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Time and Speed - Train and Boat

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উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Time and Speed - Train and Boat

PrepBank · পাতা ৯ / ১৫ · ৮০১–৯০০ / ১,৪৩৯

৮০১.
Q. 33 – 56: Read the following questions carefully and choose the right answer.
৩৩) A driver of an auto rickshaw sees a lorry 60m ahead of him. After 30 seconds the lorry is 90m behind. If the speed of the auto rickshaw is 38km/hr, then what is the speed of the lorry?
  1. ক
    ক) 23km/hr
  2. খ
    খ) 25km/hr
  3. গ
    গ) 20km/hr
  4. ঘ
    ঘ) 18km/hr
ব্যাখ্যা
Total distance is 60+90= 150 meters.
Time taken is 30 seconds.
Speed of the lorry = 150/30 
                              = 5 m/s
                              =  (5×18)/5   
                              = 18 kmph

Now
relative speed = speed of auto rickshaw – speed of lorry
or, 18 = 38 – speed of lorry
∴ Speed of lorry = 38 – 18 = 20 km/h
৮০২.
Sonar Bangla express, normally reaches its destination at 72 km/h in 6 hours. Find the speed at which it must travel to reduce the travel time by 2 hours?
  1. ক
    78 km/h
  2. খ
    66 km/h
  3. গ
    58 km/h
  4. ঘ
    108 km/h
ব্যাখ্যা

Question: Sonar Bangla express, normally reaches its destination at 72 km/h in 6 hours. Find the speed at which it must travel to reduce the travel time by 2 hours?

Solution:
Distance to be covered = Speed × Time
= 72 × 6
= 432 km

Reduced time = 6 - 2 = 4 hours

∴ Required speed = 432/4
= 108 km/h

∴ The train must travel at 108 km/h to reduce the time by 2 hours.

৮০৩.
A train traveling at 60 kmph crosses a man in 6 seconds. What is the length of the train?
  1. ক
    80 m
  2. খ
    85 m
  3. গ
    100 m
  4. ঘ
    106 m
ব্যাখ্যা
Question: A train traveling at 60 kmph crosses a man in 6 seconds. What is the length of the train?

Solution:
Speed in m/sec = 60 × (5/18) = 50/3 m/sec.
Time taken to cross the man = 6 seconds.

∴ Distance traveled = (50/3) × 6 = 100 m = length of the train.
৮০৪.
A train 120 meters long travels at a speed of 54 km/hr. How long will it take to cross a platform 180 meters long?
  1. ক
    50 seconds
  2. খ
    1 min
  3. গ
    25 seconds
  4. ঘ
    45 seconds
  5. ঙ
    20 seconds
ব্যাখ্যা
Question: A train 120 meters long travels at a speed of 54 km/hr. How long will it take to cross a platform 180 meters long?

Solution:
Total distance = 120 + 180 = 300 meters

∴ Speed = 54 × (5/18) =15 m/s

∴ Time = 300/15 = 20 seconds
৮০৫.
A student goes to school at the rate of 3 km/h and reaches 6 min late. If he travels at the speed of 4 km/h he is 12 min early. What is the distance of the school?
  1. ক
    ক) 3.6 km
  2. খ
    খ) 4 km
  3. গ
    গ) 1.2 km
  4. ঘ
    ঘ) 5 km
ব্যাখ্যা
Question: A student goes to school at the rate of 3 km/h and reaches 6 min late. If he travels at the speed of 4 km/h he is 12 min early. What is the distance of the school?

Solution:
Here, 
A student goes  3 km/h and reaches 6 min late
and goes 4 km/h he is 12 min early
Total time = (12 + 6) min = 18 min 

Let the distance between school and home be x km

ATQ,
(x/3) - (x/4) = 18/60
⇒ (4x - 3x)/12 = 3/10
⇒ x/12 = 3/10
⇒ x = (3 × 12)/10
⇒ x = 18/5
∴ x = 3.6 

∴ The distance of the school is 3.6 km
৮০৬.
Without stoppages, the bus goes 72 kmph, and with stoppages, 60 kmph. Calculate the bus’s stopping time per hour. 
  1. ক
    12 minutes
  2. খ
    10 minutes
  3. গ
    8 minutes
  4. ঘ
    18 minutes
  5. ঙ
    14 minutes
ব্যাখ্যা

Question: Without stoppages, the bus goes 72 kmph, and with stoppages, 60 kmph. Calculate the bus’s stopping time per hour. 

Solution:
Including stoppages, it covers = (72 - 60) kmph
= 12 kmph less

Time taken to cover 12 km = {(12/72) × 60} minutes
= 10 minutes

৮০৭.
A man rows at 6 km/hr in still water and 4.5 km/hr against current. His rate along the current is:
  1. ক
    9.5 km/hr
  2. খ
    7.5 km/hr
  3. গ
    7 km/hr
  4. ঘ
    5.25 km/hr
  5. ঙ
    None of these
ব্যাখ্যা

Question: A man rows at 6 km/hr in still water and 4.5 km/hr against current. His rate along the current is:

Solution:
Speed in still water is 6 km/hr
Speed of the current is x km/hr

against current,
6 - x = 4.5
⇒ x = 6 - 4.5
∴ x = 1.5

along the current,
6 + x
= 6 + 1.5
= 7.5 km/hr

৮০৮.
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
  1. ক
    5 kmph
  2. খ
    7 kmph
  3. গ
    3 kmph
  4. ঘ
    4 kmph
ব্যাখ্যা
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?

Solution:
Speed of Man = 4.5 kmph
Speed of stream = 1.5 kmph
Speed in DownStream = 6 kmph
Speed in UpStream = 3 kmph

Average Speed = (2 × 6 × 3)/9 = 4 kmph.
৮০৯.
150 individuals attended a marathon held in Sylhet. Of those only If x of the 150 individuals were from sythet and z of the individuals participated in the marathon but were not from sylhet. Which of the following represents the number of individuals who did not participate in the marathon and were not from sylhet?
  1. ক
    ক) 150-x+z
  2. খ
    খ) 150-x-y+z
  3. গ
    গ) 150-x+z
  4. ঘ
    ঘ) 150-x-z
  5. ঙ
    ঙ) None
ব্যাখ্যা
Total = 150
Total ''From-Sylhet'' = x
Total ''Not-from-Sylhet'' = 150-x
Participated & ''Not-from-Sylhet'' = z
Didn't participate & ''Not-from-Sylhet'' = 150-x -z
৮১০.
A train travels 180 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1/2 hour less for the same journey. Find the speed of the train.
  1. ক
    40 km/hr
  2. খ
    45 km/hr
  3. গ
    50 km/hr
  4. ঘ
    42 km/hr
ব্যাখ্যা
Question: A train travels 180 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1/2 hour less for the same journey. Find the speed of the train.

Solution: 
Given distance = 180 km.
Let,
The speed of the train be x km/hr.
Speed when increased by 5 km/hr will be = (x + 5) km/hr

ATQ,
(180/x) - 180/(x + 5) = 1/2
⇒ [180x + 900 - 180x]/{x(x+5)} =1/2
⇒ 900/(x2 + 5x) = 1/2
⇒ x2 + 5x = 900 × 2
⇒ 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.
৮১১.
Walking 3/4 of his normal speed, Rafi is 12 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and office-
  1. ক
    18 min
  2. খ
    24 min
  3. গ
    36 min
  4. ঘ
    48 min
  5. ঙ
    56 min
ব্যাখ্যা

Question: Walking 3/4 of his normal speed, Rafi is 12 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and office-

Solution:
Let s be Rafi's normal speed,  t be his usual time, and t' be his new time.

Since the distance to the office is constant, d = s × t
When Rafi walks at his normal speed his new time is expressed as, d = (3/4)s × t'

Again, since the distance is the same,
st = (3/4)s × t'
⇒ t' = (4/3)t 

ATQ,
t' - t = 12
⇒ (4/3)t - t = 12
⇒ (4t - 3t)/3 = 12
⇒ t/3 = 12
∴ t = 36 min

৮১২.
A train 110 m long is running at the speed of 60 km/hr. In what time will it pass a man who is running at the speed of 6 km/hr in the opposite direction in which the train is moving?
  1. ক
    10 sec
  2. খ
    12 sec
  3. গ
    6 sec
  4. ঘ
    3 sec
ব্যাখ্যা
Question: A train 110 m long is running at the speed of 60 km/hr. In what time will it pass a man who is running at the speed of 6 km/hr in the opposite direction in which the train is moving?

Solution: 
Relative speed = 60 km/hr + 6 km/hr
= 66 km/hr
= 66 ×1000/3600 m/sec 
= 66 × 5/18 m/sec
= 55/3 m/sec

Time needed = 110 /55/3 sec
= 110 × 3/55 sec 
= 6 sec
৮১৩.
A train leaves Dhaka at 4.10 P.M. and reaches Mymensingh at 7.25 PM. The average speed of the train is 40 km/hr. What is the distance from Dhaka to Mymensingh?
  1. ক
    ক) 120 km
  2. খ
    খ) 130 km
  3. গ
    গ) 135 km
  4. ঘ
    ঘ) 140 km
ব্যাখ্যা

Time taken,
7.25 P.M. - 4.10 P.M. = 3 hr. 15 min.
= 3 × (15/60) hrs.
= 3(1/4) hrs.
= (13/4) hrs.
∴ Required distance = {40 × (13/4)} km.
= 130 km.

৮১৪.
A boatman takes twice as long to go a distance upstream as to travel the same distance downstream. What is the ratio of the speed of the boatman (in still water) and the current?
  1. ক
    ক) 2 : 3
  2. খ
    খ) 3 : 1
  3. গ
    গ) 1 : 3
  4. ঘ
    ঘ) 4 : 3
ব্যাখ্যা
Let man's rate upstream be x kmph
Then, his rate downstream = 2x kmph
∴ (speed in still water) : (Speed of stream)
=(2x+x)/2: (2x−x)/2
=3x/2 : x/2
=3:1
৮১৫.
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 30 min. The total journey is-
  1. ক
    100 km
  2. খ
    120 km
  3. গ
    80 km
  4. ঘ
    160 km
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 30 min. The total journey is-

Solution:
Difference between timings = 30 min = 30/60 hr = 1/2 hr.
Let the length of the journey be x km.

Then,
(x/40) - (x/50) = 1/2
(5x - 4x)/200 = 1/2
x/200 = 1/2
x = 200/2
∴ x = 100 km.

∴ The total journey is 100 km.

৮১৬.
A train running at a speed of 90km/h crosses a platform double its length in 36 seconds. What is the length of the platform in metres?
  1. ক
    ক) 600m
  2. খ
    খ) 300m
  3. গ
    গ) 150m
  4. ঘ
    ঘ) 450m
ব্যাখ্যা
Question: A train running at a speed of 90km/h crosses a platform double its length in 36 seconds. What is the length of the platform in metres?

Solution: 
ধরি, 
ট্রেনের দৈর্ঘ্য = X 
∴ প্লাটফর্মের দৈর্ঘ্য = 2X 
মোট দূরত্ব, D = 3X

ট্রেনের বেগ, S = 90km/h
= (90 × 1000)/3600
= 25 m/s

আমরা জানি,
D = S × T
3X = 25 × 36
3X = 900
X = 300m

∴ প্লাটফর্মের দৈর্ঘ্য = 2 × 300 = 600m
৮১৭.
The speed of a boat in still water is 30 km/hr. If the boat goes upstream for a distance of 25 km in 5 hours, find the speed of the stream.
  1. ক
    ক) 10 km/hr
  2. খ
    খ) 15 km/hr
  3. গ
    গ) 20 km/hr
  4. ঘ
    ঘ) 25 km/hr
ব্যাখ্যা
Let the speed of stream be x km/hr.
⇒ Speed of boat in still water =30 km/hr
⇒ Speed of boat in upstream = 25/5 = 5 km/hr

Also, speed of boat in upstream = speed of boat in still water - speed of stream
 5 = 30 - x
x = 30 - 5 
x = 25 
∴ The speed of stream is 25 km/hr.
৮১৮.
A moving train, 66 metres long, overtakes another train of 88 metres long, moving in the same direction in 0.168 minutes. If the second train is moving at 30 km/hr, at what speed is the first train moving ?
  1. ক
    ক) 85 km/hr
  2. খ
    খ) 50 km/hr
  3. গ
    গ) 55 km/hr
  4. ঘ
    ঘ) 45 km/hr
ব্যাখ্যা

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

Relative speed of two trains = (x - 30) km/hr
= {(x - 30) × (5/18)} m/s

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

৮১৯.
A train takes 20 seconds to cross a pole. It takes 50 seconds to cross the platform. What is the ratio of the length of the platform to that of the train?
  1. ক
    5 : 2
  2. খ
    2 : 5
  3. গ
    2 : 3
  4. ঘ
    3 : 2 
ব্যাখ্যা
Question: A train takes 20 seconds to cross a pole. It takes 50 seconds to cross the platform. What is the ratio of the length of the platform to that of the train?

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

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

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

∴ Length of the platform : Length of the train = 30x : 20x = 30 : 20 = 3 : 2
৮২০.
A man completes a journey in 5 hours. He completes the first half of the distance of journey at a speed of 20 km/hr and the second half at a speed of 25 km/hr. What is the total journey in km?
  1. ক
    5.4 km
  2. খ
    222.2 km
  3. গ
    110.5 km km
  4. ঘ
    111.1 km
ব্যাখ্যা
Question: A man completes a journey in 5 hours. He completes the first half of the journey at a speed of 20 km/hr and the second half at a speed of 25 km/hr. What is the total journey in km?

Solution:
Man travelled for 5 hours
Average speed = 2(20 × 25)/(20 + 25) = 22.22
So, total distance = 22.22 × 5 = 111.1 km

∴ Total distance travelled by the man is 111.1 km
৮২১.
A boy rides his bicycle 10 km at an average speed of 10 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is-
  1. ক
    10 km/hr
  2. খ
    11.25 km/hr
  3. গ
    10.75 km/hr
  4. ঘ
    15 km/hr
ব্যাখ্যা

Question: A boy rides his bicycle 10 km at an average speed of 10 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is-

Solution:
Given that,
Distance1 = 10 km, Speed1 = 10 km/hr
Distance2 = 12 km, Speed2 = 10 km/hr

∴ Total Distance = 10 + 12 = 22 km

And,
Time1 = 10 ÷ 10 = 1 hr
Time2 = 12 ÷ 10 = 1.2 hr

∴ Total Time = 1 + 1.2 = 2.2 hr

We know,
Average Speed = Total Distance ÷ Total Time
= 22/2.2 = 10 km/hr

∴ His average speed for the entire trip is 10 km/hr.

৮২২.
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?
  1. ক
    d
  2. খ
    d/3
  3. গ
    d/2
  4. ঘ
    (3d)/4
  5. ঙ
    (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
৮২৩.
The time taken by a ship to travel 1000 km upstream is 40 hours more than the time taken by it to travel the same distance in downstream. The speed of the ship in still water is 200% more than that of the speed of stream. How much time the ship will take to travel the same distance in upstream?
  1. ক
    40 hours
  2. খ
    60 hours
  3. গ
    80 hours
  4. ঘ
    120 hours
ব্যাখ্যা
Question: The time taken by a ship to travel 1000 km upstream is 40 hours more than the time taken by it to travel the same distance in downstream. The speed of the ship in still water is 200% more than that of the speed of stream. How much time the ship will take to travel the same distance in upstream?

Solution:
Given that,
Distance travelled = 1000 km
Time taken to travel upstream = 40 hours + time taken to travel downstream

Let,
The speed of the stream = X km per hour

∴ The speed of the ship in still water = X + 200% of X
= X + 2X
= 3X km per hour

ATQ,
{1000/(3X - X)} - {1000/(3X + X)} = 40
⇒ (1000/2X) - (1000/4X) = 40
⇒ (2000 - 1000)/4X = 40
⇒ 4X × 40 = 1000
⇒ X = 1000/(4 × 40)
∴ X = 6.25 km/hr

The required time in upstream = 1000/(3X - X)
= 1000/2X
= 1000/(2 × 6.25)
= 80 hours
৮২৪.
Two trains A and B are moving in the same direction. A has speed of 8 km/h and B has speed of 13 km/h. What is relative speed of B with respect to A?
  1. ক
    21 km/h
  2. খ
    3 km/h
  3. গ
    5 km/h
  4. ঘ
    8 km/h
ব্যাখ্যা

Question: Two trains A and B are moving in the same direction. A has speed of 8 km/h and B has speed of 13 km/h. What is relative speed of B with respect to A?

Solution: 
Given that,
Speed of train A = 8 km/h
Speed of train B = 13 km/h

Since both are moving in the same direction, and B is faster.
∴ Relative speed of B with respect to A = Speed of B - Speed of A
= 13 km/h - 8 km/h
= 5 km/h

So the relative speed of B with respect to A is 5 km/h.

৮২৫.
A train 150 meter long and running at a speed of 60 km per hour takes 30 seconds to cross a bridge. What is the length of the bridge?
  1. ক
    350 meter
  2. খ
    450 meter
  3. গ
    500 meter
  4. ঘ
    650 meter
ব্যাখ্যা
Question: A train 150 meters long and running at a speed of 60 km per hour takes 30 seconds to cross a bridge. What is the length of the bridge?

Solution: 
সেকেন্ডে ট্রেনের গতিবেগ = (60×1000)/(60×60) মিটার/সেকেন্ড 
= 16.67 মিটার/সেকেন্ড
∴ 30 সেকেন্ডে অতিক্রান্ত দূরত্ব = (30×16.67)m = 500m
ব্রিজের দূরত্ব = 500 - 150 = 350 m
৮২৬.
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?
  1. ক
    ক) 50 metre
  2. খ
    খ) 60 metre
  3. গ
    গ) 40 metre
  4. ঘ
    ঘ) 45 metre
  5. ঙ
    ঙ) 35 metre
ব্যাখ্যা

Let length of each train = x metre
Total distance covered while passing the slower train = (x + x) = 2x metre
Relative speed = (46 − 36)
= 10 km/hr
= 10 × 5/18
= 50/18 m/s

Time = 36 seconds
⇒ 2 x/36 = 50/18
⇒ x = 50

৮২৭.
A bike traveled twice a many kms from X to Y as it did from Y to Z. From X to Y, the bike averaged 16 Km/gallon and from Y to Z, the bike averaged 24 Km/gallon. What is the average Km/gallon that the bike achieved on its trip from X through Y to Z?
  1. ক
    ক) 28.8
  2. খ
    খ) 32
  3. গ
    গ) 36.8
  4. ঘ
    ঘ) 48
  5. ঙ
    ঙ) None
ব্যাখ্যা
Question: A bike traveled twice a many kms from X to Y as it did from Y to Z. From X to Y, the bike averaged 16 Km/gallon and from Y to Z, the bike averaged 24 Km/gallon. What is the average Km/gallon that the bike achieved on its trip from X through Y to Z?

Solution: 
X থেকে Y এর দূরত্ব = 2a কিমি
Y থেকে Z এর দূরত্ব = a কিমি
মোট দূরত্ব = 2a + a = 3a

নির্ণেয় গড় গতিবেগ = 3a/{(2a/16) + (a/24)}
= 3a/{(6a + 2a)/48}
= 3a/(8a/48)
= 3a/(a/6)
= 3a × (6/a)
= 18 
৮২৮.
A man wishes to cross a river perpendicularly. In still water, it takes 4 minutes to cross the river, but in the flowing river, it takes 5 minutes. If the river is 100 meters wide, the velocity of the flowing water of the river is -
  1. ক
    ক) 10 m/min
  2. খ
    খ) 15 m/min
  3. গ
    গ) 20 m/min
  4. ঘ
    ঘ) 20 m/min
ব্যাখ্যা

Velocity of the river = [100 √{(1/42) - (1/52)}] m/min
= [100 √{(1/16) - (1/25)}] m/min
= 100{√(9/400)} m/min
= 100 × (3/20) m/min
= 15 m/min.

৮২৯.
Two trains of equal length are running on parallel lines in the same direction at 48km/hr and 38 km/hr. The faster train passes the slower train in 54 seconds. The length of each train is
  1. ক
    ক) 50m
  2. খ
    খ) 75m
  3. গ
    গ) 65m
  4. ঘ
    ঘ) 60m
ব্যাখ্যা
Let,
the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (48 - 38) km/hr
                        = (10 x 5/18) m/sec    [km/hr  কে m/sec পরিণত করতে 5/18  গুণ করতে হয় ]
                          = (25 /9) m/sec 

∴ 2x/ 54 = 25 /9
⇒ 2x = 150
     x = 75 
৮৩০.
The wheel of an engine of 300 cm in circumference makes 10 revolutions in 6 seconds. What is the speed of the wheel (in km/h)?
  1. ক
    12 kmh-1
  2. খ
    15 kmh-1
  3. গ
    17 kmh-1
  4. ঘ
    18 kmh-1
ব্যাখ্যা
Question: The wheel of an engine of 300 cm in circumference makes 10 revolutions in 6 seconds. What is the speed of the wheel (in km/h)?

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

speed = 30/6 ms-1 
= 5 ms-1
= (5 × 3600)/(1000) kmh-1
= 18 kmh-1 
৮৩১.
Two trains P and Q are moving in opposite direction at a rate of 36km/hr and 45km/hr respectively. A passenger is sitting in train P, finds that his train passes train Q in 8 seconds. What is the length of train Q?
  1. ক
    ক) 195m
  2. খ
    খ) 175m
  3. গ
    গ) 190m
  4. ঘ
    ঘ) 180m
ব্যাখ্যা
Question: Two trains P and Q are moving in opposite direction at a rate of 36km/hr and 45km/hr respectively. A passenger is sitting in train P, finds that his train passes train Q in 8 seconds. What is the length of train Q?

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


 The length of train Q = (45/2) × 8
= 180 m 
৮৩২.
একজন মোটর গাড়ি চালক ১৩০ কি.মি. দূরত্বে অবস্থিত দুটি শহর ২ ঘণ্টা ১০ মিনিটে ভ্রমণ করতে পারে। তাহলে প্রতি মিনিটে তার গতিবেগ কত?
  1. ক
    ক) ১২০০ মিটার/মিনিট 
  2. খ
    খ) ৬০০ মিটার/মিনিট 
  3. গ
    গ) ৫০০ মিটার/মিনিট 
  4. ঘ
    ঘ) ১০০০ মিটার/মিনিট 
ব্যাখ্যা
দূরত্ব = ১৩০ কি.মি. = (১৩০ × ১০০০)মিটার = ১৩০০০০ মিটার 
সময় = ২ ঘণ্টা ১০ মিনিট
         = (২ × ৬০) মিনিট + ১০ মিনিট 
          = ১২০ মিনিট + ১০ মিনিট 
          = ১৩০ মিনিট 

গতিবেগ = ১৩০০০০/ ১৩০
              = ১০০০ মিটার/মিনিট 
৮৩৩.
Car A travels at the speed of 65 km/hr and reaches its destination in 8 hours. Car B travels at a speed of 70 km/hr and reaches its destination in 4 hours. What is the ratio of the distance covered by car A and car B respectively?
  1. ক
    ক) 7:11
  2. খ
    খ) 13:7
  3. গ
    গ) 7:13
  4. ঘ
    ঘ) 11:7
ব্যাখ্যা

Required ratio:
= (65×8):(70×4)
= 520:280
= 13:7

৮৩৪.
A train 300 m long passes a pole in 0.4 minutes. How long will it take to cross a bridge 450 m long (in minutes)?
  1. ক
    ক) 1.8 min
  2. খ
    খ) 1 min
  3. গ
    গ) 1.2 min
  4. ঘ
    ঘ) 1.5 min
ব্যাখ্যা
প্রশ্ন : A train 300 m long passes a pole in 0.4 minutes. How long will it take to cross a bridge 450 m long (in minutes)?
সমাধান : 
Length of train = 300m
Train cross a pole in = 0.4 min
Length of bridge = 450


We Know,
Speed = distance/time
Speed of train = 300/0.4
Speed of train = 750 m/min

∴ Time taken by train to cross bridge = (450 + 300)/750 = 750/750 = 1 min
৮৩৫.
On a river, C is the mid-point between two points A and B on the same bank of the river. A boat can go from A to C and back in 14 hours and from A to B in 20 hours 20 min. How long it would take to go from B to A?
  1. ক
    7 h 40 m 
  2. খ
    3 h 50 m
  3. গ
    10 h 10 m 
  4. ঘ
    None of these
ব্যাখ্যা
Question: On a river, C is the mid-point between two points A and B on the same bank of the river. A boat can go from A to C and back in 14 hours and from A to B in 20 hours 20 min. How long it would take to go from B to A?

Solution: 
Time required to travel from A to B = 20 hour 20 min 
Time required to travel from A to C = 1/2 (20 h 20 m) 
= 10 h 10 m 

Given total time from A to C and C to A = 14 h 
∴ 10 h 10 m + C to A = 14 h 
∴ C to A = 3 h 50 m 

Time taken from B to A is twice of C to A 
then, time taken from B to A =2 × (3 h 50 m) =7 h 40 m 
৮৩৬.
Maruf is travelling on his cycle and he calculated to reach point A at 3 p.m. if he travels at 10 kmph, he will reach there at 1 p.m. if he travels at 15 kmph. At what speed must he travel to reach A at 2 p.m.
  1. ক
    15 kmph.
  2. খ
    19 kmph.
  3. গ
    17 kmph.
  4. ঘ
    12 kmph.
ব্যাখ্যা

Question: Maruf is travelling on his cycle and he calculated to reach point A at 3 p.m. if he travels at 10 kmph, he will reach there at 1 p.m. if he travels at 15 kmph. At what speed must he travel to reach A at 2 p.m.

Solution: 
Let the distance travelled by x km.

ATQ, 
x/10 - x/15 = 2 
⇒ 3x - 2x = 60 
∴ x = 60

Time taken to travel 60 km at 10km/h = 60/10 hours
= 6 hours

So, Maruf started 6 hours before 3 P.M. i.e., at 9 Α.Μ.

∴ Required speed = 60/5 kmph. 
= 12 kmph.

৮৩৭.
A car covers the first 39 kms of its journey in 45 minutes and covers the remaining 25 km in 35 minutes. What is the average speed of the car?
  1. ক
    40 km/hr
  2. খ
    48 km/hr
  3. গ
    49 km/hr
  4. ঘ
    64 km/hr
ব্যাখ্যা

Total distance travelled = (39 + 25)
= 64 km
Total time taken = (45 + 35)
= 80 min.
= (80/60) hr.
= (4/3) hr.
∴ Average speed = {64 × (3/4)} km/hr
= 48 km/hr.
Hence, the average speed of the car is 48 km/hr.

৮৩৮.
Quantity A =Time to travel 95 miles at 50 miles per hour; and Quantity B = Time to travel 125 miles at 60 miles per hour.
  1. ক
    ক) Quantity A is greater
  2. খ
    খ) Quantity A equals Quantity B
  3. গ
    গ) Quantity B is greater
  4. ঘ
    ঘ) Relationship indeterminate
  5. ঙ
    ঙ) None of these
ব্যাখ্যা
Question: Quantity A = Time to travel 95 miles at 50 miles per hour; and Quantity B = Time to travel 125 miles at 60 miles per hour.

Solution: 
Quantity A = 95/50 = 19/10 = 1.9 hour 

Quantity B = 125/60 = 25/12 = 2.083 hour 

∴ Quantity B is greater.
৮৩৯.
Length of train A is 50 % more than the train B coming from its opposite direction. Speed of train A is 40 km/hour and that of for train B is 32 km/hour and they took 15 sec time to cross each other. Find the length of train A.
  1. ক
    120 m
  2. খ
    135 m
  3. গ
    150 m
  4. ঘ
    180 m
ব্যাখ্যা
Question:  Length of train A is 50 % more than the train B coming from its opposite direction. Speed of train A is 40 km/hour and that of for train B is 32 km/hour and they took 15 sec time to cross each other. Find the length of train A.

Solution: 
let, length of train B is x km 
length of train A is x + .5x = 1.5x 

(x + 1.5x) / (40 + 32) = 15/3600 
⇒ 2.5x = (15 × 72) / 3600 
⇒ x = (15 × 72) / (3600 × 2.5) = 0.12 km 

length of train A  = 1.5 × 0.12
= 0.18 km 
= 180 m
৮৪০.
A train 240 m long passed a pole in 24 sec. How long will it take to pass the 650 m long platform?
  1. ক
    ক) 65 sec
  2. খ
    খ) 89sec
  3. গ
    গ) 100sec
  4. ঘ
    ঘ) 130sec
ব্যাখ্যা

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

৮৪১.
A man travelled a distance of 1260 km in 17 hours. He travelled partly by car at a speed of 40 km/h, and partly by train at a speed of 80 km/h. What is the distance traveled by the train?
  1. ক
    100 km
  2. খ
    340 km
  3. গ
    640 km
  4. ঘ
    1160 km
  5. ঙ
    1360 km
ব্যাখ্যা

Question: A man travelled a distance of 1260 km in 17 hours. He travelled partly by car at a speed of 40 km/h, and partly by train at a speed of 80 km/h. What is the distance traveled by the train?

Solution: 
Given,
 Total distance = 1260 km
Total time = 17 hours
Speed of car = 40 km/h
Speed of train = 80 km/h

Let,
Distance travelled by car = x km
Distance travelled by train = (1260 - x) km

ATQ,
(x/40) + [(1260 - x)/80] = 17
⇒ 2x + 1260 - x = 17 × 80
⇒ x = 1360 - 1260
⇒ x = 100

∴ Distance traveled by the train = (1260 - 100) km
= 1160 km

৮৪২.
Two trains running in opposite directions cross a man standing on the platform in 17 seconds and 7 seconds respectively and they cross each other in 13 seconds. The ratio of their speeds is-
  1. ক
    2 ∶ 1
  2. খ
    3 ∶ 2
  3. গ
    4 ∶ 3
  4. ঘ
    5 : 4
ব্যাখ্যা

Question: Two trains running in opposite directions cross a man standing on the platform in 17 seconds and 7 seconds respectively and they cross each other in 13 seconds. The ratio of their speeds is-

Solution: 
Let, the speed of the trains are x m/sec and y m/sec respectively

We know, Distance/Length = Speed × Time
∴ Length of first train = 17x meter
And, length of second train = 7y meter

Now, Total time = Total length/Total speed
(17x + 7y)/(x + y) = 13
⇒ 17x + 7y = 13x + 13y 
⇒ 17x - 13x = 13y - 7y
⇒ 4x = 6y
⇒ x/y = 3/2
∴ x ∶ y = 3 ∶ 2

৮৪৩.
A train running at the speed of 60 kmph crosses a 200 m long platform in 27 seconds. What is the length of the train?
  1. ক
    250 meters
  2. খ
    180 meters
  3. গ
    320 meters
  4. ঘ
    220 meters
ব্যাখ্যা

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

Solution: 
Given that,
Time = 27 sec
∴ Speed = (60 × 5/18)m/sec = 50/3 m/sec

Let the length of the train be x metres.
Then,
(x + 200)/27 = 50/3
⇒ x + 200 = (50/3) × 27 
⇒ x + 200 = 450
⇒ x = 450 - 200
∴ x = 250 metres

So the length of the train is 250 meters.

৮৪৪.
A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in meters) is-
  1. ক
    ক) 600
  2. খ
    খ) 750
  3. গ
    গ) 1000
  4. ঘ
    ঘ) 1250
ব্যাখ্যা

15min = 1/4hrs
1 hr → 5 kms
1/4hr → 5/4 kms
So, length of the bridge=5/4 km = 1250 metres

৮৪৫.
Mr. Rabbani running at 150 m/min alongside a railway track in 250 meters ahead of the engine of a 120 meters long train running at 750 m/min in the same direction. In how much time will the train pass him?
  1. ক
    ক) 31 sec
  2. খ
    খ) 33 sec
  3. গ
    গ) 35 sec
  4. ঘ
    ঘ) 37 sec
ব্যাখ্যা
Question: Mr. Rabbani running at 150 m/min alongside a railway track in 250 meters ahead of the engine of a 120 meters long train running at 750 m/min in the same direction. In how much time will the train pass him?

Solution:
Speed of train relative to Mr. Rabbani = (750 - 150) m/min = 600 m/min = 10 m/s

Distance to be covered = (250 + 120) m = 370 m

Time taken = 370/10 = 37 sec
৮৪৬.
A train has a length of 150 metres. It is passing a man who is moving at 4 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train?
  1. ক
    ক) 169 km/hr
  2. খ
    খ) 152 km/hr
  3. গ
    গ) 184 km/hr
  4. ঘ
    ঘ) 180 km/hr
ব্যাখ্যা
Length of the train = 150 m
Speed of the man = 4 km/hr
Relative speed = 150/3 = 50 m/s
= 50 × 18/5
= 180 km/hr
Relative speed = Speed of train - Speed of the man (as both are moving in the same direction).
Therefore,
Speed of the train = Relative speed + Speed of the man
= 180 + 4
= 184 km/hr
৮৪৭.
A train takes 20 seconds to cross a pole. It takes 50 seconds to cross the platform. What is the ratio of the length of the platform to that of the train?
  1. ক
    2 : 3
  2. খ
    2 : 5
  3. গ
    5 : 2
  4. ঘ
    3 : 2 
ব্যাখ্যা
Question: A train takes 20 seconds to cross a pole. It takes 50 seconds to cross the platform. What is the ratio of the length of the platform to that of the train?

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

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

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

∴ Length of the platform : Length of the train = 30x : 20x = 30 : 20 = 3 : 2
৮৪৮.
A boatman can row 2.5 km against the stream in 25 minutes and return in 12.5 minutes. Find the rate of flow of the current.
  1. ক
    ক) 1 km/hr
  2. খ
    খ) 3 km/hr
  3. গ
    গ) 4 km/hr
  4. ঘ
    ঘ) 5 km/hr
ব্যাখ্যা
Question: A boatman can row 2.5 km against the stream in 25 minutes and return in 12.5 minutes. Find the rate of flow of the current.

Solution: 
Let,
x be the speed of man in still water
y be the speed of current

Speed of downstream = (2.5/12.5) × 60 = 12 km / hr
Speed of upstream = (2.5/ 25) × 60 = 6 km / hr

∴ rate of current = (12 - 6)/2 = 3 km/hr
৮৪৯.
A train traveled p miles in 40 minutes and completed the remaining 200 miles of the trip in q minutes. What was its average speed in miles per hour for the entire trip?
  1. ক
    ক) 60(p+200)/(40+q)
  2. খ
    খ) 240/(p+q)
  3. গ
    গ) 4(p+q)
  4. ঘ
    ঘ) None
ব্যাখ্যা
Speed = Distance/Time = (p + 200)/(40 + q) miles/min = (p + 200)/(40 + q)/60 miles/hr = 60(p + 200)/(40 + q).
৮৫০.
Noyon walking at a speed of 20 km/h reaches his college 10 minutes late. Next time he increases his speed by 5 km/h, but finds that he is still late by 4 minutes. What is the distance of his college from his house?
  1. ক
    ক) 10 km
  2. খ
    খ) 6 km
  3. গ
    গ) 12 km
  4. ঘ
    ঘ) 15 km
  5. ঙ
    ঙ) 20 km
ব্যাখ্যা

By increasing his speed by 25%, he will reduce his time by 20%. (This corresponds to a 6 minutes drop in his time.)
Hence, his time originally must have been 30 minutes.
Thus required distance = 20 kmph × 0.5 hours = 10 km.

৮৫১.
A train covers a distance 10 km in 12 minutes. If its speed is decreased by 10 km/hr, the time taken by it to cover the same distance will be-
  1. ক
    ক) 10 min
  2. খ
    খ) 12 min
  3. গ
    গ) 15 min
  4. ঘ
    ঘ) 18 min
ব্যাখ্যা
Question: A train covers a distance 10 km in 12 minutes. If its speed is decreased by 10 km/hr, the time taken by it to cover the same distance will be-

Solution:
Old speed = (10 × 60)/12 = 50 kmph
New speed = 50 - 10 = 40 kmph

Time taken to go 10km at 40kmph = 10/40 hr
= (10 × 60)/40 min
= 15 min
৮৫২.
A train 180 meters long takes 9 seconds to pass a man standing on the platform. How much time will it take to pass a platform 420 meters long?
  1. ক
    15 sec
  2. খ
    30 sec
  3. গ
    20 sec
  4. ঘ
    40 sec
ব্যাখ্যা
Question: A train 180 meters long takes 9 seconds to pass a man standing on the platform. How much time will it take to pass a platform 420 meters long?

Solution:
Length of the train = 180 m
Time to pass the man = 9 sec

∴ Speed of the train =180/9 m/sec
= 20 m/sec

Now, total length of the train and platform = (180 + 420) m
= 600 m

∴ Time taken = 600/20 sec
= 30 sec
৮৫৩.
A boat can travel 36 km upstream in 5 hours. If the speed of the stream is 2.4 kmph, how much time will the boat take to cover a distance of 78 km downstream?(in hours)
  1. ক
    4 hours
  2. খ
    5.4 hours
  3. গ
    6.5 hours
  4. ঘ
    7 hours
ব্যাখ্যা
Question: A boat can trave 36 km upstream in 5 hours. If the speed of the stream is 2.4 kmph, how much time will the boat take to cover a distance of 78 km downstream?(in hours)

Solution:
Distance covered by a boat in 5 hours = 36 km
Rate upstream of boat = 36/5
= 7.2 kmph
Speed of the stream = 2.4 kmph

∴ Speed of the boat in still water = (7.2 + 2.4) kmph
= 9.6 kmph
∴ Rate downstream of the boat = (9.6 + 2.4) kmph
= 12 kmph

So, Time taken in covering 78 km distance = 78/12 = 6.5 hours
৮৫৪.
A person travels a certain distance at 3 km/hr and reaches 15 min late. If he travels at 4 km/hr, he reaches 15 min earlier. The distance he has to travel is 
  1. ক
    ক) 4.5 km
  2. খ
    খ) 6 km
  3. গ
    গ) 7.2 km
  4. ঘ
    ঘ) 12 km
ব্যাখ্যা
Let
the time taken by him to travel certain distance be 't' hr
Since the distance travelled in both cases is constant,
we have
⇒ 3 × (t + 15/60) = 4 × (t - 15/60)
⇒ 3t + 3/4 = 4t - 1
⇒ t = 7/4 hr

∴ required distance = 3 × (t + 15/60) = 3 × (7/4 + 15/60) = 6 km
৮৫৫.
A is twice as fast as B and B is thrice as fast as C. The journey covered by C in 42 minutes will be covered by A in:
  1. ক
    12 minutes
  2. খ
    9 minutes
  3. গ
    8 minutes
  4. ঘ
    7 minutes
  5. ঙ
    None of the above
ব্যাখ্যা
Question: A is twice as fast as B and B is thrice as fast as C. The journey covered by C in 42 minutes will be covered by A in:

Solution:
Let C's speed be x metres/min
Let the time taken by A be y min

Then, B's speed = 3x metres/min
And, A's speed = 6x metres/min

Ratio of speed of A and C = Ratio of time taken by C and A

6x : x = 42 : y
⇒ 6x/x = 42/y
∴ y = 7 minutes

Hence, The journey covered by C in 42 minutes will be covered by A in 7 minutes.
৮৫৬.
A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
  1. ক
    3.6
  2. খ
    7.2
  3. গ
    8.4
  4. ঘ
    10
ব্যাখ্যা
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

Solution:
600 m = 600/1000 km
= 3/5 km

5 minutes = 5/60 = 1/12 hr

Speed = (3/5)/(1/12) 
= (3 × 12)/5 km/hr
= 36/5 km/hr
= 7.2 km/hr
৮৫৭.
A man completes a certain journey in 8 hours. He covers one-third distance at 60 kmph and the rest at 80 kmph. The length of the journey-
  1. ক
    ক) 320 km
  2. খ
    খ) 360 km
  3. গ
    গ) 480 km
  4. ঘ
    ঘ) 576 km
ব্যাখ্যা
Question: A man completes a certain journey in 8 hours. He covers one-third distance at 60 kmph and the rest at 80 kmph. The length of the journey-

Solution:
Let, the length of the journey be x km
he covers x/3 km  at 60 kmph
he covers (x - x/3) = 2x/3 at 80 kmph

ATQ,
(x/3)/60 + (2x/3)/80 = 8
x/180 + x/120 = 8
5x/360 = 8
x = 576 km
৮৫৮.
Sharif travelled a distance of 41 km in 9 hours. He travelled partly on foot 3 km/hr and partly on bicycle 9 km/hr. The distance travelled on bicycle is:
  1. ক
    ক) 22 km.
  2. খ
    খ) 21 km.
  3. গ
    গ) 24 km.
  4. ঘ
    ঘ) 25 km.
ব্যাখ্যা
Question: Sharif travelled a distance of 41 km in 9 hours. He travelled partly on foot 3 km/hr and partly on bicycle 9 km/hr. The distance travelled on bicycle is:

Solution: 
Let,
the distance travelled on bicycle be x km.
distance travelled on foot = (41 -x) km.

ATQ,
Or, (x/9) + (41 − x)/3 = 9
Or, x + 123 − 3x = 81
Or, 2x = 42
Or, x = 21
৮৫৯.
Two trains start from station P and Q and travel towards each other at speeds of 60 km/hr and 80 km/hr respectively. At the time of their meeting, the second train has traveled 80 km more than the first. The distance between P and Q is:
  1. ক
    450 km
  2. খ
    520 km
  3. গ
    560 km
  4. ঘ
    610 km
ব্যাখ্যা

Question: Two trains start from station P and Q and travel towards each other at speeds of 60 km/hr and 80 km/hr respectively. At the time of their meeting, the second train has traveled 80 km more than the first. The distance between P and Q is:

সমাধান:
দ্বিতীয় ট্রেনের গতিবেগ বেশি = (80 - 60) কিমি/ঘন্টা
= 20 কিমি/ঘন্টা।

দ্বিতীয় ট্রেনটি প্রথম ট্রেনের চেয়ে 80 কিমি বেশি ভ্রমণ করেছে।
এই বাড়তি দূরত্ব অতিক্রম করার সময় = দূরত্ব/গতিবেগ
= 80 কিমি/20 কিমি/ঘন্টা
= 4 ঘন্টা

যেহেতু ট্রেন দুটি একই সময়ে যাত্রা শুরু করেছিল, তাই তাদের মিলিত হতে 4 ঘন্টা সময় লেগেছে।

ট্রেন দুটির আপেক্ষিক গতিবেগ (Relative speed) = (60 + 80) কিমি/ঘন্টা
= 140 কিমি/ঘন্টা।

সুতরাং, মোট অতিক্রান্ত দূরত্ব = আপেক্ষিক গতিবেগ × সময়
= 140 কিমি/ঘন্টা × 4 ঘন্টা
= 560 কিমি

সুতরাং, P এবং Q স্টেশনের মধ্যবর্তী দূরত্ব হলো 560 কিমি।

৮৬০.
A man can row 1.8 kilometer against the stream in 15 minutes and down the stream in 3 minutes. The speed (in m/sec) of the man in still water is-
  1. ক
    6 m/sec
  2. খ
    9 m/sec
  3. গ
    10 m/sec
  4. ঘ
    15 m/sec
ব্যাখ্যা
Question: A man can row 1.8 kilometer against the stream in 15 minutes and down the stream in 3 minutes. The speed (in m/sec) of the man in still water is-

Solution:
1.8 kilometer = 1800 meters
15 minutes = 15 × 60
= 900 sec
3 minutes = 3 × 60
= 180 sec
Rate upstream = 1800/900 m/sec
= 2 m/sec
Rate downstream = 1800/180 m/sec
= 10 m/sec
∴ Rate in still water = (1/2)(2 + 10) m/sec
= 6 m/sec
৮৬১.
How much time does a train 50 m long, moving at 68 km/hr takes to pass another train 75 m long moving at 50 km/hr in the same direction?
  1. ক
    ক) 5 sec
  2. খ
    খ) 15 sec
  3. গ
    গ) 25 sec
  4. ঘ
    ঘ) 30 sec
ব্যাখ্যা
Question: How much time does a train 50 m long, moving at 68 km/hr takes to pass another train 75 m long moving at 50 km/hr in the same direction?

Solution:
Total distance covered by the length of both trains = (50 + 75) m = 125 m
And, their relative speed in same direction = (68 - 50) = 18 km/hr

Then, the time to cross each other will be = 125 m/18 km/hr.
= (125 × 3600)/(18 × 1000) s
= 25 sec
৮৬২.
A train moving at speed of 90 km/hr crosses a pole in 7 seconds. Find the length of the train.
  1. ক
    150 m
  2. খ
    165 m
  3. গ
    175 m
  4. ঘ
    170 m
ব্যাখ্যা
Question: A train moving at speed of 90 km/hr crosses a pole in 7 seconds. Find the length of the train.

Solution:
Length of the train is equal to the distance covered by train to cross the pole.
So, we will find the distance travelled by the train in 7 seconds by applying the following formula:
Distance= Speed × Time

Speed is given in Km/hr so we will convert it into m/s as answers are given in meters.
Speed = 90 × (5/18)  = 25 m/s

Time = 7 seconds
Distance = 25 × 7 = 175 meters
৮৬৩.
A boat running upstream takes 12 hours to cover a certain distance, while it takes 8 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and the speed of the water current respectively?
  1. ক
    4 : 1
  2. খ
    5 : 1
  3. গ
    3 : 5
  4. ঘ
    5 : 2
ব্যাখ্যা

Question: A boat running upstream takes 12 hours to cover a certain distance, while it takes 8 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and the speed of the water current respectively?

Solution:
ধরি,
স্থির পানিতে নৌকার গতি = b কিমি/ঘণ্টা
স্রোতের গতি = c কিমি/ঘণ্টা
দূরত্ব = d কিমি

স্রোতের প্রতিকূলে নৌকার গতিবেগ = (b - c) কিমি/ঘণ্টা
∴ d/(b - c) = 12
⇒ d = 12(b - c) 

স্রোতের অনুকূলে নৌকার গতিবেগ = (b + c) কিমি/ঘণ্টা
∴ d/(b + c) = 8
⇒ d = 8(b + c) 

এখন, উভয় ক্ষেত্রে দূরত্ব সমান হওয়ায়,
12(b - c) = 8(b + c) 
⇒ 3(b - c) = 2(b + c)
⇒ 3b - 3c = 2b + 2c
⇒ b = 5c
⇒ b/c = 5/1

∴ b : c = 5 : 1

৮৬৪.
A train of 180 m long is moving at 72 km/h. The time taken by the train to cross a tunnel of 420 m long is-
  1. ক
    25 seconds
  2. খ
    30 seconds
  3. গ
    35 seconds
  4. ঘ
    40 seconds
ব্যাখ্যা

Question: A train of 180 m long is moving at 72 km/h. The time taken by the train to cross a tunnel of 420 m long is-

Solution:
মোট অতিক্রান্ত দূরত্ব = ট্রেনের দৈর্ঘ্য + টানেলের দৈর্ঘ্য
= (180 + 420) মিটার
= 600 মিটার

ট্রেনের গতিবেগ = 72 কিমি/ঘন্টা
= (72 × 1000) মিটার/3600 সেকেন্ড
= 20 মিটার/সেকেন্ড

সময় = দূরত্ব ÷ গতিবেগ
= 600 মিটার ÷ 20 মিটার/সেকেন্ড
= 30 সেকেন্ড

সুতরাং, টানেলটি অতিক্রম করতে ট্রেনটির 30 সেকেন্ড সময় লাগবে।

৮৬৫.
A boat can travel from point A to point B and return back to point A in 9 hours. Speed of the boat in still water is 8 km/h and the speed of the stream is 4 km/h. Find the distance between A and B.
  1. ক
    29 km
  2. খ
    27 km
  3. গ
    25 km
  4. ঘ
    24 km
  5. ঙ
    20 km
ব্যাখ্যা
Speed of boat along the stream = 8 + 4 = 12 km/h
Speed of boat against stream = 8 - 4 = 4 km/h
ATQ, 
x/12 + x/4 = 9
⇒ (x+3x)/12 = 9
⇒ 4x = 108
⇒ x = 27 km
৮৬৬.
A certain distance is covered at a certain speed. If half the distance is covered in double the time, the ratio of the two speeds is:
  1. ক
    1 : 3
  2. খ
    4 : 3
  3. গ
    4 : 1
  4. ঘ
    2 : 3
  5. ঙ
    None of the above
ব্যাখ্যা
Question: A certain distance is covered at a certain speed. If half the distance is covered in double the time, the ratio of the two speeds is:

Solution:
Let x km be covered in y hours.

Then, speed = (x/y) km/hr

In the second case, x/2 km is covered in 2y hours.

∴ New speed = (x/2) × (1/2y ) km/hr = (x/4y) km/hr

∴ Ratio of speeds = (x/y) : (x/4y)
= 1 : (1/4)
= 4 : 1
৮৬৭.
A train covers the distance x between two cities in y hours, arriving 2 hours late. What rate would permit the train to arrive on schedule?
  1. ক
    (x/y) - 2
  2. খ
    x/(y - 2)
  3. গ
    xy - 2
  4. ঘ
    x/(y + 2)
  5. ঙ
    None of these
ব্যাখ্যা

Since the train is late, the allotted time = Y - 2.
D = T × S
X = (Y - 2) × S
or, S = X/(Y - 2)

৮৬৮.
A train runs at the speed of 72 kmph and crosses a 250 meter long platform in 26 seconds. What is the length of the train?
  1. ক
    ক) 270 meter
  2. খ
    খ) 210 meter
  3. গ
    গ) 340 meter
  4. ঘ
    ঘ) 130 meter
ব্যাখ্যা

Distance covered in 26 seconds.
= 26 × 72 × (5/18)
= 520 meter.
Length of the train = (520 - 250) meter
= 270 meter.

৮৬৯.
Rakib is walking at 5m/s. Tanvir was 200m behind Rakib and started walking at 7m/s towards Rakib. After how much time will Tanvir catch Rakib?
  1. ক
    100 seconds
  2. খ
    110 seconds
  3. গ
    90 seconds
  4. ঘ
    200 seconds
ব্যাখ্যা
Question: Rakib is walking at 5m/s. Tanvir was 200m behind Rakib and started walking at 7m/s towards Rakib. After how much time will Tanvir catch Rakib?

Solution:
let after t seconds Tanvir will catch Rakib.
in t seconds,
Rakib will cover = 5t m 
Tanvir will cover = 7t m

∴ 7t = 5t + 200
2t = 200
t = 100 seconds
৮৭০.
In a race of 1000m, A can beat B by 100m. In a 400m, B beats C by 40m. In a race of 500m. A will beat C by-
  1. ক
    75m
  2. খ
    85m
  3. গ
    90m
  4. ঘ
    95m
ব্যাখ্যা
Question: In a race of 1000m, A can beat B by 100m. In a 400m, B beats C by 40m. In a race of 500m. A will beat C by-

Solution:
While A covers 1000 B covers 900
while A covers 500 B covers 450m

While B covers 400, C covers 360m
While B covers 450, C covers (360 × 450)/400 = 405m

∴ in a 500m race A will beat C  by = (500 - 405) = 95m
৮৭১.
The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
  1. ক
    8 kmph
  2. খ
    6 kmph
  3. গ
    7.5 kmph
  4. ঘ
    5.5 kmph
  5. ঙ
    5 Kmph
ব্যাখ্যা

Speed of the stream = 1
Motor boat speed in still water be = x kmph
Downstream = x + 1 kmph
Up Stream = x - 1 kmph
[35/(x + 1)] + [35/(x - 1)] = 12
x = 6 kmph

৮৭২.
A man rows 24 km upstream in 6 hours and a distance of 35 km downstream in 7 hours. Then the speed of the man in still water is
  1. ক
    ক) 5 km/hr
  2. খ
    খ) 5.5 km/hr
  3. গ
    গ) 4 km/hr
  4. ঘ
    ঘ) 4.5 km/hr
ব্যাখ্যা
Question: A man rows 24 km upstream in 6 hours and a distance of 35 km downstream in 7 hours. Then the speed of the man in still water is

Solution:
Let,
The speed of the man in still water is x km/hr
The speed of stream is y km/hr

∴ x - y = 24/6 = 4
∴ x + y = 35/7 = 5

∴ x - y + x + y = 4 + 5
⇒ 2x = 9
∴ x = 4.5 

∴ The speed of the man in still water is 4.5 km/hr
৮৭৩.
With a uniform speed, a car covers a distance in 6 hours. Had the speed been increased by 3 km/hr the same distance could have been covered in 5 hours. What is the distance covered?
  1. ক
    ক) 90 km 
  2. খ
    খ) 120 km 
  3. গ
    গ) 150 km 
  4. ঘ
    ঘ) 210 km 
ব্যাখ্যা
Question: With a uniform speed, a car covers a distance in 6 hours. Had the speed been increased by 3 km/hr the same distance could have been covered in 5 hours. What is the distance covered?

Solution: 
Let, the ditance is x km

ATQ,
(x/5) - (x/6) = 3 [If we devide distance by time we get speed] 
⇒ (6x - 5x)/30 = 3
⇒ x/30 = 3
⇒ x = 30 × 3
∴ x = 90

∴ The distance covered is 90 km
৮৭৪.
The speed of A and B are in the ratio 4 : 7. B takes 21 minutes less than A to reach a destination. Time in which B reach the destination?
  1. ক
    49 minutes
  2. খ
    35 minutes
  3. গ
    28 minutes
  4. ঘ
    30 minutes
ব্যাখ্যা
Question: The speed of A and B are in the ratio 4 : 7. B takes 21 minutes less than A to reach a destination. Time in which B reach the destination?

Solution:
Given
The speed of A and B are in the ratio = 4 : 7

So the ratio of time taken = 7 : 4  [As Speed ∝ 1/Time, When distance remains constant.]

Let,
time taken by A and B be 7x and 4x minutes respectively.

ATQ,
7x - 4x = 21
⇒ 3x = 21
∴ x = 7

Hence, time taken by B = (4 × 7) minutes
= 28 minutes
৮৭৫.
A train travelled from A to B and back in a certain time at the rate of 60 Km/hr. But if the train had travelled from A to B at the rate of 80 Km/hr and back from B to A at the rate of 40 Km/hr it would take two hours longer. The distance between A and B is-
  1. ক
    ক) 320 km
  2. খ
    খ) 540 km
  3. গ
    গ) 180 km
  4. ঘ
    ঘ) 210 km
  5. ঙ
    ঙ) 480 km
ব্যাখ্যা

(d/80 + d/40) - (d/60 + d/60) = 2
(3d + 6d - 4d - 4d)/240 = 2
d = 480 km

৮৭৬.
A boatman goes 2 km against the current of the stream in 2 hour and goes 1km along the current in 20 minutes. How long will it take to go 5 km in stationary water?
  1. ক
    ক) 4 hr 25 min
  2. খ
    খ) 3 hr 25 min
  3. গ
    গ) 2 hr 30 min
  4. ঘ
    ঘ) 1 hr 15 min
  5. ঙ
    ঙ) 3 hr 53 min
ব্যাখ্যা

Speed upstream = 2/2 = 1 km/hr
Speed downstream = 1/(20/60) = 3 km/hr
Speed in still water = (1/2)(3+1) = 2 km/hr
Time taken to travel 5 km in still water = 5/2
= 2(1/2)
= 2 hr 30 min

৮৭৭.
Kamal can run 1000 meters in 4 minutes. He has a car that has a top speed of 75 km/hr. What percentage of Kamal's speed is his car's top speed?
  1. ক
    30%
  2. খ
    25%
  3. গ
    20%
  4. ঘ
    10%
  5. ঙ
    None
ব্যাখ্যা
Question: Kamal can run 1000 meters in 4 minutes. He has a car that has a top speed of 75 km/hr. What percentage of Kamal's speed is his car's top speed?

Solution:
এখানে, দূরুত্ব = 1000 মিটার
= 1 কি.মি.

4 মিনিট = 4/60 ঘণ্টা = 1/15 ঘণ্টা

কামালের গতিবেগ = 1/(1/15) কি.মি./ঘণ্টা = 15 কি.মি./ঘণ্টা
গাড়ির গতিবেগ = 75 কি.মি./ঘণ্টা

∴ কামালের গতিবেগ তার গাড়ির গতিবেগের = {(15/75) × 100}%
= 20%
৮৭৮.
A person goes from place A to another place B at a speed of 4 km/h and returns at a speed of 3 km/h. If this takes 7 h in all, then what is the distance between two places?
  1. ক
    ক) 12 km
  2. খ
    খ) 8 km
  3. গ
    গ) 6 km
  4. ঘ
    ঘ) 5 km
  5. ঙ
    ঙ) 7 km
৮৭৯.
A train, 150 meter long and running at a speed of 60 km per hour, takes 30 seconds to cross a bridge. What is the length (in meter) of the bridge?
  1. ক
    350
  2. খ
    450
  3. গ
    500
  4. ঘ
    650
ব্যাখ্যা
Question: A train, 150 meters long and running at a speed of 60 km per hour, takes 30 seconds to cross a  bridge. What is the length (in meters) of the bridge?

Solution: 
সেকেন্ডে ট্রেনের গতিবেগ = (60×1000)/(60×60) মিটার/সেকেন্ড 
= 16.67 মিটার/সেকেন্ড
∴ 30 সেকেন্ডে অতিক্রান্ত দূরত্ব = (30×16.67)m = 500m
ব্রিজের দূরত্ব = 500 - 150 = 350 m
৮৮০.
A, B, and C start together from the same place to walk around a circular path of length 12km. A walk at the rate of 4 km/h, B 3 km/h and C 3/2 km/h. They will meet together at the starting place at the end of-
  1. ক
    12 hours.
  2. খ
    18 hours.
  3. গ
    24 hours
  4. ঘ
    28 hours
ব্যাখ্যা
Question: A, B, and C start together from the same place to walk around a circular path of length 12km. A walk at the rate of 4 km/h, B 3 km/h and C 3/2 km/h. They will meet together at the starting place at the end of-

Solution:
We know,
Time = Distance/speed

Time taken to complete the revolution
A = 12/4 = 3 hours
B = 12/3 = 4 hours
C = 12 × (2/3) = 8 hours

Now, required time = LCM of 3, 4, and 8
= 24 hours
৮৮১.
A train can cross a pole in 32 sec and a 420-meter platform in 62 seconds. Find the length of the train.
  1. ক
    520 m
  2. খ
    448 m
  3. গ
    552 m
  4. ঘ
    360 m
ব্যাখ্যা
Question: A train can cross a pole in 32 sec and a 420-meter platform in 62 seconds. Find the length of the train.

Solution:
Let the length of the train be x m

Speed equal in both case,
then
x/32 = (x + 420)/62
⇒ 62x = 32x + 420 × 32
⇒ 62x - 32x = 420 × 32
⇒ 30x = 420 × 32
⇒ x = (420 × 32)/30
∴ x = 448 m

∴ Length of train is 448 m.
৮৮২.
A 225 m long train can cover a 405 m platform in 21 seconds. Find the speed of the train in km/hr is?
  1. ক
    ক) 98 km/hr
  2. খ
    খ) 90 km/hr
  3. গ
    গ) 96 km/hr
  4. ঘ
    ঘ) 108 km/hr
ব্যাখ্যা
Length of platform = 405 m
Length of train = 225 m
Time taken to cover the length of train = 21 seconds
Distance need to cover = Length of platform + length of train
                                      = 405 + 225
                                     = 630 m
Speed of train = 630/21 = 30 m/s

∴ Speed of train = 30 × (18/5) = 6 × 18 = 108 km/hr.
৮৮৩.
Munna covers one-third of a road at 3 km/h and the remaining distance at 6 km/h. His average speed is-
  1. ক
    ক) 4 km/hr
  2. খ
    খ) 4.5 km/hr
  3. গ
    গ) 5 km/hr
  4. ঘ
    ঘ) 5.5 km/hr
ব্যাখ্যা
Question: Munna covers one-third of a road at 3 km/h and the remaining distance at 6 km/h. His average speed is-

Solution: 
ধরি, রাস্তাটির দূরত্ব x km
3 km/h বেগে অতিক্রম করে x/3 কিমি ও
6 km/h বেগে অতিক্রম করে = (x - x/3) কিমি
= 2x/3 কিমি 

গড় বেগ = (2x)/{(x/3/3) + (2x/3/6)}
= x/(x/9 + x/9)
= 9/2
= 4.5 kmph
৮৮৪.
A person can swim in water with a speed of 14 km/hr in still water. If the speed of the stream is 4 km/hr, what will be the time taken by the person to go 90 km downstream?
  1. ক
    5 hrs.
  2. খ
    7 hrs.
  3. গ
    4 hrs.
  4. ঘ
    6 hrs.
  5. ঙ
    None of these
ব্যাখ্যা
Question:  A person can swim in water with a speed of 14 km/hr in still water. If the speed of the stream is 4 km/hr, what will be the time taken by the person to go 90 km downstream?

Solution:
Speed downstream = Speed of Boat in still water + Speed od the stream =
(14 + 4)km/hr.
= 18 km/hr.

∴ Time taken to travel 90 km downstream = Distance/Speed
= (90/18)hrs
= 5 hrs.
৮৮৫.
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.
  1. ক
    35 km/hr
  2. খ
    40 km/hr
  3. গ
    42 km/hr
  4. ঘ
    45 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.
৮৮৬.
A man travels for 2 hours at 35 miles an hour and he covers 65 miles in the next 3 hours. What is the average speed per hour for the entire trip? 
  1. ক
    ক) 22
  2. খ
    খ) 24
  3. গ
    গ) 26
  4. ঘ
    ঘ) 27
ব্যাখ্যা
লোকটি প্রথম 2 ঘণ্টায় অতিক্রম করে 35 × 2 মাইল 
                                                            = 70 মাইল 

লোকটি পরবর্তী 3 ঘণ্টায় অতিক্রম করে = 65 মাইল 

গড় গতিবেগ = (70 + 65)/(2 + 3) মাইল  
                    = 135/5
                    = 27 মাইল
৮৮৭.
A monkey climbs a 60 m high pole. In the first minute, he climbs 6 m and slips down 3 m in the next minute. How much time is required by it to reach the top?
  1. ক
    25 minutes
  2. খ
    33 minutes
  3. গ
    35 minutes
  4. ঘ
    37 minutes
  5. ঙ
    None of the above
ব্যাখ্যা
Question: A monkey climbs a 60 m high pole. In the first minute, he climbs 6 m and slips down 3 m in the next minute. How much time is required by it to reach the top?

Solution:
According to the question,
For 1st min, he climbs 6 m and comes down 3 m in 2nd min.
Effectively in 2 min, he climbs 3 m.

In 1 min, he climbs (3/2) m

So, in 36 mins he climbs = (3/2) × 36 = 54 m

So, in the 37th minute, he climbs the next 6 m.

∴ The required value is 37 minutes.
৮৮৮.
A train passes a station platform in 42 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 72 km/hr, what is the length of the platform?
  1. ক
    360 m 
  2. খ
    420 m 
  3. গ
    440 m 
  4. ঘ
    380 m 
  5. ঙ
    None
ব্যাখ্যা

Question: A train passes a station platform in 42 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 72 km/hr, what is the length of the platform?

Solution:
ট্রেনটি 3600 সেকেন্ডে অতিক্রম করে 72000 মিটার 
ট্রেনটি 1 সেকেন্ডে অতিক্রম করে 72000/3600 মিটার 
ট্রেনটি 20 সেকেন্ডে অতিক্রম করে (72000 × 20)/3600 মিটার 
= 400 মিটার 

ট্রেনের দৈর্ঘ্য = 400 মিটার 
আবার 
ট্রেনটি 3600 সেকেন্ডে অতিক্রম করে 72000 মিটার 
ট্রেনটি 1 সেকেন্ডে অতিক্রম করে 72000/3600 মিটার 
ট্রেনটি 42 সেকেন্ডে অতিক্রম করে (72000 × 42)/3600 মিটার 
= 840 মিটার 

প্লাটফর্মের দৈর্ঘ্য  = (840 - 400) = 440 মিটার 

৮৮৯.
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boating till water.
  1. ক
    ক) 3 km/hr
  2. খ
    খ) 4 km/hr
  3. গ
    গ) 8 km/hr
  4. ঘ
    ঘ) 6 km/hr
ব্যাখ্যা

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

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

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

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

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

৮৯০.
If one man or two women or three boys can finish a work in 88 days, then how many days will one man, one woman and one boy together take to finish the same work?
  1. ক
    ক) 46 days
  2. খ
    খ) 54 days
  3. গ
    গ) 48 days
  4. ঘ
    ঘ) 44 days
  5. ঙ
    ঙ) 45 days
ব্যাখ্যা
1 man = 2 women = 3 boys
1 man + 1 woman + 1 boy
= (3 + 3/2 + 1) boys
= 11/2 boys
Here, M1 = 3, M2 = 11/2,
D1 = 88 and D2 = ?

According to the formula,

M1D1 =M2D2
D2 = (M1D1)/M2

Required number of days,
= (3 × 2 × 88)/11
= 3 × 2 × 8
= 48 days
৮৯১.
A swimmer can swim at 5 km/hour in still water. When the river flows at 1 km/hour, then he takes 75 minutes to go to a certain point and come back to the starting point. How far is this place?
  1. ক
    5 km
  2. খ
    6 km
  3. গ
    4 km
  4. ঘ
    3 km
  5. ঙ
    None of these
ব্যাখ্যা
Question: A swimmer can swim at 5 km/hour in still water. When the river flows at 1 km/hour, then he takes 75 minutes to go to a certain point and come back to the starting point. How far is this place?

Solution:
Given that,
Total time = 5 hours and Speed of river = 1 km/hour
Total time to go to a certain point and come back = 75 min = 75/60 h = 5/4 h

Now, Let the distance to the point be x km.
When swimming downstream, the swimmer's speed = (5 + 1) = 6 km/h.
When swimming upstream, the swimmer's speed = (5 - 1) = 4 km/h

Now,
T1 + T2 = T
⇒ (x/6) + (x/4) = 5/4
⇒ (2x + 3x)/12 = 5/4
⇒ 5x = 15
⇒ x = 15/5
∴ x = 3 km.

∴ The place is 3 km away from the starting point.

৮৯২.
In covering a certain distance, The speeds of A and B are in the ratio of 5 : 6. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is-  
  1. ক
    ক) 2 hours
  2. খ
    খ) 3 hours
  3. গ
    গ) 4 hours
  4. ঘ
    ঘ) 5 hours
ব্যাখ্যা
Ratio of speeds =5 : 6 
⇒ Ratio of times taken =6 : 5
Let A and B take 6x and 5x hrs. to reach the destination. 
Then
6x - 5x=30​/60
x =1/2​

∴ Time taken by A =(6 × 1​)/2 hours
                               = 3 hours
৮৯৩.
A cyclist rides 24 km at 16 kmph and further 36 km at 20 kmph. Find his average speed for the journey. 
  1. ক
    ক) 18.18 km/hr.
  2. খ
    খ) 27.18 km/hr.
  3. গ
    গ) 15.18 km/hr.
  4. ঘ
    ঘ) 22.18 km/hr.
ব্যাখ্যা
Total distance travelled :
= (24 + 36) km
= 60 km


Total time taken :
(24/16) + (36/20) hours 
= (3/2) + (9/5) hours
= (15 + 18)/10 hours
= 33/10 hours

∴ Average speed : 60 × (10/33) km/hr.
                            = 600/33 km/hr.
                              = 18.18 km/hr.
৮৯৪.
A bus 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 bus for the whole journey is:
  1. ক
    16 km/hr
  2. খ
    18 km/hr
  3. গ
    20 km/hr
  4. ঘ
    22 km/hr
ব্যাখ্যা
Question: A bus 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 bus for the whole journey is:

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

ATQ,
Total time = {a/(3 × 10)} + {a/(3 × 20)} + {a/(3 × 60)}
= (a/30) + (a/60) + (a/180)
= (6a + 3a + a)/180
= 10a/180
= a/18

∴ Average speed = (a × 18)/a km/hr
= 18 km/hr
৮৯৫.
An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of-
  1. ক
    720 kmph
  2. খ
    300 kmph
  3. গ
    600 kmph
  4. ঘ
    360 kmph
ব্যাখ্যা

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

Solution: 
Given that,
Speed = 240 kmph 
Time = 5 hours 

We know,
 Distance = Speed × Time 
= 240 × 5
∴ Distance = 1200 km

Again,
Given: 
Distance = 1200 km 
New Time = 5/3 hours 
 
 New Speed = Distance/New Time
= 1200/(5/3)
= (1200 × 3)/5
= 720 kmph
 
 ∴ The aeroplane must travel at a speed of 720 kmph.

৮৯৬.
A train 175 m long crosses a bridge which is 125 m long in 1 min 40 seconds. What is the speed of the train?
  1. ক
    ক) 2 m/sec
  2. খ
    খ) 3 m/sec
  3. গ
    গ) 4 m/sec
  4. ঘ
    ঘ) 5 m/sec
ব্যাখ্যা
Question: A train 175 m long crosses a bridge which is 125 m long in 1 min 40 seconds. What is the speed of the train?

Solution: 
মোট অতিক্রান্ত দূরত্ব = ১৭৫ + ১২৫ মিটার 
= ৩০০ মিটার 

সময় = ১ মিনিট ৪০ সেকেন্ড 
= ৬০ + ৪০ সেকেন্ড 
= ১০০ সেকেন্ড 

বেগ = ৩০০/১০০ মিটার/সেকেন্ড
= ৩ মিটার/সেকেন্ড 
৮৯৭.
A man can row upstream at 24km/hr and downstream at 16km/hr. The man rowing speed in still water is?
  1. ক
    ক) 20 km/hr
  2. খ
    খ) 15 km/hr
  3. গ
    গ) 25 km/hr
  4. ঘ
    ঘ) 27 km/hr
ব্যাখ্যা
Speed of boat in still water = (x+y)/2
Where (x = downstream speed) and (y = upstream speed)
∴ Boat's speed = (24+16)/2 = 40/2 = 20 km/hr
৮৯৮.
A man decided to cover a distance of 6 km in 84 minutes. He decided to cover two thirds of the distance at 4 kmph and the remaining at some different speed. Find the speed after the two third distance has been covered.
  1. ক
    5 kmph
  2. খ
    7 kmph
  3. গ
    9 kmph
  4. ঘ
    3 kmph
ব্যাখ্যা
Question: A man decided to cover a distance of 6 km in 84 minutes. He decided to cover two thirds of the distance at 4 kmph and the remaining at some different speed. Find the speed after the two third distance has been covered.

Solution:
We are given that two thirds of the 6 km was covered at 4 kmph 
∴ 4 km distance was covered at 4 kmph.
Time taken to cover 4 km = (4 km)/(4 kmph) = 1 hr = 60 minutes

Time left = 84 - 60 = 24 minutes

Now,
The man has to cover remaining 2 km in 24 minutes = 24/60 hours = 0.4 hours

Speed required for remaining 2 km = 2/ 0.4 = 5 kmph
৮৯৯.
A man travels equal distances of his journey at 15, 20 and 30 km/hour respectively. What is his average speed for whole journey?
  1. ক
    15
  2. খ
    20
  3. গ
    30
  4. ঘ
    25
  5. ঙ
    35
ব্যাখ্যা
Required average speed
= (3 × 15 × 20 × 30)/(15 × 20 + 20 × 30 + 30 × 15)
= 20 km/hour
----------------------------------------------------------------
Alternative way:
Distance 30 km, Speed 30 km/h, Time 1 Hour
Distance 30 km, Speed 15 km/h, Time 2 Hours
Distance 30 km, Speed 20 km/h, Time 1 hour & 30 minutes.
Total Distance 90 km, Total Time 4.5 Hours,
Average Speed 90/4.5 km/h = 20 km/h
--------------------------------------------------------------
Alternative way:
Let, equal distances travelled by the man be ’s’.
Time taken to travel first distance, s at 15 kmph = s/15
Time taken to travel second distance, s at 20 kmph = s/20
Tine taken to travel last distance, s at 30 kmph = s/30
Therefore, total time taken by the man = s(1/15 +1/20 +1/30)
Total distance travelled by the man = 3s
Hence, average speed of the man
= 3s / [ s(1/15 +1/20 +1/30) ] =3/(1/15 +1/20 +1/30)
= 20 kmph
---------------------------------------------------------------
Alternative way:
Avg speed formula= 3 ÷ (1/x +1/y +1/z)
Now we have 1/30 +1/20 +1/15
L.C.M. of 20, 30 and15 is 60.
Then (3 + 4 + 8)/60=9/60 = 3/20
From above formula, average speed = 3 ÷ 3/20=20 km/h
৯০০.
A motorist must complete 180-mile trip is 4 hours. If he averages 50 miles an hour for the first three hours of the trip, how fast must (in terms of mile per hour) he travel in the last hour?
  1. ক
    ক) 30
  2. খ
    খ) 32
  3. গ
    গ) 40
  4. ঘ
    ঘ) None
ব্যাখ্যা
Question: A motorist must complete 180-mile trip is 4 hours. If he averages 50 miles an hour for the first three hours of the trip, how fast must (in terms of mile per hour) he travel in the last hour?

Solution:
প্রথম তিনঘণ্টায় বেগ ৫০ মাইল/ঘণ্টা 
প্রথম ৩ ঘণ্টায় অতিক্রম করে ৫০ × ৩ মাইল 
= ১৫০ মাইল  

∴ শেষ ঘণ্টায় যেতে হবে = ১৮০ - ১৫০ 
= ৩০ মাইল