 + 450) = 570 m.
∴ Required time = 570/10 = 57 seconds

৩৫৮.

A train crosses a platform 90 m long in 50 seconds at a speed of 36 km/hr. What is the time taken by the train to cross an electric pole?

ক
ক) 31 sec
খ
খ) 33 sec
গ
গ) 37 sec
ঘ
ঘ) 41 sec

ব্যাখ্যা

Question: A train crosses a platform 90 m long in 50 seconds at a speed of 36 km/hr. What is the time taken by the train to cross an electric pole?

Solution:
Speed of the train = (36 × 1000)/(60 × 60) = 10 m/sec
So, in 50 sec it goes = (10 × 50) = 500 m

Since the platform is 90 m so, only train = (500 - 90) m = 410 m [ খুঁটি অতিক্রম করতে হলে শুধু এতটুকু যেতে হবে ]

∴ Time taken by the train to cross an electric pole = (410/10) sec = 41 sec

৩৫৯.

Two trains start from station A and B and travels towards each other at speed of 48km/hr and 72km/hr respectively. At the time of their meeting, the second train has traveled 144 km more than the first. The distance between A and B is-

ক
680 km
খ
720 km
গ
760 km
ঘ
800 km

ব্যাখ্যা

Question: Two trains start from station A and B and travels towards each other at speed of 48km/hr and 72km/hr respectively. At the time of their meeting, the second train has traveled 144 km more than the first. The distance between A and B is-

Solution:
The second train has traveled 144 km more than the first train because the speed of second train is 24 km/hr more than first.
Time taken by second train to cover 144 km with surplus 24km/hr = 144/24 = 6 hours.
then, time taken by both train before meeting is 6 hours.
So, their relative speed = 48 + 72 = 120
Total distance travel by both = 120 × 6 = 720 km
Distance between A and B = 720 km

৩৬০.

A man covers half of his journey by train at 60 km/hr, half of the remaining by bus at 30 km/hr and the rest by cycle at 10 km/hr. Find his average speed during the entire journey?

ক
32 kmph
খ
20 kmph
গ
18 kmph
ঘ
24 kmph

ব্যাখ্যা

Question: A man covers half of his journey by train at 60 km/hr, half of the remaining by bus at 30 km/hr and the rest by cycle at 10 km/hr. Find his average speed during the entire journey?

Solution:
Let the total distance be 120 km
⇒Time taken to cover distance at 60 km/h = 60/60 = 1 hr
⇒ Time taken to cover distance at 30 km/h = 30/30 = 1 hr
⇒ Time taken to cover distance at 10 km/h = 30/10 = 3 hr

∴ Average speed = 120/(1 + 1 + 3) = 24 km/h

৩৬১.

A train is moving at the rate 8 mi/h along a piece of circular track of radius 2,500 ft. Through what angle does it turn in 1 min?

ক
ক) 0.3816 rad or 18.13°
খ
খ) 0.2816 rad or 16.13°
গ
গ) 0.2844 rad or 16.30°
ঘ
ঘ) 0.2916 rad or 17.13°

ব্যাখ্যা

A train is moving at the rate 8 mi/h along a piece of circular track of radius 2,500 ft. Through what angle does it turn in 1 min?

সমাধান:
৮ মাইল/ঘণ্টা = (৮ × ৫২৮০)/৬০ ফুট/মিনিট [১ মাইল = ৫২৮০ ফুট]
= ৭০৪ ফুট/মিনিট

২৫০০ ফুট ব্যাসার্ধ বিশিষ্ট পথের পরিধি = ২ × π × ২৫০০ ফুট
= ৫০০০π ফুট

মোট সময় = ৫০০০π ÷ ৭০৪ মিনিট
= ৬২৫π/৮৮ মিনিট

একবার ঘুরলে ট্রেনটি অতিক্রম করে ৩৬০° = ২π রেডিয়ান

৬২৫π/৮৮ মিনিটে উৎপন্ন করে ২π রেডিয়ান
∴ ১ মিনিটে উৎপন্ন করে (২π × ৮৮)/৬২৫π রেডিয়ান
= ০.২৮১৬ রেডিয়ান

এখন,
০.২৮১৬ রেডিয়ান
= (০.২৮১৬ × ১৮০)/π
= ১৬.১৩°

৩৬২.

A 280 metre long train crosses a platform thrice its length in 50 seconds. What is the speed of the train in km/hr?

ক
40.64 km/h
খ
80.64 km/h
গ
50.64 km/h
ঘ
70.64 km/h

ব্যাখ্যা

Question: A 280 metre long train crosses a platform thrice its length in 50 seconds. What is the speed of the train in km/hr?

Solution:
Given that,
Length of the train = 280 m
Length of the platform = 3 × 280 = 840 m

∴ Total distance to be covered
= Train length + Platform length
= 280 + 840
= 1120m
And, Time taken = 50 seconds

∴ Speed = Distance/Time
= 1120/50
= 22.4 m/s
= 22.4 × 3.6 ;[1 m/s = 3.6 km/h]
= 80.64 km/h

∴ The speed of the train is 80.64 km/h.

৩৬৩.

A moving train, 66 metres long, overtakes another train of 88 metres long, moving in the same direction in 0.168 minutes. If the second train is moving at 40 km/hr, at what speed is the first train moving ?

ক
ক) 95 km/hr
খ
খ) 85 km/hr
গ
গ) 75 km/hr
ঘ
ঘ) 79 km/hr

ব্যাখ্যা

Let the speed of the first train be x km/hr.
Then,
Sum of lengths of trains = (66 + 88)m = 154 m.

Relative speed of two trains = (x - 40) km/hr
= {(x - 40) × (5/18)} m/s

∴ 154/{(x - 40) × (5/18)} = 0.168 × 60
⇒ 5(x - 40) = (154 × 18)/10.08
⇒ 5(x - 40) = 275
⇒ x - 40 = 55
⇒ x = 95 km/hr.

৩৬৪.

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 meters) is :

ক
ক) 360
খ
খ) 500
গ
গ) 540
ঘ
ঘ) 130

ব্যাখ্যা

Let the length of the tunnel = x meter
Then, distance = (800 + x) meter.

Given,
Time = 1 minute = 60 seconds.
Speed = 78 km/hr
= 78 × (5/18)
= (65/3) m/s

According to the question,
800 + x = 60 × (65/3)
⇒ 800 + x = 1300
⇒ x = 500 meter.

So, the length of the tunnel = 500 meter

৩৬৫.

A train moves past a telegraph post and a bridge 240 m long in 8 seconds and 20 seconds respectively. What is the speed (km/h) of the train?

ক
60 km/h
খ
68 km/h
গ
72 km/h
ঘ
76 km/h

ব্যাখ্যা

Question: A train moves past a telegraph post and a bridge 240 m long in 8 seconds and 20 seconds respectively. What is the speed (km/h) of the train?

Solution:
Let,
the length of the train = x metres
and its speed = y m/sec

ATQ,
x/y = 8
⇒ x = 8y

and,
(x + 240)/20 = y
⇒ x + 240 = 20y
⇒ 8y + 240 = 20y
⇒ 240 = 20y - 8y
⇒ 12y = 240
∴ y = 20

∴ The speed of the train = 20 m/sec
= 20 × (18/5) km/h
= 72 km/h

৩৬৬.

Two trains A and B start running together from the same point in the same direction, at the speed of 60 kmph and 72 kmph respectively. If the length of each of the trains is 240 meters, how long will it take for B to cross train A?

ক
2 min 16 sec
খ
2 min 24 sec
গ
3 min 6 sec
ঘ
1 min 12 sec

ব্যাখ্যা

Question: Two trains A and B start running together from the same point in the same direction, at the speed of 60 kmph and 72 kmph respectively. If the length of each of the trains is 240 meters, how long will it take for B to cross train A?

Solution:
Relative speed = (72 - 60) km/hr
= 12 km/hr
= {12 × (5/18)} m/sec
= (10/3) m/sec

Now,
Total distance covered = Both trains start from the same point, so train B has to cover 240 m

∴ Time taken = {240 × (3/10)} sec
= 72 sec
= 1 min 12 sec

৩৬৭.

A train crosses platform in 50 seconds travelling with a speed of (x + 6) km/hr. If the length of the train be 250 m and the length of the platform be (x + 220) m, then, find the value of x?

ক
30
খ
35
গ
40
ঘ
50

ব্যাখ্যা

Question: A train crosses platform in 50 seconds travelling with a speed of (x + 6) km/hr. If the length of the train be 250 m and the length of the platform be (x + 220) m, then, find the value of x?

Solution:
Speed of train = (x + 6) km/hr
= (x + 6) × (5/18) m/s

Length of train = 250 m
Length of platform = (x + 220) m

Distance = Length of train + Length of platform
= (250 + x + 220) m
= (470 + x) m

Time = 50 seconds

ATQ,
(x + 6) × (5/18) = (470 + x)/50
⇒ 5 × 50 (x + 6) = 18(470 + x)
⇒ 125(x + 6) = 9(470 + x)
⇒ 125x + 750 = 4230 + 9x
⇒ 125x - 9x = 4230 - 750
⇒ 116x = 3480
⇒ x = 3480/116
⇒ x = 30

∴ The value of x is 30

৩৬৮.

A car travels a distance of 60 km in 1 hour and 40 minutes. How much faster, in kilometers per hour, on an average, must it travel to make the same trip in 20 minutes less time?

ক
9 km/h
খ
12 km/h
গ
10.5 km/h
ঘ
15 km/h

ব্যাখ্যা

Question: A car travels a distance of 60 km in 1 hour and 40 minutes. How much faster, in kilometers per hour, on an average, must it travel to make the same trip in 20 minutes less time?

সমাধান:
দেওয়া আছে,
মোট অতিক্রান্ত দূরত্ব = 60 কিমি।
প্রাথমিক সময় = 1 ঘন্টা 40 মিনিট = 1 + 40/60 ঘন্টা = 1 + 2/3 = 5/3 ঘন্টা।

প্রাথমিক গতিবেগ = দূরত্ব/সময়
= 60 / (5/3) কিমি/ঘন্টা
= (60 × 3/5) কিমি/ঘন্টা
= 36 কিমি/ঘন্টা।

20 মিনিট কম সময় = 20/60 = 1/3 ঘন্টা কম।
∴ নতুন সময় = (প্রাথমিক সময় - কমানো সময়)
= 5/3 - 1/3 ঘন্টা
= 4/3 ঘন্টা।

∴ নতুন গতিবেগ = 60/(4/3) কিমি/ঘন্টা
= (60 × 3/4) কিমি/ঘন্টা
= 45 কিমি/ঘন্টা।

গতি বৃদ্ধি করতে হবে = (নতুন গতিবেগ - প্রাথমিক গতিবেগ)
= (45 - 36) কিমি/ঘন্টা
= 9 কিমি/ঘন্টা।

∴ গাড়িটিকে গড়ে 9 কিমি/ঘন্টা বেশি গতিতে যেতে হবে।

৩৬৯.

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

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

ব্যাখ্যা

Speed of the first train = 48 km/hr.
Let the length of the first train = 2x meter.
Speed of the second train = 42 km/hr.
Let the length of the second train = x meter.
Distance = (2x + x) = 3x meter.
Time = 12 seconds
Relative speed = 48 + 42 = 90 km/hr.
= 90 × (5/18) = 25 m/s.
3x = 25 × 12
⇒ x = 100 meter.
Length of the first train = 200
Time is taken to cross the platform = 45 seconds.
Speed of first train = 48 km/hr
= 48 × (5/18)
= 40/3 m/s.
Let the length of the platform = y meter.
Distance = 200 + y meter.
⇒ 200 + y = 45 × (40/3)
⇒ 200 + y = 600
⇒ y = 400 meter.

৩৭০.

নৌকার গতিবেগ ঘণ্টায় ২০ কি.মি. ও স্রোতের গতিবে ঘণ্টায় ৫ কি.মি. হলে, নদীপথে ৭৫ কি.মি. যেয়ে আবার ফিরে আসতে কত সময় লাগবে?

ক
৬ ঘণ্টা
খ
৭ ঘণ্টা
গ
৮ ঘণ্টা
ঘ
৯ ঘণ্টা
ঙ
কোনোটিই নয়

ব্যাখ্যা

প্রশ্ন: নৌকার গতিবেগ ঘণ্টায় ২০ কি.মি. ও স্রোতের গতিবে ঘণ্টায় ৫ কি.মি. হলে, নদীপথে ৭৫ কি.মি. যেয়ে আবার ফিরে আসতে কত সময় লাগবে?

সমাধান:
স্রোতের অনুকূলে,
নৌকার গতিবেগ = (২০ + ৫) কি.মি./ঘণ্টা
= ২৫ কি.মি./ঘণ্টা
∴ ৭৫ কি.মি. পথ যেতে প্রয়োজনীয় সময় = ৭৫/২৫ ঘন্টা = ৩ ঘণ্টা

আবার,
স্রোতের প্রতিকূলে,
নৌকার গতিবেগ = (২০ - ৫) কি.মি./ঘণ্টা
= ১৫ কি.মি./ঘন্টা।
∴ ৭৫ কি.মি. পথ ফিরে আসতে প্রয়োজনীয় সময় = ৭৫/১৫ ঘন্টা = ৫ ঘণ্টা

∴ নির্ণেয় সময় = ৩ + ৫ ঘণ্টা
= ৮ ঘণ্টা

৩৭১.

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

ক
65 sec
খ
89 sec
গ
100 sec
ঘ
150 sec

ব্যাখ্যা

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

Solution:
Speed = 240/24 = 10 m/s
∴ Required time = (240 + 650)/10
= 89 sec

৩৭২.

A train passes two bridges of lengths 500 meters and 250 meters in 100 seconds and 60 seconds respectively. The length of the train is-

ক
ক) 150 meters
খ
খ) 200 meters
গ
গ) 125 meters
ঘ
ঘ) 175 meters

ব্যাখ্যা

Question: A train passes two bridges of lengths 500 meters and 250 meters in 100 seconds and 60 seconds respectively. The length of the train is-

Solution:
Let the length of train be x m

ATQ,
(x + 500)/100 = (x + 250)/60
⇒ 100x + 25000 = 60x + 30000
⇒ 40x = 5000
⇒ x = 125

৩৭৩.

If a car travels 20 meters in a second, what is it speed (in kilometer) per hour?

ক
72 km/hr
খ
66 km/hr
গ
88 km/hr
ঘ
60 km/hr

ব্যাখ্যা

Question: If a car travels 20 meters in a second, what is it speed (in kilometer) per hour?

Solution:
speed = 20 meters/second
= (20 /1000) km/second [1km = 1000m]
= 1/50 km/second
= (3600/50) km/hr [1 hour = 3600 second]
= 72 km/hr

৩৭৪.

The speed of A and B are in the ratio 3 : 4. A takes 15 minutes more than B to reach a destination. Time in which A reach the destination?

ক
ক) 1 hour
খ
খ) 2 hours
গ
গ) 1.5 hours
ঘ
ঘ) 2.5 hours

ব্যাখ্যা

Question: The speed of A and B are in the ratio 3 : 4. A takes 15 minutes more than B to reach a destination. Time in which A reach the destination?

Solution:
Ratio of speed = 3 : 4
Ratio of time taken = 4 : 3

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

Now
4x - 3x = 15/60
x = 1/4

Hence, time taken by A = 4x hours
= 4 × 1/4
= 1 hour

৩৭৫.

A person crosses a 1200 m long street in 10 minutes. What is his speed in km per hour?

ক
3.6 km/hr
খ
7.2 km/hr
গ
8.4 km/hr
ঘ
10 km/hr

ব্যাখ্যা

Question: A person crosses a 1200 m long street in 10 minutes. What is his speed in km per hour?

Solution:
Speed = 1200 meters/10 minutes
= (1200 × 60)/(10× 1000) km/hr
= 7.2 km/hr

৩৭৬.

A train running at a certain speed crosses a 496-meter-long platform in 56 seconds. If the length of the train is 560 meters, how long will it take to cross a bridge that is 100 meters in length?

ক
21 seconds
খ
27 seconds
গ
28 seconds
ঘ
35 seconds

ব্যাখ্যা

Question: A train running at a certain speed crosses a 496-meter-long platform in 56 seconds. If the length of the train is 560 meters, how long will it take to cross a bridge that is 100 meters in length?

Solution:
We know,
When a train crosses any object, it covers a distance equal to the sum of the object's length and its own length.

So, when crossing a platform, the distance covered by the train = (496 + 560) meters = 1056 meters
And
when crossing a bridge, the distance covered by the train = (100 + 560) meters = 660 meters

Now,
The train covers 1056 meters in = 56 seconds
∴ It covers 1 meter in = (56/1056) seconds
∴ It covers 660 meters in = (56 × 660)/1056 seconds = 35 seconds

৩৭৭.

Speed of a boat along and against the current are 14 kms/hr and 8 kms/hr respectively. If there is no current how much time will the boat take to travel 22km?

ক
2 hours
খ
3 hours
গ
3.5 hours
ঘ
4 hours

ব্যাখ্যা

Question: Speed of a boat along and against the current are 14 kms/hr and 8 kms/hr respectively. If there is no current how much time will the boat take to travel 22km?

Solution:
Let,
Speed of the boat in still water = S km/h
Speed of the current = W km/h

According to the question,
S + W = 14 …… (i) (Downstream speed)
S − W = 8 …… (ii) (Upstream speed)

Adding equations (i) and (ii):
(S + W) + (S − W) = 14 + 8
⇒ 2S = 22
⇒ S = 11 km/h

So, the boat’s speed in still water is 11 km/h.

Time to travel 22 km in still water = Distance/Speed = 22 / 11 = 2 hours

৩৭৮.

Over a span of 9 hours, a man traveled 61 km, part of it on foot at 4 km/hr and part by bike at 9 km/hr. What distance did he walk?

ক
20 km
খ
14 km
গ
16 km
ঘ
18 km

ব্যাখ্যা

Question: Over a span of 9 hours, a man traveled 61 km, part of it on foot at 4 km/hr and part by bike at 9 km/hr. What distance did he walk?

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

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

৩৭৯.

Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?

ক
2 hrs
খ
20 min
গ
40 min
ঘ
30 min

ব্যাখ্যা

Question: Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?

Solution:
In 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (60 - 40) km = 20 km at 60 km/hr.

∴ stoppage time = 20/60 hrs
= 1/3 hrs
= 20 min.

৩৮০.

A man can row 9 km/hr 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) 2 km/hr.
খ
খ) 3 km/hr.
গ
গ) 4 km/hr.
ঘ
ঘ) 5 km/hr.

ব্যাখ্যা

Question: A man can row 9 km/hr in still water and he finds that it takes him twice as long to row upstream as to row downstream the river. Find the rate of the stream.

Solution:
Let, the speed of the current be x km/hr
Thus upstream speed = (9 - x) km/h and
downstream speed = (9 + x) km/hr

Let distance traveled be y

Then,
y/(9 - x) = 2y/(9 + x)
1/(9 - x) = 2/(9 + x)
9 + x = 18 - 2x
x + 2x = 18 - 9
3x = 9
x = 3

the speed of the current be 3 km/hr.

৩৮১.

While covering a distance of 24 km, a man noticed that after walking for 1 hour and 40 minutes, the distance covered by him was 5/7 of the remaining distance. What was his speed in meters per second?

ক
ক) 1(1/3) m/s
খ
খ) 1 (2/3) m/s
গ
গ) 1 m/s
ঘ
ঘ) 2 (1/3) m/s

ব্যাখ্যা

Let,
The speed is x km/hr.
Then,
Distance covered in 1 hr. 40 min
i.e., 1(2/3) hrs. = 5x/3 km.
Remaining Distance = {24 - (5x/3)}
∴ 5x/3 = 5/7{24 - (5x/3)
⇒ 5x/3 = 5/7{(72 - 5x)/3}
⇒ 7x = 72 - 5x
⇒ 12x = 72
⇒ x = 72/12
⇒ x = 6.
Hence, Speed = 6 km/hr
= {6 × (5/18)} m/s
= 5/3 m/s
= 1(2/3) m/s.

৩৮২.

A train with a length of 150m long, takes 30 seconds to cross a 500m long bridge. How much time will the train take to cross a 370m long platform?

ক
18 sec
খ
24 sec
গ
30 sec
ঘ
36 sec

ব্যাখ্যা

Question: A train with a length of 150m long, takes 30 seconds to cross a 500m long bridge. How much time will the train take to cross a 370m long platform?

Solution:
Length of the train = 150 m
Length of the bridge = 500 m
∴ Total length = (500 + 150)m
= 650m

∴ Speed of the train =650/30 m/sec
= 65/3 m/sec

Now total length of the train and new bridge = (370 + 150)m
= 520m

∴ Time taken = (520 × 3)/65 sec
= 24 sec

৩৮৩.

A person standing on a railway platform noticed that a train took 15 seconds to completely pass through the platform which was 80 m long and it took 9 seconds in passing him. What is the speed of the train in km/hr?

ক
ক) 46 km/hr
খ
খ) 48 km/hr
গ
গ) 50 km/hr
ঘ
ঘ) 52 km/hr

ব্যাখ্যা

Question: A person standing on a railway platform noticed that a train took 15 seconds to completely pass through the platform which was 80 m long and it took 9 seconds in passing him. What is the speed of the train in km/hr?

Solution:
Let the length of the train be x meters
Then, the train covers x meters in 9 seconds
and (x + 80) meters in 15 seconds

ATQ,
x/9 = (x + 80)/15 [ উভয় পাশেই ১ সেকেন্ডের গতিবেগ নেওয়া হয়েছে ]
⇒ 15x = 9x + 720
⇒ 15x - 9x = 720
⇒ 6x = 720
⇒ x = 720/6
∴ x = 120

So, the length of the train is 120 m

∴ Speed of the train = (120/9) m/sec = 40/3 m/sec

Speed of the train in km/hr = (40/3) × (3600/1000) km/hr
= (40/3) × (36/10) km/hr
= 48 km/hr

৩৮৪.

Two trains are running in the same direction on parallel tracks. The first train is 200 meters long and is moving at a speed of 15 meters per second. The second train is 250 meters long and is moving at 10 meters per second. How much time will the faster train take to completely overtake the slower one?

ক
82 seconds
খ
65 seconds
গ
90 seconds
ঘ
70 seconds

ব্যাখ্যা

Question: Two trains are running in the same direction on parallel tracks. The first train is 200 meters long and is moving at a speed of 15 meters per second. The second train is 250 meters long and is moving at 10 meters per second. How much time will the faster train take to completely overtake the slower one?

Solution:
Given that,
Length of faster train = 200 m
Length of slower train = 250 m
Speed of faster train = 15 m/s
Speed of slower train = 10 m/s

Since both trains are moving in the same direction, their relative speed
= (15 - 10)m/s
= 5 m/s

To completely overtake, the faster train must cover the length of both trains
= 200 + 250 = 450 m

We know that,
Time = Distance/Speed = 450/5 = 90 seconds
So the faster train will take 90 seconds to overtake the slower one.

৩৮৫.

A train running at the speed of 66 km/h crosses a pole in 15 seconds. What is the length of the train?

ক
275 m
খ
250 m
গ
235 m
ঘ
220 m

ব্যাখ্যা

Question: A train running at the speed of 66 km/h crosses a pole in 15 seconds. What is the length of the train?

Solution:
Given,
Speed = 66 km/h
= (66 × 5/18) m/sec
= 55/3 m/sec

So the length of the train = (55/3 × 15) m
= 275 m

৩৮৬.

A boat moves downstream at the rate of 1 km in 15/2 minutes and upstream at the rate of 6 km an hour. What is the speed of the boat in the still water?

ক
8 km/hour
খ
9 km/hour
গ
7 km/hour
ঘ
5 km/hour

ব্যাখ্যা

Question: A boat moves downstream at the rate of 1 km in 15/2 minutes and upstream at the rate of 6 km an hour. What is the speed of the boat in the still water?

Solution:
দেওয়া আছে,
স্রোতের অনুকূলে ১৫/২ মিনিটে যায় ১ কিমি
∴ স্রোতের অনুকূলে ১ মিনিটে যায় ১/(১৫/২) কিমি
∴ স্রোতের অনুকূলে ৬০ মিনিট বা (১ ঘণ্টায়) যায় (১ × ৬০)/(১৫/২) কিমি
= (৬০ × ২)/১৫ কিমি
= ৮ কিমি

স্রোতের প্রতিকূলে ১ ঘণ্টায় যায় ৬ কিমি

∴ স্থির পানিতে নৌকার বেগ = (৮ + ৬)/২ কিমি/ঘণ্টা
= ১৪/২ কিমি/ঘণ্টা
= ৭ কিমি/ঘণ্টা

৩৮৭.

The speed of a boat in still water is 22 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 24 minutes is:

ক
12.5 km
খ
10.4 km
গ
8.7 km
ঘ
9,7 km
ঙ
6.9 km

ব্যাখ্যা

Speed downstream = (22 + 4) = 26 kmph
Time = 24 minutes
= 24/60 hour = 2/5 hour
Distance travelled = Time × speed
= (2/5) × 26 = 10.4 km

৩৮৮.

A 240 metre long train crosses a platform twice its length in 40 seconds. What is the speed of the train in km/hr?

ক
ক) 64.8km/hr
খ
খ) 62.8km/hr
গ
গ) 60.8km/hr
ঘ
ঘ) 57.8km/hr

ব্যাখ্যা

Length of train = 240 m
Length of platform = (2 × 240) m = 480m

∴Speed of train (240 + 480)/40 m/sec
= 720/40 m/sec
= 18 × (18/5) km/hr
= 64.8km/hr

৩৮৯.

A person travels 20 km at 10 km/h and then 30 km at 15 km/h. What is the average speed of the entire journey?

ক
12.5 km/h
খ
13.5 km/h
গ
14 km/h
ঘ
15 km/h

ব্যাখ্যা

Question: A person travels 20 km at 10 km/h and then 30 km at 15 km/h. What is the average speed of the entire journey?

Solution:
The total distance traveled is: 20 km + 30 km = 50 km
For the first part of the journey (20 km at 10 km/h), the time taken is: 20/10 = 2 hours
For the second part of the journey (30 km at 15 km/h), the time taken is: 30/15 = 2 hours
Total Time = 2hours + 2hours = 4 hours

∴ Average Speed = Total Distance/Total Time = 50/4 km/h = 12.5 km/h

৩৯০.

A boatman can row a boat upstream at 14 km/hr and downstream at 20 km/hr. Find the speed of the boat in still water.

ক
3 km/hr
খ
11 km/hr
গ
15 km/hr
ঘ
17 km/hr

ব্যাখ্যা

Question: A boatman can row a boat upstream at 14 km/hr and downstream at 20 km/hr. Find the speed of the boat in still water.

Solution:
We are given that speed downstream, D = 20 km/hr
and speed upstream, U = 14 km/hr
Therefore, Speed of boat in still water = 0.5 × (D + U) km / hr = 0.5 × (14 + 20) = 17 km/hr

Another method:
Speed of the stream = 0.5 × (D - U) = 0.5 × 6 = 3 km/hr
Speed of the boat in still water = Speed of the stream + Speed Upstream = 3 + 14 = 17 km/hr

৩৯১.

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

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

ব্যাখ্যা

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

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

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

The speed of the train is 40 km/hr.

৩৯২.

Two towns P & Q are 275 km apart. A motorcycle rider starts from P towards Q at 8 a.m. at the speed of 25 km/hr. Another rider starts from Q towards P at 9 a.m. at the speed of 20 km/hr. Find at what time they will cross each other?

ক
2.45 p.m.
খ
2.30 p.m.
গ
1.35 p.m.
ঘ
1.15 p.m.

ব্যাখ্যা

Assume, distance traveled by P in x hrs = 25 x km -----(1)
distance traveled by Q in (x-1) hrs = 20 (x-1) km -----(2)

Adding (1) & (2),
25 x + 20 (x -1) = 275
x = 6.5 hrs
(x -1) = (6.5 -1) = 5.5 hrs

Time at which they cross each other = 9 a.m. + 5.5hrs = 2.30 p.m.
The two motorcycle riders cross each other at 2.30 p.m.

৩৯৩.

In a race of 200 meters, B can give a start of 10 meters to A, and C can give a start of 20 meters to B. The starts that C can give to A, in the same race is -

ক
27 meters
খ
28 meters
গ
31 meters
ঘ
29 meters

ব্যাখ্যা

Question: In a race of 200 meters, B can give a start of 10 meters to A, and C can give a start of 20 meters to B. The starts that C can give to A, in the same race is -

Solution:
According to the question,
When B runs 200 m meters, A runs 190 meters;
Hence, when B runs 180 meters,
A runs = (190×180)/200
= 171 meters

When C runs 200m, B runs 180 meters.
Hence,
C will give a start to A by = 200 - 171
= 29 meters

৩৯৪.

A dog sees a cat 80 m away. The cat runs at a speed of 5 m/s while the dog chases it at a speed 2 m/s more than that of the cat. Before the dog is able to catch the cat, how much distance has it already run?

ক
50 m
খ
100 m
গ
130 m
ঘ
200 m

ব্যাখ্যা

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

Let distance traveled by cat before dog catches it be D
We know, time for which Dog and Cat ran is the same
∴ T = T
∴ D/5 = (D + 80)/7
⇒ 7D = 5D + 400
⇒ 7D - 5D = 400
⇒ 2D = 400
⇒ D = 200 m.

৩৯৫.

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

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

ব্যাখ্যা

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

Solution:
Time taken in walking both ways = 7 hours 45 minutes ..............(i)
Time taken in walking one way and riding back = 6 hours 15 minutes ...................(ii)

By equation (ii) × 2 - (i), we have
Time taken to man ride both ways = 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45 minutes

৩৯৬.

A train crosses two bridges that are 600 meters and 200 meters long in 60 seconds and 40 seconds respectively. What is the length of the train?

ক
300 meters
খ
500 meters
গ
400 meters
ঘ
600 meters

ব্যাখ্যা

Question: A train crosses two bridges that are 600 meters and 200 meters long in 60 seconds and 40 seconds respectively. What is the length of the train?

Solution:
We know,
To cross a bridge, a train must cover the length of the bridge along with its own length.

Let the length of the train = x meters

Then,
For the first bridge, the distance covered by the train = (x + 600) meters
And,
For the second bridge, the distance covered by the train = (x + 200) meters

According to the question,
(x + 600)/60 = (x + 200)/40
⇒ 40(x + 600) = 60(x + 200)

⇒ 40x + 24000 = 60x + 12000
⇒ 60x - 40x = 24000 - 12000
⇒ 20x = 12000
⇒ x = 12000/20
⇒ x = 600

∴ The length of the train is 600 meters.

৩৯৭.

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

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

ব্যাখ্যা

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

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

⇒ (2x + 3)(x - 1) = 0

∴ x = 1 hr. [neglecting the (- ve) value of x]

৩৯৮.

Simi is walking at a speed of 10 kmph. After every km she takes rests for 5 minutes. The taken to cover a distance of 5 kilometers by Simi is -

ক
ক) 55 minutes
খ
খ) 35 minutes
গ
গ) 50 minutes
ঘ
ঘ) 75 minutes

ব্যাখ্যা

Question: Simi is walking at a speed of 10 kmph. After every km she takes rests for 5 minutes. The taken to cover a distance of 5 kilometers by Simi is -

Solution:
Time taken to 5 km at 10 kmph = 5/10 hr = 1/2 hr = 30 minutes
In 5 km she will rest 4 times
Time taken to rest = 4 × 5 = 20 minutes

So, total time taken = 30 + 20 = 50 minutes

৩৯৯.

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

ক
10 km/hr
খ
9 km/hr
গ
3 km/hr
ঘ
5 km/hr
ঙ
7 km/hr

ব্যাখ্যা

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

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

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

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

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

৪০০.

A runner crosses a square field diagonally with a side length of 200√2 m in just 20 seconds. How much time will it take to complete the full perimeter of the field?

ক
40√2 seconds
খ
30√2 seconds
গ
40 seconds
ঘ
20√2 seconds

ব্যাখ্যা

Question: A runner crosses a square field diagonally with a side length of 200√2 m in just 20 seconds. How much time will it take to complete the full perimeter of the field?

Solution:
Diagonal of the square field is = √2 × 200√2 = 400 m

speed = 400 / 20 = 20 mps

perimeter = 4 × 200√2 m

time = 800√2 / 20 = 40√2 seconds