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Time and Speed - Train and Boat

মোট প্রশ্ন১,৪৩৯এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Time and Speed - Train and Boat

PrepBank · পাতা ১১ / ১৫ · ১,০০১–১,১০০ / ১,৪৩৯

১,০০১.
Ratio of speed of boat in still water and speed of stream is 7 : 2. Boat cover 120 km upstream in 8 hours and x km in 3 hours downstream. Find the value of x?
  1. ক
    84 km
  2. খ
    72 km
  3. গ
    81 km
  4. ঘ
    78 km
  5. ঙ
    96 km
সঠিক উত্তর: গ
81 km
উত্তর
সঠিক উত্তর: গ
81 km
গ
ব্যাখ্যা
Question: Ratio of speed of boat in still water and speed of stream is 7 : 2. Boat cover 120 km upstream in 8 hours and x km in 3 hours downstream. Find the value of x?

Solution:
Speed of boat : stream = 7 : 2
⇒ Let boat = 7x, stream = 2x

Now,
Upstream = 7x - 2x = 5x
Downstream = 7x + 2x = 9x

Upstream 120 km in 8 hours = 15 km/hr
⇒ 5x = 15
∴ x = 3
Downstream speed = 9x = 27 km/hr
In 3 hrs. Distance is = 27 × 3 = 81 km

১,০০২.
Mr. Farhan and Mr. Rafiq start walking in the park along a circular track from opposite directions at 6:30 am. If they walk at speeds of 2 rounds per hour and 3 rounds per hour respectively, how many times will they cross each other by 8.00 am?
  1. ক
    5
  2. খ
    6
  3. গ
    7
  4. ঘ
    8
  5. ঙ
    9
সঠিক উত্তর: গ
7
উত্তর
সঠিক উত্তর: গ
7
গ
ব্যাখ্যা
Question: Mr. Farhan and Mr. Rafiq start walking in the park along a circular track from opposite directions at 6:30 am. If they walk at speeds of 2 rounds per hour and 3 rounds per hour respectively, how many times will they cross each other by 8.00 am?

Solution:
6 : 30 am থেকে 8 : 00 am পর্যন্ত সময় = 1.5 ঘণ্টা
দুইজন বিপরীত দিকে হাঁটছেন, তাই প্রতি ঘণ্টায় তারা যতবার একে অপরকে অতিক্রম করবেন তা হব,
আপেক্ষিক বেগ = 2 + 3 = 5 চক্কর প্রতি ঘণ্টা
সুতরাং 1.5 ঘণ্টায় তারা একে অপরকে অতিক্রম করবে = 5 × 1.5 = 7.5 বার
তবে আংশিক অতিক্রম (0.5) গণনায় ধরা হবে না, কারণ ঘুরার ক্ষেত্রে পূর্ণ সংখ্যা গ্রহণযোগ্য।
১,০০৩.
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
    ক) 40 km/hr
  2. খ
    খ) 48 km/hr
  3. গ
    গ) 49 km/hr
  4. ঘ
    ঘ) 64 km/hr
সঠিক উত্তর: খ
খ) 48 km/hr
উত্তর
সঠিক উত্তর: খ
খ) 48 km/hr
খ
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.

১,০০৪.
An athlete runs 200 meters race in 24 seconds. His speed in km/h is-
  1. ক
    50
  2. খ
    40
  3. গ
    30
  4. ঘ
    15
  5. ঙ
    None of the above
সঠিক উত্তর: গ
30
উত্তর
সঠিক উত্তর: গ
30
গ
ব্যাখ্যা
Question: An athlete runs 200 meters race in 24 seconds. His speed in km/h is-

Solution:
Speed of athlete
= 200 m/24 sec
= (200 × 18)/(5 × 24)
= 30 km/hour
১,০০৫.
A train 300 metres long is running at a speed of 25 metre per second. It will cross a bridge of 200 metres long in:
  1. ক
    ক) 10 sec
  2. খ
    খ) 15 sec
  3. গ
    গ) 20 sec
  4. ঘ
    ঘ) 25 sec
সঠিক উত্তর: গ
গ) 20 sec
উত্তর
সঠিক উত্তর: গ
গ) 20 sec
গ
ব্যাখ্যা
Question: A train 300 metres long is running at a speed of 25 metre per second. It will cross a bridge of 200 metres long in:

Solution:
Speed of train = 25 m/s.
Total distance covered while passing bridge = 300 + 200 = 500 m

∴ Time = 500​/25 
= 20 seconds.
১,০০৬.
The speed of a boat in still water in 20 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 20 minutes is:
  1. ক
    ক) 8.5 km
  2. খ
    খ) 7.5 km
  3. গ
    গ) 8 km
  4. ঘ
    ঘ) 10 km
সঠিক উত্তর: গ
গ) 8 km
উত্তর
সঠিক উত্তর: গ
গ) 8 km
গ
ব্যাখ্যা
Question: The speed of a boat in still water in 20 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 20 minutes is:

Solution:
Speed downstream = (20 + 4) kmph = 24 km/hr

Distance travelled in 20 min = 24 × (20/60) km
= 8 km
১,০০৭.
A vehicle travels at the rate of 80 kmph. What distance will it travel in 15 minutes?
  1. ক
    24000 meter
  2. খ
    25000 meter
  3. গ
    20000 meter
  4. ঘ
    22000 meter
সঠিক উত্তর: গ
20000 meter
উত্তর
সঠিক উত্তর: গ
20000 meter
গ
ব্যাখ্যা
Question: A vehicle travels at the rate of 80 kmph. What distance will it travel in 15 minutes?

Solution:
In 60 minutes it goes 80 k.m. = 80000 m
In 1 minute it goes 80000/60 m
In 15 minutes it goes (80000 × 15)/60 k.m.
= 20000 meters.
১,০০৮.
A motorboat can travel at 5 km/hr in still water. It travelled 90 km downstream in a river and then returned, taking altogether 100 hours. Find the rate of flow of the river.
  1. ক
    3 km/hr
  2. খ
    3.5 km/hr
  3. গ
    2.5 km/hr
  4. ঘ
    2 km/hr
  5. ঙ
    4 km/hr
সঠিক উত্তর: ঙ
4 km/hr
উত্তর
সঠিক উত্তর: ঙ
4 km/hr
ঙ
ব্যাখ্যা
Question: A motorboat can travel at 5 km/hr in still water. It travelled 90 km downstream in a river and then returned, taking altogether 100 hours. Find the rate of flow of the river.

Solution:
Speed of boat in still water = x = 5 km/hr.
Let rate of flow of river = y km/hr.
∴ Speed of u/s = 5 - y
and speed of d/s = 5 + y

∴ 90/(5 + y) + 90/(5 - y) = 100
⇒ 450 - 9y + 450 + 9y = 100(25 - y2)
⇒ 9 = 25 - y2
⇒ y2 = 16
⇒ y = 4 km/hr.
১,০০৯.
Speed of a boat in standing water is 18 kmph and the speed of the stream is 3 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
  1. ক
    12 hours
  2. খ
    16 hours
  3. গ
    18 hours
  4. ঘ
    20 hours
সঠিক উত্তর: ক
12 hours
উত্তর
সঠিক উত্তর: ক
12 hours
ক
ব্যাখ্যা
Question: Speed of a boat in standing water is 18 kmph and the speed of the stream is 3 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

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

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

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

Total time taken
= (105/15 + 105/21) hours
= 7 + 5 hours
= 12 hours
১,০১০.
The ratio between the speeds of a bus and a bike is 5 : 8. If the bus travels 120 km in 2 hours, find the speed of the bike.
  1. ক
    56 km/hr
  2. খ
    72 km/hr
  3. গ
    84 km/hr
  4. ঘ
    96 km/hr
সঠিক উত্তর: ঘ
96 km/hr
উত্তর
সঠিক উত্তর: ঘ
96 km/hr
ঘ
ব্যাখ্যা
Question: The ratio between the speeds of a bus and bike is 5 : 8. If the bus travels 120 km in 2 hours, find the speed of the
bike.
Solution:
Let,
the speed of bus and bike is 5X and 8X.
Speed of bus = 120/2 = 60 km/hr
So, 5X= 60
.. X = 60/5
= 12 km/hr

Speed of bike = 8X
= 8 × 12
= 96 km/hr
১,০১১.
Two trains of equal length are running on parallel lines in the same direction at 66 km and 56 km per hour. The faster train passes the slower train in 36 seconds. The length of each train is-
  1. ক
    30 m
  2. খ
    40 m
  3. গ
    50 m
  4. ঘ
    60 m
সঠিক উত্তর: গ
50 m
উত্তর
সঠিক উত্তর: গ
50 m
গ
ব্যাখ্যা
Question: Two trains of equal length are running on parallel lines in the same direction at 66 km and 56 km per hour. The faster train passes the slower train in 36 seconds. The length of each train is-

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

So the distance to be covered = 2a
Now the trains are running int he same direction.
∴ Their relative speed = (66 - 56) km/hr.
=10km/hr. = 10 × (5/18) km/hr. = (25/9) m/sec.

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

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

So, the length of each train = 50 m.
১,০১২.
A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
  1. ক
    2:1
  2. খ
    3:1
  3. গ
    2:3
  4. ঘ
    3:4
  5. ঙ
    2:5
সঠিক উত্তর: খ
3:1
উত্তর
সঠিক উত্তর: খ
3:1
খ
ব্যাখ্যা

Let man's rate upstream be x km/hr
Then, his rate downstream = 2x km/hr
∴ (speed in still water) : (Speed of stream)
(2x + x)/2 : (2x - x)/2
3x/2 : x/2
3 : 1

১,০১৩.
Two trains are moving in opposite directions at (50/3) m/s and 25 m/s. Their lengths are 1100 m and 900 m respectively. The time taken by the slower train to cross the faster train is:
  1. ক
    ক) 36 sec
  2. খ
    খ) 45 sec
  3. গ
    গ) 48 sec
  4. ঘ
    ঘ) 49 sec
সঠিক উত্তর: গ
গ) 48 sec
উত্তর
সঠিক উত্তর: গ
গ) 48 sec
গ
ব্যাখ্যা
Question: Two trains are moving in opposite directions at (50/3) m/s and 25 m/s. Their lengths are 1100 m and 900 m respectively. The time taken by the slower train to cross the faster train is:

Solution:
Relative speed = (50/3) + 25 m/s
= (50 + 75)/3 m/s
= 125/3 m/s

Distance covered = 1100 + 900 = 2000 m

Required time = (2000 × 3)/125 sec
= 48 sec
১,০১৪.
Anik crosses a 600 m long street in 5 minutes, What is his speed in km per hour?
  1. ক
    ক) 120
  2. খ
    খ) 20
  3. গ
    গ) 7.2
  4. ঘ
    ঘ) None of these
সঠিক উত্তর: গ
গ) 7.2
উত্তর
সঠিক উত্তর: গ
গ) 7.2
গ
ব্যাখ্যা
Question: Anik crosses a 600 m long street in 5 minutes, What is his speed in km per hour?

Solution: 
his speed = 600/5
= 120 m/min
= (120 × 60)/1000 km/hr
= 7.2 km/hr 
১,০১৫.
A man can row 12 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of the stream-
  1. ক
    12 km/hour
  2. খ
    6 km/hour
  3. গ
    9 km/hour
  4. ঘ
    24 km/hour
সঠিক উত্তর: খ
6 km/hour
উত্তর
সঠিক উত্তর: খ
6 km/hour
খ
ব্যাখ্যা

Question: A man can row 12 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of the stream-

Solution:
Given that,
Speed of man in still water = 12 km/h
Time upstream = 3 × Time downstream

Let,
Rate of the stream = x km/h

Now,
Downstream speed = 12 + x
Upstream speed = 12 - x

And, let the distance travelled is = D km

According to the Question,
Time taken upstream = 3 × (Time taken downstream)
D/(12 - x) = 3 × {D/(12 + x)}
⇒ 1/(12 - x) = 3/(12 + x)
⇒ 12 + x = 36 - 3x
⇒ 4x = 24
∴ x = 6

So, rate of the stream = 6 km/h

১,০১৬.
A boat goes 10km in one hour along the stream and 4 km in one hour against the stream. What is the speed of the boat?
  1. ক
    7 km/hr
  2. খ
    6 km/hr
  3. গ
    5 km/hr
  4. ঘ
    8 km/hr
সঠিক উত্তর: ক
7 km/hr
উত্তর
সঠিক উত্তর: ক
7 km/hr
ক
ব্যাখ্যা
Question: A boat goes 10km in one hour along the stream and 4 km in one hour against the stream. What is the speed of the boat?
Solution:
Let,
boat speed is x
stream speed is y

∴ x+y = 10
and, x-y = 4
so,
x+y+x-y = 10+4
2x = 14
x = 7
১,০১৭.
Two trains having equal lengths take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when travelling in opposite directions?
  1. ক
    ক) 12 seconds
  2. খ
    খ) 15 seconds
  3. গ
    গ) 18 seconds
  4. ঘ
    ঘ) 21 seconds
সঠিক উত্তর: ক
ক) 12 seconds
উত্তর
সঠিক উত্তর: ক
ক) 12 seconds
ক
ব্যাখ্যা
Speed of first train = 120 /10 = 12 m/s
Speed of second train = 120/15 = 8 m/s
If they travel in opposite direction, relative speed = 12 + 8 = 20 m/s
Distance covered = 120 + 120 = 240 meters

Time
= (240/20) seconds
= 12 seconds
১,০১৮.
A person is walking at a speed of 5 km/hr along a railway track. If he is 200 m ahead of the train which is 150 m long and runs at a speed of 60 km/hr in same direction, then what is the time required to pass the person?
  1. ক
    ক) 17.34 sec
  2. খ
    খ) 18.47 sec
  3. গ
    গ) 22.92 sec
  4. ঘ
    ঘ) 19.49 sec
সঠিক উত্তর: গ
গ) 22.92 sec
উত্তর
সঠিক উত্তর: গ
গ) 22.92 sec
গ
ব্যাখ্যা
Given: Speed of the person = 5 km/hr, length of train = 100 m, speed of train = 60 km/hr
Speed of train relative to walking person = (60–5) = 55 km/hr
Convert km/hr into m/s
55 km/hr = 55 x(5/18) = 15.27 m/s
Distance to be covered by the train = 200 + 150 = 350 m
Therefore, time taken by the train to cross the person
= Distance over speed =350/15.27 = 22.92 sec
১,০১৯.
A train running at the speed of 25m/s can cross a 200 metres platform in 11 seconds. What is the length of the train?
  1. ক
    ক) 50m
  2. খ
    খ) 60m
  3. গ
    গ) 75m
  4. ঘ
    ঘ) 80m
সঠিক উত্তর: গ
গ) 75m
উত্তর
সঠিক উত্তর: গ
গ) 75m
গ
ব্যাখ্যা
Question: A train running at the speed of 25m/s can cross a 200 metres platform in 11 seconds. What is the length of the train?

Solution: 
Here, 
Speed, S = 25m/s
Time, T = 11s

Let, the distance is = D

We know that,
D = S × T
D = 25 × 11
= 275m 

The length of the train is = 275 - 200 = 75m
১,০২০.
Two trains are running in opposite directions at the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is -
  1. ক
    ক) 42 km/hr
  2. খ
    খ) 36 km/hr
  3. গ
    গ) 28 km/hr
  4. ঘ
    ঘ) 20 km/hr
সঠিক উত্তর: খ
খ) 36 km/hr
উত্তর
সঠিক উত্তর: খ
খ) 36 km/hr
খ
ব্যাখ্যা

Distance covered = (120 + 120)
= 240 meter.
Time = 12 seconds.
Relative speed = 240/12
= 20 m/s.
= 20 × (18/5) km/hr.
= 72 km/hr.
The relative speed, in this case, is the sum of the speeds of the trains and each train has the same speed,
speed as each train = 72/2 km/hr.
= 36 km/hr.

১,০২১.
The speed of a boat in still water is 25 kmph. If it can travel 10 km upstream in 1 hr, what time would it take to travel the same distance downstream?
  1. ক
    ক) 21 minute
  2. খ
    খ) 22 minute
  3. গ
    গ) 30 minute
  4. ঘ
    ঘ) 35 minute
  5. ঙ
    ঙ) 15 minute
সঠিক উত্তর: ঙ
ঙ) 15 minute
উত্তর
সঠিক উত্তর: ঙ
ঙ) 15 minute
ঙ
ব্যাখ্যা

Speed of boat in still water = 25 km/hr
Speed upstream = 10 km/hr
Speed of the stream = (25 − 10) = 15 km/hr
Speed downstream = (25 + 15) = 40 km/hr

Time taken to travel 10 km downstream = 10/40 hour
= (10 × 60)/40
= 15 minute

১,০২২.
A fisher man can push 2 km against the stream in 20 min. What's more, return in 15 min. What is the rate of the current?
  1. ক
    ক) 1 km/hr
  2. খ
    খ) 2 km/hr
  3. গ
    গ) 3 km/hr
  4. ঘ
    ঘ) None of these
সঠিক উত্তর: ক
ক) 1 km/hr
উত্তর
সঠিক উত্তর: ক
ক) 1 km/hr
ক
ব্যাখ্যা

Speed upstream = (2/20)×60 km/hr
= 6 km/hr
Speed downstream = (2/15)×60 km /hr
= 8km/hr
Speed of the current
= 1/2(8-6) km /hr
= 1 km/hr

১,০২৩.
Two buses start from a bus terminal with a speed of 60 km/h at interval of 15 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at interval of 12 minutes?
  1. ক
    15 kmph
  2. খ
    9 kmph
  3. গ
    16 kmph
  4. ঘ
    20 kmph
সঠিক উত্তর: ক
15 kmph
উত্তর
সঠিক উত্তর: ক
15 kmph
ক
ব্যাখ্যা

Question: Two buses start from a bus terminal with a speed of 60 km/h at interval of 15 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at interval of 12 minutes?

Solution:
Let Speed of the man is x kmph.
Distance covered in 15 minutes at 60 kmph = distance covered in 12 minutes at (60 + x) kmph.
60 × (15/60) = (12/60)(60 + x)}
900 = 720 + 12x
12x = 180
x = 180/12
x = 15

So the speed of the man coming from the opposite direction is 15kmph 

১,০২৪.
A train starts from city Y at 2 PM and travels towards city X at 75 km/hr. Another train starts from city X at 1 PM and travels towards Y at 60 km/hr. If the distance between theses two cities is 330 km then at what time will they meet ? 
  1. ক
    ক) 6 : 00 PM 
  2. খ
    খ) 5 : 30 PM 
  3. গ
    গ) 5 : 00 PM 
  4. ঘ
    ঘ) 4 : 00 PM 
সঠিক উত্তর: ঘ
ঘ) 4 : 00 PM 
উত্তর
সঠিক উত্তর: ঘ
ঘ) 4 : 00 PM 
ঘ
ব্যাখ্যা
দ্বিতীয় ট্রেনটি 1 ঘণ্টা পূর্বে ছেড়েছে ফলে ২য় ট্রেনটি 60 km এগিয়ে থাকবে। 

ট্রেন দুটির মধ্যবর্তী  দূরত্ব হবে = (330 - 60) km= 270km 
ট্রেন দুটি  মিলিত হতে সময় লাগবে = 270/(75 + 60) = 2 ঘণ্টা 

সময় লাগবে =  2 PM  + 2 = 4PM
১,০২৫.
A train of 250 m long is moving at 54 km/h. The time taken by the train to cross a bridge of 350 m long is-
  1. ক
    36 seconds
  2. খ
    40 seconds
  3. গ
    30 seconds
  4. ঘ
    45 seconds
সঠিক উত্তর: খ
40 seconds
উত্তর
সঠিক উত্তর: খ
40 seconds
খ
ব্যাখ্যা

Question: A train of 250 m long is moving at 54 km/h. The time taken by the train to cross a bridge of 350 m long is-

Solution:
মোট অতিক্রান্ত দূরত্ব = ট্রেনের দৈর্ঘ্য + সেতুর দৈর্ঘ্য
= (250 + 350) মিটার
= 600 মিটার

ট্রেনের গতিবেগ = 54 কিমি/ঘন্টা
= (54 × 1000) মিটার/3600 সেকেন্ড
= 15 মিটার/সেকেন্ড

সময় = দূরত্ব ÷ গতিবেগ
= 600 মিটার ÷ 15 মিটার/সেকেন্ড
= 40 সেকেন্ড

সুতরাং, সেতুটি অতিক্রম করতে ট্রেনটির 40 সেকেন্ড সময় লাগবে।

১,০২৬.
In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
  1. ক
    ক) 8 km/hr
  2. খ
    খ) 11 km/hr
  3. গ
    গ) 12 km/hr
  4. ঘ
    ঘ) 10 km/hr
সঠিক উত্তর: খ
খ) 11 km/hr
উত্তর
সঠিক উত্তর: খ
খ) 11 km/hr
খ
ব্যাখ্যা

Let speed of the boat in still water = a and speed of the stream = b
Then
a+b = 14
a-b = 8
Adding these two equations, we get 2a = 22
=> a = 11
ie, speed of boat in still water = 11 km/hr

১,০২৭.
Two men start together to walk a certain distance, one at 4 km/hr and another at 3 km/hr. The former arrives half an hour before the latter. Find the distance -
  1. ক
    ক) 8 km
  2. খ
    খ) 7 km
  3. গ
    গ) 6 km
  4. ঘ
    ঘ) 9 km
সঠিক উত্তর: গ
গ) 6 km
উত্তর
সঠিক উত্তর: গ
গ) 6 km
গ
ব্যাখ্যা

If the required distance be x km, then
(x/3)−(x/4)= 1/2
⇒ (4x−3x)/12= 1/2
⇒ x/12= 1/2
⇒ x= 6 km

১,০২৮.
A boat running downstream covers a distance of 24 km in 3 hours while for covering the same distance upstream, it takes 6 hours. What is the speed of the boat in still water?
  1. ক
    ক) 4 km/hr
  2. খ
    খ) 6 km/hr
  3. গ
    গ) 8 km/hr
  4. ঘ
    ঘ) 10 km/hr
সঠিক উত্তর: খ
খ) 6 km/hr
উত্তর
সঠিক উত্তর: খ
খ) 6 km/hr
খ
ব্যাখ্যা
Question: A boat running downstream covers a distance of 24 km in 3 hours while for covering the same distance upstream, it takes 6 hours. What is the speed of the boat in still water?

Solution:
speed downstream = 24/3  km/hr = 8 km/hr
speed upstream = 24/6 km/hr = 4 km/hr 

∴ Speed in still water = (8 + 4)/2 km/hr = 6 km/hr.
১,০২৯.
The distance between A and B is 30 km. A boat makes a return journey from point A to point B and back in 10 hours 30 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 17 hours 30 minutes. What is the speed of the boat in still water?
  1. ক
    ক) 5 km/hr
  2. খ
    খ) 6 km/hr
  3. গ
    গ) 7 km/hr
  4. ঘ
    ঘ) 8 km/hr
সঠিক উত্তর: গ
গ) 7 km/hr
উত্তর
সঠিক উত্তর: গ
গ) 7 km/hr
গ
ব্যাখ্যা
Question: The distance between A and B is 30 km. A boat makes a return journey from point A to point B and back in 10 hours 30 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 17 hours 30 minutes. What is the speed of the boat in still water?

Solution:
Let, 
x km/hr be the speed of boat upstream
y km/hr be the speed of boat downstream

∴ 30/x + 30/y = 10 hours 30 minutes = 10.5 hour = 105/10 hour = 21/2
⇒ 30/x + 30/y = 21/2
⇒ 60/x + 60/y = 21
⇒ 20/x + 20/y = 7
⇒ 20/x = 7 - 20/y
⇒  20/x = (7y - 20)/y
⇒ x/20 = y/(7y - 20)
∴ x = 20y/(7y - 20) ............(1)


If the speed of the stream increases by 2 km/hr
30/(x - 2) + 30/(y + 2) = 17 hours 30 minutes = 17.5 hour = 175/10 = 35/2
⇒ 30/(x - 2) + 30/(y + 2) = 35/2
⇒ 60/(x - 2) + 60/(y + 2) = 35
⇒ 12/(x - 2) + 12/(y + 2) = 7
⇒ 12/(x - 2) = 7 - 12/(y + 2)
⇒ 12/(x - 2) = (7y + 14 -12)/(y + 2)
⇒ 12/(x - 2) = (7y + 2)/(y + 2)
⇒ (x - 2)/12 = (y + 2)/(7y + 2)
⇒ x - 2 = (12y + 24)/(7y + 2)
⇒ x = (12y + 24)/(7y + 2) + 2
⇒ x = (12y + 24 + 14y + 4)/(7y + 2)
∴ x = (26y + 28)/(7y + 2) ...............(2)

From (1) and (2) we get,
20y/(7y - 20) = (26y + 28)/(7y + 2)
⇒ 20y(7y + 2) = (26y + 28)(7y - 20)
⇒ 140y2 + 40y = 182y2 - 324y - 560
⇒ 42y2 - 364y - 560 = 0
⇒ 3y2 - 26y - 40 = 0
⇒ 3y2 - 30y + 4y - 40 = 0
⇒ 3y(y - 10) + 4(y - 10) = 0
⇒ (y - 10)(3y + 4) = 0
∴ y = 10 or  y = - 4/3 [which is not acceptable]
∴ y =10

From (1) we get 
x = 20y/(7y - 20)
= 200/(70 - 20)
= 4 
 
∴ The speed of the boat in still water = (10 + 4)/2 km/hr
= 7 km/hr
১,০৩০.
A swimmer can swim at a speed of 4 km/h in still water. If the river current flows at 2 km/h, how long will it take to swim 12 km downstream and then return to the starting point?
  1. ক
    6 hours
  2. খ
    7 hours
  3. গ
    5 hours
  4. ঘ
    8 hours
সঠিক উত্তর: ঘ
8 hours
উত্তর
সঠিক উত্তর: ঘ
8 hours
ঘ
ব্যাখ্যা

Question: A swimmer can swim at a speed of 4 km/h in still water. If the river current flows at 2 km/h, how long will it take to swim 12 km downstream and then return to the starting point?

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

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

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

∴ Total time = 6 + 2 
= 8 hours

১,০৩১.
A man takes 6 hours 30 min in going by cycle and coming back by scooter. He would have lost 2 hours 10 min by going on cycle both ways. How long would it take him to go by scooter both ways?
  1. ক
    ক) 2 hr 40 min
  2. খ
    খ) 3 hr 20 min
  3. গ
    গ) 4 hr 20 min
  4. ঘ
    ঘ) 2 hr 20 min
সঠিক উত্তর: গ
গ) 4 hr 20 min
উত্তর
সঠিক উত্তর: গ
গ) 4 hr 20 min
গ
ব্যাখ্যা

Let,
The distance be x km.
Then,
Time taken to cover x km by cycle + Time taken to cover x km by scooter = 6 hr 30 min
⇒ (Time taken to cover 2x km by cycle) + (Time taken to cover 2x km by scooter) = 13 hrs
But,
Time taken to cover 2x km by cycle = 8 hr 40 min.
∴ Time Taken to cover 2x km by scooter = 13 hrs - 8 hr 40 min
= 4 hr 20 min.
Hence, required time = 4 hours 20 min.

১,০৩২.
A train passes two bridges of length 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is -
  1. ক
    150 meters
  2. খ
    200 meters
  3. গ
    220 meters
  4. ঘ
    250 meters
সঠিক উত্তর: খ
200 meters
উত্তর
সঠিক উত্তর: খ
200 meters
খ
ব্যাখ্যা
Question: A train passes two bridges of length 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is -

Solution:
Let length of the train be x m and speed of the train is s kmph.
Speed, s = (x + 800)/100 . . . . . (i)
Speed, s = (x + 400)/60. . . . . (ii) 

Equating equation (i) and (ii),
we get,
(x + 800)/100 = (x + 400)/60
Or, (x + 800)/5 = (x + 400)/3
Or, 5x + 2000 = 3x + 2400
Or, 2x = 400
∴ x = 200m

∴ The length of the train is 200 meters.
১,০৩৩.
A man on tour travels first 60 km at 20 km/hr and the next 60 km at 30 km/hr. The average speed for the first 120 km of the tour is :
  1. ক
    28 km/hr
  2. খ
    18 km/hr
  3. গ
    27 km/hr
  4. ঘ
    24 km/hr
সঠিক উত্তর: ঘ
24 km/hr
উত্তর
সঠিক উত্তর: ঘ
24 km/hr
ঘ
ব্যাখ্যা

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

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

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

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

∴ গড় গতিবেগ = মোট দূরত্ব/মোট সময় 
= 120 কিমি/5 ঘন্টা
= 24 কিমি/ঘন্টা

১,০৩৪.
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
    450 meter
  2. খ
    500 meter
  3. গ
    350 meter
  4. ঘ
    650 meter
সঠিক উত্তর: গ
350 meter
উত্তর
সঠিক উত্তর: গ
350 meter
গ
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
১,০৩৫.
If your car runs from A to B at 60 km/hr and on returning from B to A, it is 40 km/hr, then average speed in km/hr of the car will be-
  1. ক
    60 km/hr
  2. খ
    50 km/hr
  3. গ
    42 km/hr
  4. ঘ
    48 km/hr
সঠিক উত্তর: ঘ
48 km/hr
উত্তর
সঠিক উত্তর: ঘ
48 km/hr
ঘ
ব্যাখ্যা

Question: If your car runs from A to B at 60 km/hr and on returning from B to A, it is 40 km/hr, then average speed in km/hr of the car will be-

Solution:
Given that,
The speed of the car is travelling and the returning are 60 km/hr and 40 km/hr

We know,
Average speed = Total distance/Total time

Time = Distance/Speed

Now,
Let the distance between A and B be x

∴ Total time = (x/60) + (x/40)
= (2x + 3x)/120
= 5x/120 = x/24
∴ Total time = x/24

And total distance = x + x = 2x 

∴ Average speed = 2x/(x/24) = 48 km/hr

১,০৩৬.
Traveling at 108 kilometers per hour, a 120-meter train will cross a railway platform that is 210 meters long in…
  1. ক
    12 sec
  2. খ
    15 sec
  3. গ
    13 sec
  4. ঘ
    11 sec
সঠিক উত্তর: ঘ
11 sec
উত্তর
সঠিক উত্তর: ঘ
11 sec
ঘ
ব্যাখ্যা

Question: Traveling at 108 kilometers per hour, a 120-meter train will cross a railway platform that is 210 meters long in…

Solution:
Here,
Speed of the running train = 108 km/hr
= {108 × (5/18)} m/sec
= 30 m/sec

And length of the train is = 120 metres
Length of platform = 210 m

So, the time will taken by the train = (Length of train + Length of platform)/Speed
= (120 + 210)/30
= 330/30 
= 11 sec

১,০৩৭.
If a train stops on the way, its speed is 35 km/hr but if it doesn't, its speed is 40 km/hr. Find the number of minutes the train halts per hour.
  1. ক
    ক) 4 minutes
  2. খ
    খ) 6 minutes
  3. গ
    গ) 7.5 minutes
  4. ঘ
    ঘ) 8 minutes
সঠিক উত্তর: গ
গ) 7.5 minutes
উত্তর
সঠিক উত্তর: গ
গ) 7.5 minutes
গ
ব্যাখ্যা

The difference in speed due to stopping = Speed without stoppage - Speed with stoppage
∴ Difference = 40-35 = 5km/hr
Thus, in 1-hour train covers 5 km less.

Time taken to cover 4km = 5km/(40 km/hr)
= 1/8 hours.
= (1/8 × 60) minutes.
= 7.5 minutes.

Hence, The train halts 7.5 minutes per hour.

১,০৩৮.
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.
  1. ক
    ক) 2 km/hr
  2. খ
    খ) 3 km/hr
  3. গ
    গ) 4 km/hr
  4. ঘ
    ঘ) 5 km/hr
সঠিক উত্তর: খ
খ) 3 km/hr
উত্তর
সঠিক উত্তর: খ
খ) 3 km/hr
খ
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.
= 3 km/hr.
১,০৩৯.
A boatman can row 2 km against the stream in 20 minutes and return in 10 minutes. Find the rate of flow of the current.
  1. ক
    2 km/h
  2. খ
    1 km/h
  3. গ
    3 km/h
  4. ঘ
    5 km/h
  5. ঙ
    None of these
সঠিক উত্তর: গ
3 km/h
উত্তর
সঠিক উত্তর: গ
3 km/h
গ
ব্যাখ্যা
Question: A boatman can row 2 km against the stream in 20 minutes and return in 10 minutes. Find the rate of flow of the current.

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

Speed of d/s = (2/10) × 60 = 12 km/hr.
Speed of u/s = (2/20) × 60 = 6 km/hr.

∴ rate of current = (12 - 6)/2 = 3 km/hr.
১,০৪০.
Rakib and Tanveer start running towards each other at the same time with speeds in the ratio 3 : 4. If the initial distance between them is 4.2 km and they meet after 3 minutes, what is the difference between their speeds?
  1. ক
    16.5 km/h
  2. খ
    12 km/h
  3. গ
    18.25 km/h
  4. ঘ
    14 km/h
সঠিক উত্তর: খ
12 km/h
উত্তর
সঠিক উত্তর: খ
12 km/h
খ
ব্যাখ্যা

Question: Rakib and Tanveer started running simultaneously towards each other with speeds in the ratio 3 : 4 if the initial separation between the two is 4.2 km and they meet in 3 minutes, what is the difference between their speeds?

Solution:
Given that,
Rakib and Tanveer have speeds in the ratio 3 : 4.
The initial distance between them is 4.2 km, and they meet in 3 minutes, which is 3/60 = 1/20 hours

Let,
Rakib's speed be 3x km/h and Josh's speed be 4x km/h. 
The relative speed when running towards each other is = 3x + 4x = 7x km/h.

Now we know,
Relative speed × time = distance
7x × (1/20) = 4.2
⇒ x = (4.2 × 20)/7
∴ x = 12

Thus, Rakib's speed is = 3 × 12 = 36 km/h.
And Tanveer's speed is = 4 × 12 = 48 km/h.

So the difference in speeds is = 48 - 36 = 12 km/h.

১,০৪১.
A train moving at speed of 72 km/hr crosses a pole in 10 seconds. Find the length of the train.
  1. ক
    180 meters
  2. খ
    190 meters
  3. গ
    200 meters
  4. ঘ
    220 meters
সঠিক উত্তর: গ
200 meters
উত্তর
সঠিক উত্তর: গ
200 meters
গ
ব্যাখ্যা
Question: A train moving at speed of 72 km/hr crosses a pole in 10 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 10 seconds by applying the following formula:
Distance = Speed × Time
Speed is given in Km/hr so we will convert it into m/s
Speed = 72 × (5/18) = 20 m/s
Time = 10 seconds
Distance = 20 × 10 = 200 meters
১,০৪২.
A 120 meters long train is running at a speed of 108 km per hour. It will cross a railway platform 210 m long in-
  1. ক
    11 sec
  2. খ
    13 sec
  3. গ
    15 sec
  4. ঘ
    12 sec
সঠিক উত্তর: ক
11 sec
উত্তর
সঠিক উত্তর: ক
11 sec
ক
ব্যাখ্যা
Question: A 120 meters long train is running at a speed of 108 km per hour. It will cross a railway platform 210 m long in-

Solution:
Here,
Speed of the running train = 108 km/hr
= {108 × (5/18)} m/sec
= 30 m/sec

And length of the train is = 120 metres
Length of platform = 210 m

So, the time will taken by the train = (Length of train + Length of platform)/Speed
= (120 + 210)/30
= 330/30 
= 11 sec
১,০৪৩.
A man can row 6 km/hr in still water. If the speed of the current is 2 km / hr. It takes 3 hrs more in upstream than in the downstream for the same distance. The distance is -
  1. ক
    ক) 30 km
  2. খ
    খ) 24 km
  3. গ
    গ) 20 km
  4. ঘ
    ঘ) 32 km
সঠিক উত্তর: খ
খ) 24 km
উত্তর
সঠিক উত্তর: খ
খ) 24 km
খ
ব্যাখ্যা

Speed of man in still water, x = 6 km/h
Speed of current, y = 2 km/h

Let Distance = M
Upstream time = Downstram time + 3
M/4 = M/8 + 3 [As, speed of the boat upstream = 6 + 2 = 8 km/h; and downstream = 6 - 2 = 4 km/h]
M/4 - M/8 = 3
M/8 = 3
∴ M = 24
∴ Distance = 24 km

১,০৪৪.
An UberX car charges Tk. 40 as base fare, Tk. 3.6 for each 0.2 of a kilometre and Tk. 180/hour as the travelling time charge. What will be the fare for a 6 kilometre trip if the travelling time is 110 minutes.
  1. ক
    ক) 230
  2. খ
    খ) 340
  3. গ
    গ) 460
  4. ঘ
    ঘ) 478
সঠিক উত্তর: ঘ
ঘ) 478
উত্তর
সঠিক উত্তর: ঘ
ঘ) 478
ঘ
ব্যাখ্যা

Base fare = Tk. 40
Distance Charge = Tk. 3.6 per 0.2 km = Tk. 18 per km
Travelling Time Charge = Tk. 180/1 hour
= 180/60
= Tk. 3 per minute
Total Distance = 6 kms
Total Time = 110 mins
Total Charge = Tk. 40 + Tk. (6 × 18) + Tk. (110 × 3)
= Tk. 478.

১,০৪৫.
A car reaches from City A to City B in 9 hours travelling at a speed of 40 km/hr. If its speed is increased by 20 km/hr, then the time of journey is reduced by-
  1. ক
    45 minutes
  2. খ
    2 hours
  3. গ
    1.5 hours
  4. ঘ
    3 hours
সঠিক উত্তর: ঘ
3 hours
উত্তর
সঠিক উত্তর: ঘ
3 hours
ঘ
ব্যাখ্যা

Question: A car reaches from City A to City B in 9 hours travelling at a speed of 40 km/hr. If its speed is increased by 20 km/hr, then the time of journey is reduced by-

Solution:
দুটি শহরের মধ্যে মোট দূরত্ব = গতিবেগ × সময়
= 40 কিমি/ঘন্টা × 9 ঘন্টা
= 360 কিমি

এখন, গতিবেগ 20 কিমি/ঘন্টা বৃদ্ধি করা হলে,
নতুন গতিবেগ = (40 + 20) কিমি/ঘন্টা
= 60 কিমি/ঘন্টা

এই নতুন গতিবেগে একই দূরত্ব অতিক্রম করতে,
নতুন সময় = মোট দূরত্ব/নতুন গতিবেগ
= 360 কিমি/60 কিমি/ঘন্টা
= 6 ঘন্টা

সুতরাং, সময় কমেছে = (আসল সময় - নতুন সময়)
= (9 - 6) ঘন্টা
= 3 ঘন্টা

অর্থাৎ, ভ্রমণের সময় 3 ঘন্টা কমেছে।

১,০৪৬.
On Tuesday Ray rode his bike 10 miles, On Wednesday he increased Tuesday's distance by 5 miles. On Thursday he decreased Wednesday's distance by 7 miles. On Friday he increased Thursday's by 12 miles. How many total miles did Ray ride over the 4 day period?
  1. ক
    ক) 50
  2. খ
    খ) 51
  3. গ
    গ) 52
  4. ঘ
    ঘ) 53
সঠিক উত্তর: ঘ
ঘ) 53
উত্তর
সঠিক উত্তর: ঘ
ঘ) 53
ঘ
ব্যাখ্যা
Question: On Tuesday Ray rode his bike 10 miles, On Wednesday he increased Tuesday's distance by 5 miles. On Thursday he decreased Wednesday's distance by 7 miles. On Friday he increased Thursday's by 12 miles. How many total miles did Ray ride over the 4-day period?

Solution: 
On Tuesday, Ray goes = 10 miles
On Wednesday, Ray goes = 10 + 5 = 15 miles
On Thursday, Ray goes = 15 - 7 = 8 miles
On Friday, Ray goes = 8 + 12 = 20 miles

∴ Total distance = 10 + 15 + 8 + 20
= 53 miles
১,০৪৭.
How much time will taken by a train to cross a total distance of 500km if 1/4 of the distance is covered at 62.5kmph and the rest of the distance is at 37.5kmph.
  1. ক
    8 hour.
  2. খ
    10 hour.
  3. গ
    12 hour.
  4. ঘ
    15 hour.
সঠিক উত্তর: গ
12 hour.
উত্তর
সঠিক উত্তর: গ
12 hour.
গ
ব্যাখ্যা
Question: How much time will taken by a train to cross a total distance of 500km if 1/4 of the distance is covered at 62.5kmph and the rest of the distance is at 37.5kmph.

Solution: 
1/4 of 500km = (500 × 1/4) = 125km
time = 125/62.5 = 2 hour.

remaining distance = 500 - 125 = 375km
time = 375/37.5 = 10 hour.

total time = 10 + 2 = 12 hour.
১,০৪৮.
Fardin starts climbing a 11 m high wall at 4 pm. In each minute he climbs up 1 m but slips down 50 cm. At what time will he climb the wall? 
  1. ক
    ক) 4.20 p.m.
  2. খ
    খ) 4.21 p.m.
  3. গ
    গ) 4.25 p.m.
  4. ঘ
    ঘ) 5.20 p.m.
সঠিক উত্তর: খ
খ) 4.21 p.m.
উত্তর
সঠিক উত্তর: খ
খ) 4.21 p.m.
খ
ব্যাখ্যা
Question: Fardin starts climbing a 11 m high wall at 4 pm. In each minute he climbs up 1 m but slips down 50 cm. At what time will he climb the wall? 

Solution: 
প্রতি মিনিটে উঠে ১ মিটার বা ১০০ সেমি, নামে ৫০ সেমি 
প্রতি মিনিটে উঠে ১০০ - ৫০ সেমি = ৫০ সেমি বা ১/২ মিটার  

১/২ মিটার উঠতে সময় লাগে ১ মিনিট
১ মিটার উঠতে সময় লাগে ২ মিনিট 
১০ মিটার উঠতে সময় লাগে ২০ মিনিট 

পরের ১ মিটার ১ মিনিটে উঠে যায়।

সময় লাগে = ২০ + ১ মিনিট 
= ২১ মিনিট 
১,০৪৯.
In a river flowing at 2 km/hr, a boat travels 40 km upstream and then returns downstream to the starting point. If its speed in still water is 6 km/hr, find the total journey time.
  1. ক
    ক) 15 hours
  2. খ
    খ) 13 hours
  3. গ
    গ) 12 hours
  4. ঘ
    ঘ) 11 hours
সঠিক উত্তর: ক
ক) 15 hours
উত্তর
সঠিক উত্তর: ক
ক) 15 hours
ক
ব্যাখ্যা
Speed of the boat in still water = 6 km/hr
Speed of the stream = 2 km/hr
Speed downstream = (6 + 2) = 8 km/hr
Speed upstream = (6 − 2) = 4 km/hr
Total journey time = 40/8 + 40/4 = 15 hr
১,০৫০.
A man swimming in a stream which flows 3/2 km/hr finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?
  1. ক
    5 km/hr
  2. খ
    4.5 km/hr
  3. গ
    8 km/hr
  4. ঘ
    9 km/hr
সঠিক উত্তর: খ
4.5 km/hr
উত্তর
সঠিক উত্তর: খ
4.5 km/hr
খ
ব্যাখ্যা
Question: A man swimming in a stream which flows 3/2 km/hr finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?

Solution:
Let, speed upstream = x km/hr.
Speed downstream = 2x km/hr.

Speed of stream = (2x - x)/2 km/hr. = x/2 km/hr

ATQ,
x/2 = 3/2
∴ x = 3

speed upstream = 3 km/hr.
Speed downstream = 2 × 3 = 6 km/hr.

Rate of swimming = (3 + 6)/2 = 9/2 = 4.5 km/hr
১,০৫১.
A car travels at 50 km/h. If it had traveled 10 km/h faster, it would have reached its destination 30 minutes earlier. What is the distance of the journey?
  1. ক
    150 km
  2. খ
    180 km
  3. গ
    200 km
  4. ঘ
    250 km 
সঠিক উত্তর: ক
150 km
উত্তর
সঠিক উত্তর: ক
150 km
ক
ব্যাখ্যা

Question: A car travels at 50 km/h. If it had traveled 10 km/h faster, it would have reached its destination 30 minutes earlier. What is the distance of the journey?

Solution:
Let the distance be x km.

Time at 50 km/h = x/50 hours
Time at 60 km/h = x/60 hours

According to the question, the difference in time = 0.5 hours
⇒ x/50 − x/60 = 0.5
⇒ (6x − 5x) / 300 = 0.5
⇒ x / 300 = 0.5
⇒ x = 0.5 × 300
⇒ x = 150 km

∴ Distance of the journey = 150 km

১,০৫২.
A man takes 8 hours in walking a distance and riding back to starting place. He could walk both ways in 10 hours. The time taken by him to ride back both ways is:
  1. ক
    6 hours
  2. খ
    5 hours
  3. গ
    4.5 hours
  4. ঘ
    5.5 hours
সঠিক উত্তর: ক
6 hours
উত্তর
সঠিক উত্তর: ক
6 hours
ক
ব্যাখ্যা
Question: A man takes 8 hours in walking a distance and riding back to starting place. He could walk both ways in 10 hours. The time taken by him to ride back both ways is:

Solution:
Time taken in walking both the ways = 10 hours.................(i)
Time taken in walking one way and riding back = 8 hours...................(ii)

By the equation (ii) × 2 - (i), we have,
Time taken by the man in riding both ways,
= 16 hours - 10 hours
= 6 hours
১,০৫৩.
In a 100m race, Rakib defeats Tanvir by 5 seconds. If the speed of Rakib is 18 kmph, then the speed of Tanvir is:
  1. ক
    18.4 km/h
  2. খ
    14.4 km/h
  3. গ
    14.9 km/h
  4. ঘ
    15.6 km/h
সঠিক উত্তর: খ
14.4 km/h
উত্তর
সঠিক উত্তর: খ
14.4 km/h
খ
ব্যাখ্যা
Question: In a 100m race, Rakib defeats Tanvir by 5 seconds. If the speed of Rakib is 18 kmph, then the speed of Tanvir is:
Solution:
Hints: (km/h)/3.6 = m/s
Time taken by Rakib = 100 / (18/3.6) seconds
= 20 seconds

Hence,
Time taken by Tanvir is = 20 + 5 = 25 seconds
So, Tanvir's speed=100/25 m/s
= 4 m/s
= 4 × 3.6 km/h
=14.4 km/h
১,০৫৪.
Four pipes can fill a tank in 15, 20, 30 and 60 hours respectively. The first pipe was opened at 8 a.m, second at 9 a.m, third at 10 a.m. and fourth at 11 a.m. When will the tank be full-
  1. ক
    1 p.m.
  2. খ
    2 p.m.
  3. গ
    3 p.m.
  4. ঘ
    4 p.m.
সঠিক উত্তর: গ
3 p.m.
উত্তর
সঠিক উত্তর: গ
3 p.m.
গ
ব্যাখ্যা
Question: Four pipes can fill a tank in 15, 20, 30 and 60 hours respectively. The first pipe was opened at 8 a.m, second at 9 a.m, third at 10 a.m. and fourth at 11 a.m. When will the tank be full-

Solution:
Let,
the time be x hours after 8 am.
Then, the first pipe worked for x hours
Second pipe for (x - 1) hours;
Third pipe for (x - 2) hours;
Fourth pipe for (x - 3) hours.

ATQ,
(x/15) + {(x - 1)/20} + {(x - 2)/30} + {(x - 3)/60} = 1
⇒ (4x + 3x - 3 + 2x - 4 + x - 3)/60 = 1
⇒ 10x - 10 = 60
⇒ 10x = 70
∴ x = 7

So, the tank will be full 7 hours after 8 am = 8 + 7 = 15 = 3 p.m.
১,০৫৫.
Sue planted 4 times as many apple seeds as she planted orange seeds 15% of the apple seeds grow into trees and 10% of the orange seeds grew into trees. If a total of 420 apple trees and orange trees grew from the seeds, how many orange seeds did Sue plant? 
  1. ক
    ক) 540
  2. খ
    খ) 600
  3. গ
    গ) 660
  4. ঘ
    ঘ) 720
সঠিক উত্তর: খ
খ) 600
উত্তর
সঠিক উত্তর: খ
খ) 600
খ
ব্যাখ্যা
ধরি,
Sue কমলার চারা বুনেছিল x টি
Sue আপেলের চারা বুনেছিল 4x টি
প্রশ্নমতে,
 4x এর 15% + x এর 10%= 420
4x এর 15/100 + x এর 10/100= 420
60x/100 + 10x/100 = 420 
70x/100 = 420 
70x = 42000
x = 42000/70
x = 600
১,০৫৬.
A motor boat takes 12 hours to go downstream and it takes 24 hours to return the same distance. What is the time taken by boat in still water?
  1. ক
    ক) 16 h
  2. খ
    খ) 18 h
  3. গ
    গ) 21 h
  4. ঘ
    ঘ) 24 h
সঠিক উত্তর: ক
ক) 16 h
উত্তর
সঠিক উত্তর: ক
ক) 16 h
ক
ব্যাখ্যা
If t1 and t2 are the upstream and down stream times.
Then time taken in still water is given by
(2 × t1 × t2) / (t1 + t2)
= (2 × 12 × 24) / 36
= 16h
১,০৫৭.
A man rows downstream 54 km and upstream 42 km, taking 6 hours each time. The speed of the man is?
  1. ক
    8 km/hr
  2. খ
    9 km/hr
  3. গ
    12 km/hr
  4. ঘ
    6 km/hr
সঠিক উত্তর: ক
8 km/hr
উত্তর
সঠিক উত্তর: ক
8 km/hr
ক
ব্যাখ্যা
Question: A man rows downstream 54 km and upstream 42 km, taking 6 hours each time. The speed of the man is?

Solution:
Speed of upstream = 42/6 = 7 km/hr
Speed of downstream = 54/6 = 9 km/hr

Speed of man in still water = (7 + 9)/2 = 16/2 = 8 km/hr
১,০৫৮.
Mr. Tamim travelled from A to B at a speed of 3 km/hr and returned from B to A at a speed of 5 km/hr. If the entire trip required 8 hours what is the distance between A and B in km?
  1. ক
    15km
  2. খ
    10km
  3. গ
    14km
  4. ঘ
    18km
  5. ঙ
    40km
সঠিক উত্তর: ক
15km
উত্তর
সঠিক উত্তর: ক
15km
ক
ব্যাখ্যা
Question: Mr. Tamim travelled from A to B at a speed of 3 km/hr and returned from B to A at a speed of 5 km/hr. If the entire trip required 8 hours what is the distance between A and B in km?

Solution:
Let, the distance between A to B be x km.

According to the question,
⇒ (x/3) + (x/5) = 8
⇒ (5x + 3x)/15 = 8
⇒ (8x)/15 = 8
⇒ x = (15 × 8)/8
∴ x = 15

∴ Distance between A to B is = 15km
১,০৫৯.
A train passes a stationary pole in 8 seconds. The train also passes a 200 m long bridge in 28 seconds. What is the length of the train?
  1. ক
    100 meters
  2. খ
    160 meters
  3. গ
    120 meters
  4. ঘ
    80 meters
সঠিক উত্তর: ঘ
80 meters
উত্তর
সঠিক উত্তর: ঘ
80 meters
ঘ
ব্যাখ্যা

Question: A train passes a stationary pole in 8 seconds. The train also passes a 200 m long bridge in 28 seconds. What is the length of the train?

Solution: 
Given that,
Time to pass a pole = 8 s
Time to pass a 200 m bridge = 28 s

Let the length of the train = L meters
When passing a pole, the train covers distance = L in 8 s
And when passing a bridge, distance = (L + 200) in 28 s

Now, 
From pole,
Speed = Distance/Time = L/8 m/s 

And, 
From bridge,
Speed = Distance/Time = (L + 200)/28 m/s

ATQ, 
L/8 = (L + 200)/28
⇒ 28L = 8L + 1600
⇒ 28L - 8L = 1600
⇒ 20L = 1600
⇒ L = 1600/20
∴ L = 80 m

So the length of the train is 80 meters. 

১,০৬০.
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 210 meters, how long will it take for B to cross train A?
  1. ক
    ক) 124 sec
  2. খ
    খ) 128 sec
  3. গ
    গ) 126 sec
  4. ঘ
    ঘ) 144 sec
সঠিক উত্তর: গ
গ) 126 sec
উত্তর
সঠিক উত্তর: গ
গ) 126 sec
গ
ব্যাখ্যা
Relative speed = (72 - 60) km/hr
                       = 12 km/hr
                       = 12 × (5/18) m/sec
                       = 10/3 m/sec

Total distance covered = Sum of lengths of trains = (210 + 210) m = 420 m
Time taken = (420 × 3)/10sec=126sec
১,০৬১.
A 180 meter long train running at the speed of 72 km/h crosses another train running in the opposite direction at the speed of 108 km/h in 10 seconds. What is the length of the other train? 
  1. ক
    120 meters
  2. খ
    320 meters
  3. গ
    220 meters
  4. ঘ
    420 meters
সঠিক উত্তর: খ
320 meters
উত্তর
সঠিক উত্তর: খ
320 meters
খ
ব্যাখ্যা

Question: A 180 meter long train running at the speed of 72 km/h crosses another train running in the opposite direction at the speed of 108 km/h in 10 seconds. What is the length of the other train?

Solution:
Relative speed = (72 + 108) km/h
= 180 × (5/18) m/sec
= 50 m/sec

Let,
Length of the other train = x metres

Then,
(x + 180)/10 = 50
⇒ x + 180 = 500
⇒ x = 500 - 180
∴ x = 320

∴ The length of the other train is 320 meters.

১,০৬২.
A train 240m long passed a pole in 24 seconds. How long will it take to pass a platform 650m long?
  1. ক
    ক) 65 s
  2. খ
    খ) 89 s
  3. গ
    গ) 100 s
  4. ঘ
    ঘ) 130 s
সঠিক উত্তর: খ
খ) 89 s
উত্তর
সঠিক উত্তর: খ
খ) 89 s
খ
ব্যাখ্যা

ট্রেনের দৈর্ঘের তুলনায় খুটির দৈর্ঘ্য নগণ্য বলে 24 সেকেন্ডে ট্রেনটি মূলত নিজের দৈর্ঘ্য অতিক্রম করবে ।
240 মিটার অতিক্রম করে = 24 সেকেন্ডে
∴ (650 + 240) বা 890 মিটার অতিক্রম করে = (24 × 890)/240
= 89 সেকেন্ডে ।

১,০৬৩.
রাজেশ সাইকেলে ৬কি.মি./ঘণ্টা গতিতে ৫০ মিনিটে একটি নির্দিষ্ট দূরত্ব অতিক্রম করে। যদি সে ঘণ্টায় ১০ কি.মি. গতিতে হাঁটে, তাহলে একই দূরত্ব হেঁটে অতিক্রম করতে তার কত মিনিট লাগবে? 
  1. ক
    ক) ৪০ মিনিট 
  2. খ
    খ) ৫০ মিনিট 
  3. গ
    গ) ৪৫ মিনিট 
  4. ঘ
    ঘ) ৩০ মিনিট 
সঠিক উত্তর: ঘ
ঘ) ৩০ মিনিট 
উত্তর
সঠিক উত্তর: ঘ
ঘ) ৩০ মিনিট 
ঘ
ব্যাখ্যা
৬০ মিনিটে অতিক্রম করে  ৬০০০ মিটার 
১ মিনিটে অতিক্রম করে  ৬০০০/৬০ মিটার 
৫০মিনিটে অতিক্রম করে  (৬০০০ × ৫০)/৬০ মিটার 
                                  = ৫০০০ মিটার 
                                    = ৫ কি.মি. 

সময় = ৫/১০ ঘণ্টা 
         = ১/২  ঘণ্টা 
         = (১/২) × ৬০ মিনিট 
         = ৩০ মিনিট
১,০৬৪.
A train 250m long passes a pole in 25 seconds. How long will it take to pass a platform 480m long?
  1. ক
    ক) 89 sec
  2. খ
    খ) 73 sec
  3. গ
    গ) 75 sec
  4. ঘ
    ঘ) 85 sec
সঠিক উত্তর: খ
খ) 73 sec
উত্তর
সঠিক উত্তর: খ
খ) 73 sec
খ
ব্যাখ্যা
Question: A train 250m long passes a pole in 25 seconds. How long will it take to pass a platform 480m long?

Solution: 
সমাধান:
ট্রেনটির মোট দূরত্ব অতিক্রম করতে হবে = (250 + 480) মিটার = 730 মিটার 

ট্রেনটি 250 মিটার অতিক্রম করতে সময় নেয় = 25 সেকেন্ড 
ট্রেনটি 1 মিটার অতিক্রম করতে সময় নেয় = 25/250 সেকেন্ড 
ট্রেনটি 730 মিটার অতিক্রম করতে সময় নেয় = (25 × 730)/250 সেকেন্ড 
= 73 সেকেন্ড
১,০৬৫.
A delivery cart went from Candle ford to Lark Rise and back at an average speed of 2/3 miles per hour. If the distance from Candle ford to Lark Rise is 1 mile and the trip back took half as much time as the trip there, what was the average speed of the delivery cart on the way to Lark Rise?
  1. ক
    ক) 1/3
  2. খ
    খ) 3/4
  3. গ
    গ) 1/2
  4. ঘ
    ঘ) 2/3
সঠিক উত্তর: গ
গ) 1/2
উত্তর
সঠিক উত্তর: গ
গ) 1/2
গ
ব্যাখ্যা
Question: A delivery cart went from Candle ford to Lark Rise and back at an average speed of 2/3 miles per hour.  If the distance from Candle ford to Lark Rise is 1 mile and the trip back took half as much time as the trip there,  what was the average speed of the delivery cart on the way to Lark Rise?

Solution: 
Total distance = Average speed × total time
So, 2 = 2/3×T
⇒ T = 3 hours
So, the whole journey took 3 hours
Since trip back took half as much time as the trip there, it took 2 hours to reach there and 1 hour to come back.
So, speed of the delivery cart while going to Lark Rise = distance/time = 1/2 mph
১,০৬৬.
A train takes 18 sec to pass completely through a station 162m long and 15 seconds through another station 120m long.The length of the train-
  1. ক
    ক) 70m
  2. খ
    খ) 80m
  3. গ
    গ) 90m
  4. ঘ
    ঘ) 100m
সঠিক উত্তর: গ
গ) 90m
উত্তর
সঠিক উত্তর: গ
গ) 90m
গ
ব্যাখ্যা

Let length of the train be x m
Speed of train,
(x+162)/18 = (x+120)/15
∴ x = 90 m

১,০৬৭.
Mr. Kamal travelled from P to Q at a speed of 4 km/hr and returned from Q to P at a speed of 6 km/hr. If the entire trip required 10 hours, what is the distance between P and Q in km?
  1. ক
    15 km
  2. খ
    18 km
  3. গ
    24 km
  4. ঘ
    30 km
  5. ঙ
    45 km
সঠিক উত্তর: গ
24 km
উত্তর
সঠিক উত্তর: গ
24 km
গ
ব্যাখ্যা

Question: Mr. Kamal travelled from P to Q at a speed of 4 km/hr and returned from Q to P at a speed of 6 km/hr. If the entire trip required 10 hours, what is the distance between P and Q in km?

Solution:
ধরা যাক, P থেকে Q এর দূরত্ব হলো x কিমি।
সুতরাং, P থেকে Q তে যেতে সময় লাগে = x/4 ঘন্টা
Q থেকে P তে ফিরে আসতে সময় লাগে = x/6 ঘন্টা

প্রশ্ন অনুযায়ী, মোট সময় লেগেছে 10 ঘন্টা।
∴ (x/4) + (x/6) = 10
⇒ (3x + 2x)/12 = 10
⇒ 5x/12 = 10
⇒ 5x = 10 × 12
⇒ 5x = 120
⇒ x = 120 / 5
⇒ x = 24

সুতরাং, P এবং Q এর মধ্যবর্তী দূরত্ব হলো 24 কিমি।

১,০৬৮.
A train 250 meters long is running at a speed of 90 km/h. How long will it take to cross a platform 150 meters long?
  1. ক
    24 seconds
  2. খ
    28 seconds
  3. গ
    16 seconds
  4. ঘ
    30 seconds
সঠিক উত্তর: গ
16 seconds
উত্তর
সঠিক উত্তর: গ
16 seconds
গ
ব্যাখ্যা

Question: A train 250 meters long is running at a speed of 90 km/h. How long will it take to cross a platform 150 meters long?

Solution:
speed = 90 km/h = 90 × (5/18) m/s
= 25 m/s

To cross the platform have to travel = (250 + 150) m
= 400 m

∴ Required time = 400/25 seconds
= 16 seconds

১,০৬৯.
Abul, Billal and Rahim start together from the same place to walk round a circular path of length 24km. Abul walks at the rate of 6 km/h, Billal 3 km/h and Rahim (3/2) km/h. After how many hours will they meet again at the starting point together?
  1. ক
    16
  2. খ
    12
  3. গ
    14
  4. ঘ
    48
  5. ঙ
    None
সঠিক উত্তর: ক
16
উত্তর
সঠিক উত্তর: ক
16
ক
ব্যাখ্যা

Question: Abul, Billal and Rahim start together from the same place to walk round a circular path of length 24km. Abul walks at the rate of 6 km/h, Billal 3 km/h and Rahim (3/2) km/h. After how many hours will they meet again at the starting point together?

Solution: 
Abul এর সময় লাগবে = 24/6 = 4 ঘণ্টা 
Billal এর সময় লাগবে = 24/3 = 8 ঘণ্টা 
Rahim এর সময় লাগবে = 24 ÷ (3/2)
= 24 × (2/3)
= 16 ঘণ্টা 

4, 8, 16 এর লসাগু = 16 

অতএব, 
Abul, Billal এবং  Rahim 16 ঘণ্টা পর মিলিত হবে। 

১,০৭০.
When the speed is increased by 4 kmph, it takes 4 hours less to cover a distance of 32km. Find the previous speed.
  1. ক
    ক) 2kmph
  2. খ
    খ) 4kmph
  3. গ
    গ) 8kmph
  4. ঘ
    ঘ) 12kmph
সঠিক উত্তর: খ
খ) 4kmph
উত্তর
সঠিক উত্তর: খ
খ) 4kmph
খ
ব্যাখ্যা
ধরি
প্রকৃত গতিবেগ ছিল = x kmph

প্রশ্নমতে,
(32/x) - {32/(x + 4)} = 4
⇒ (32x + 128 - 32x)/{x(x + 4)}= 4
⇒ 128/{x(x + 4)} = 4
⇒ (x + 4)x = 32
⇒ x2 + 4x - 32 = 0
⇒ x2 + 8x - 4x - 32 = 0
⇒ (x + 8) (x - 4) = 0
এখানে          অথবা 
x + 8 = 0       x - 4 = 0
x= - 8            x = 4 

প্রকৃত গতিবেগ ছিল = 4 kmph
১,০৭১.
A boatman goes 1 km against the current of the stream in 1/2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?
  1. ক
    1 hour 15 min
  2. খ
    2 hour
  3. গ
    2 hour 15 min
  4. ঘ
    2 hour 30 min
সঠিক উত্তর: খ
2 hour
উত্তর
সঠিক উত্তর: খ
2 hour
খ
ব্যাখ্যা
Question: A boatman goes 1 km against the current of the stream in 1/2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?

Solution:
Speed upstream = 1/(1/2) = 2 km/hr

Speed downstream = 1/(20/60) = 3 km/hr

Speed in still water = (1/2)(3 + 2) = 2.5 km/hr

Time taken to travel 5 km in still water = 5/2.5 hr
= 2 hr
১,০৭২.
A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 320 km of tour.
  1. ক
    ক) 70.11 km/hr
  2. খ
    খ) 71.11 km/hr
  3. গ
    গ) 72.11 km/hr
  4. ঘ
    ঘ) 73.11 km/hr
সঠিক উত্তর: খ
খ) 71.11 km/hr
উত্তর
সঠিক উত্তর: খ
খ) 71.11 km/hr
খ
ব্যাখ্যা

We know Time = Distance/speed
So total time taken = (160/64) + (160/80)
Time taken for 320 Km = 320× (2/9) = 71.11km/hr

১,০৭৩.
With an uniform speed, a car covers a distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 hr and 30 min. What is the distance covered?
  1. ক
    ক) 320 km
  2. খ
    খ) 410 km
  3. গ
    গ) 480 km
  4. ঘ
    ঘ) 490 km
সঠিক উত্তর: গ
গ) 480 km
উত্তর
সঠিক উত্তর: গ
গ) 480 km
গ
ব্যাখ্যা
Let the speed of car be x km/hr
Distance= Speed × Time
Distance = 8x km
According to the question,
⇒ (x+4)×7.5= 8x
⇒ 7.5x+30= 8x
⇒ 8x−7.5x= 30
⇒ 0.5x= 30
⇒x= (30/0.5)= 60 km/hr
Required distance: = 8 × 60 = 480 km
১,০৭৪.
A boat can travel 20 km downstream in 24 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 15 km upstream?
  1. ক
    15 min
  2. খ
    20 min
  3. গ
    25 min
  4. ঘ
    30 min
সঠিক উত্তর: ঘ
30 min
উত্তর
সঠিক উত্তর: ঘ
30 min
ঘ
ব্যাখ্যা
Question: A boat can travel 20 km downstream in 24 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 15 km upstream?

Solution:
Downstream speed = {(20/24) × 60} km/hr
= 50 km/hr

Let,
speed of water and stream is 4a and a.
Downstream speed = (4a + a) = 5a
and upstream speed = (4a - a) = 3a

ATQ,
5a = 50
∴ a = 10
So, upstream speed = (3 × 10) = 30 km/hr.
∴ Time taken to go 15 km upstream = (15 × 60)/30 = 30 min.
১,০৭৫.
If A travels to his school from his house at the speed of 5 km/hr, then he reaches the school 5 minutes late. If he travels at the speed of 6 km/hr, he reaches the school 5 minutes earlier than school time. The distance of his school from his house is:
  1. ক
    ক) 2 km
  2. খ
    খ) 3 km
  3. গ
    গ) 5 km
  4. ঘ
    ঘ) 6 km
সঠিক উত্তর: গ
গ) 5 km
উত্তর
সঠিক উত্তর: গ
গ) 5 km
গ
ব্যাখ্যা
Question: If A travels to his school from his house at the speed of 5 km/hr, then he reaches the school 5 minutes late. If he travels at the speed of 6 km/hr, he reaches the school 5 minutes earlier than school time. The distance of his school from his house is:

Solution:
Let the distance between school and home be x km.
The difference of time when A goes school to school with these two different speed is 10 min
= 10/60 hour.
Now,
x/5 - x/6 = 10/60
Or, (6x - 5x)/30 = 1/6
Or, x/30 = 1/6
Or, x = 30/6
∴ x = 5 km

∴ The distance between school and home 5 km.

১,০৭৬.
A man can swim a distance of 360 m in still water in 4 minutes. If the speed of the current is 1 m / sec, how much time will he take to cover the distance of 180 m upstream?
  1. ক
    ক) 5 minutes
  2. খ
    খ) 6 minutes
  3. গ
    গ) 7 minutes
  4. ঘ
    ঘ) 8 minutes
সঠিক উত্তর: খ
খ) 6 minutes
উত্তর
সঠিক উত্তর: খ
খ) 6 minutes
খ
ব্যাখ্যা
Distance covered by a man by swimming in still water = 360 m
Time taken by man = 4 minutes = 240 seconds
Speed of man = 360/240 = (3/2) m/sec
Speed of stream is = 1 m/sec.

Time taken in upstream 
= 180/[(3/2) - 1)]
 = 180/(1/2)
= 360 seconds
⇒ Time = 6 minutes

∴ He will cover 150 m upstream in 6 minutes
১,০৭৭.
A boy runs opposite to that of a train at a speed of 20 km/hr. If the relative speed between the train and the boy running in the opposite direction is 50 km/hr. What is the length of the train, if it takes 20 seconds to cross the boy, when he is at rest?
  1. ক
    159.1 m
  2. খ
    160.23 m
  3. গ
    166.6 m
  4. ঘ
    154.12 m
সঠিক উত্তর: গ
166.6 m
উত্তর
সঠিক উত্তর: গ
166.6 m
গ
ব্যাখ্যা

Speed = Distance/Time

Relative speed = Speed of train + Speed of boy
50 = Speed of train + 20

Speed of train = 50 – 20 = 30 km/hr

Convert km/hr into m/s
30 km/hr = 30 × (5/18) = 8.33 m/s

Distance = Speed x Time
= 8.33 x 20 = 166.6 m.

১,০৭৮.
Two bikes start at the same time from two destination 300 km apart and travel towards each other. If they cross each other at a distance of 130 km from one of the destinations, what is the ratio of their speeds?
  1. ক
    17 : 13
  2. খ
    7 : 3
  3. গ
    1 : 3
  4. ঘ
    2 : 3
সঠিক উত্তর: ক
17 : 13
উত্তর
সঠিক উত্তর: ক
17 : 13
ক
ব্যাখ্যা
Solution: Two bikes start at the same time from two destination 300 km apart and travel towards each other. If they cross each other at a distance of 130 km from one of the destinations, what is the ratio of their speeds?

Solution:
ধরি,
প্রথম বাইকারের গতি = V1
 দ্বিতীয় বাইকারের গতি = V2

প্রথম বাইকার অতিক্রম করে = 130 km
 দ্বিতীয় বাইকার অতিক্রম করে = 300 - 130 = 170 km


এখন
130/V1 =170/V2
130V2 = 170V1
V2/V1 = 170/130
V2 : V1 = 17 ; 13
১,০৭৯.
A fisherman can row his boat to the market for 80 km along the stream. For this he takes 1 hour 20 minutes. His son says that his father’s rowing speed in still water is 45 km/hr. How much time should he take to row the same distance back, against the stream?
  1. ক
    ক) 3 hours 10 minutes
  2. খ
    খ) 2 hours 40 minutes
  3. গ
    গ) 2 hours 30 minutes
  4. ঘ
    ঘ) 3 hours 50 minutes
সঠিক উত্তর: খ
খ) 2 hours 40 minutes
উত্তর
সঠিক উত্তর: খ
খ) 2 hours 40 minutes
খ
ব্যাখ্যা

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

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

X+Y = (45+Y) km/hr
1 hour 20 munites = 1 hour + 20/60 = (1 + 1/3) = (4/3) hours
Downstream speed = Distance covered/Time taken

∴ 45 + y = 80/(4/3)
∴ Y = 15 km/hr
X - Y = 45 - 15 = 30 km/hr

Time is taken to go against the stream = 80/30 hours = 2 Hours 40 minutes.

১,০৮০.
A is twice fast as B and B is thrice fast as C is. The journey covered by C in 3/2 hours will be covered by A is-
  1. ক
    ক) 15 minutes
  2. খ
    খ) 20 minutes
  3. গ
    গ) 30 minutes
  4. ঘ
    ঘ) 1 hour
সঠিক উত্তর: ক
ক) 15 minutes
উত্তর
সঠিক উত্তর: ক
ক) 15 minutes
ক
ব্যাখ্যা

Let speed of C = X
Then Speed of B = 3X
Then Speed of A = 6X
Ratio of the speed of A and C = 1:6
So, Greater the speed less time taken in journey.
C’s speed is 6 times less than A So A will take
1/6 of the total time taken C to covered same distance.
So, Time taken by A
= 3/(2×6)
= 1/4 hours
= 15minutes

১,০৮১.
A train passes a 254-meter-long bridge in 20 seconds and a 100-meter-long bridge in 13 seconds. Determine the length of the train.
  1. ক
    220 meters
  2. খ
    104 meters
  3. গ
    150 meters
  4. ঘ
    186 meters
সঠিক উত্তর: ঘ
186 meters
উত্তর
সঠিক উত্তর: ঘ
186 meters
ঘ
ব্যাখ্যা
Question: A train passes a 254-meter-long bridge in 20 seconds and a 100-meter-long bridge in 13 seconds. Determine the length of the train.

Solution:

১,০৮২.
A ferry can travel twice as fast when empty as when it is full. It travels 20 miles with full load, spends 1 hour for unloading and returns to its original post empty. It took 11 hours to complete the journey. What is the speed of the ferry when it is empty?
  1. ক
    5
  2. খ
    6
  3. গ
    6.5
  4. ঘ
    8
সঠিক উত্তর: খ
6
উত্তর
সঠিক উত্তর: খ
6
খ
ব্যাখ্যা
Question: A ferry can travel twice as fast when empty as when it is full. It travels 20 miles with full load, spends 1 hour for unloading and returns to its original post empty. It took 11 hours to complete the journey. What is the speed of the ferry when it is empty?

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

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

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

প্রশ্নমতে,
20/x + 10/x = 11 - 1
⇒ (20 + 10)/x = 10 
⇒ 30/x = 10 
⇒ 10x = 30 
⇒ x = 3 

∴ ফেরিটির খালি অবস্থায় গতি বেগ 2 × 3 = 6  মাইল/ঘণ্টা। 
১,০৮৩.
তিনটি গাড়ির গতির অনুপাত  ৩ : ৪ : ৫। গাড়ি তিনটি একই দূরত্ব অতিক্রম করতে যে সময় নেয় তার অনুপাত কত? 
  1. ক
    ক) ১৬ : ১৫ : ১২ 
  2. খ
    খ) ২০ : ১৫ : ১৬ 
  3. গ
    গ) ২০ : ১৫ : ১২ 
  4. ঘ
    ঘ) ২০ : ১৭ : ১৮ 
সঠিক উত্তর: গ
গ) ২০ : ১৫ : ১২ 
উত্তর
সঠিক উত্তর: গ
গ) ২০ : ১৫ : ১২ 
গ
ব্যাখ্যা
দেয়া আছে,
তিনটি গাড়ির গতির অনুপাত  = ৩ : ৪ : ৫

মনেকরি,
দূরত্ব = ১ 

তিনটি গাড়ির সময়ের অনুপাত  = ১/৩ : ১/৪ : ১/৫ 
                                                 = (১/৩) × ৬০ : (১/৪) × ৬০ : (১/৫) × ৬০
                                                  = ২০ : ১৫ : ১২ 
১,০৮৪.
A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and speed of the stream is:
  1. ক
    ক) 5 : 3
  2. খ
    খ) 3 : 1
  3. গ
    গ) 2 : 3
  4. ঘ
    ঘ) 2 : 1
সঠিক উত্তর: খ
খ) 3 : 1
উত্তর
সঠিক উত্তর: খ
খ) 3 : 1
খ
ব্যাখ্যা
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and speed of the stream is:

Solution: 
Ratio of downstream time : upstream time = 1 : 2
 Ratio of downstream speed : upstream speed = 2 : 1

Let
Downstream speed = 2x and
Upstream speed = x
Speed of the boat in still water = (2x + x)/2 = 3x/2
Speed of stream = (2x - x)/2 = x/2
∴ Required ratio = 3x/2 : x/2 = 3 : 1
১,০৮৫.
With a uniform speed, a car covers a distance in 8 hours. had the speed been increased by 4 km/hr, the same distance could have been covered in 7 hr and 30 min. What is the distance covered?
  1. ক
    ক) 420 km
  2. খ
    খ) 480 km
  3. গ
    গ) 520 km
  4. ঘ
    ঘ) 640 km
সঠিক উত্তর: খ
খ) 480 km
উত্তর
সঠিক উত্তর: খ
খ) 480 km
খ
ব্যাখ্যা

Let the speed of car be x km/hr
Distance= Speed × Time
Distance = 8x km
According to the question,
⇒ (x+4)×7.5= 8x
⇒ 7.5x+30= 8x
⇒ 8x−7.5x= 30
⇒ 0.5x= 30
⇒x= (30/0.5)= 60 km/hr
Required distance:
= 8 × 60
= 480 km

১,০৮৬.
Two buses start from a bus terminal with a speed of 30 km/h at interval of 15 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at interval of 10 minutes?
  1. ক
    15 kmph
  2. খ
    12 kmph
  3. গ
    10 kmph
  4. ঘ
    8 kmph
সঠিক উত্তর: ক
15 kmph
উত্তর
সঠিক উত্তর: ক
15 kmph
ক
ব্যাখ্যা
Question: Two buses start from a bus terminal with a speed of 30 km/h at interval of 15 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at interval of 10 minutes?

Solution:
Let Speed of the man is x kmph.

Let the speed of the man be x km/h
Distance covered by the man in 10 min = Distance covered by the bus in 5 min

According to the question
⇒ x × 10/60 = 30 × 5/60
⇒ 10x = 150 ⇒
x = 15 km/h

∴ Speed of the man is 15 km/h
১,০৮৭.
An aeroplane flying 800 km covers the first 200 km at the rate of 200 km/hr, the second 200 km at 400 km/hr, the third 200 km at 600 km/hr & last 200 km at the rate of 800 km/hr. Determine the average speed of the aeroplane.
  1. ক
    ক) 384 km/hr
  2. খ
    খ) 300 km/hr
  3. গ
    গ) 480 km/hr
  4. ঘ
    ঘ) 600 km/hr
সঠিক উত্তর: ক
ক) 384 km/hr
উত্তর
সঠিক উত্তর: ক
ক) 384 km/hr
ক
ব্যাখ্যা
Question: An aeroplane flying 800 km covers the first 200 km at the rate of 200 km/hr, the second 200 km at 400 km/hr, the third 200 km at 600 km / hr & last 200 km at the rate of 800 km/hr. Determine the average speed of the aeroplane.

Solution: 
We know that,
Time =    Distance/Speed

Total time taken =  200/200 + 200/400 + 200/600 + 200/800
= 1 + 1/2 + 1/3 + 1/4
= 25/12

∴ Average speed = (800 × 12)/25 = 384 km/hr
১,০৮৮.
A and B start at the same time with speeds of 40 km/hr and 50 km/hr respectively. If in covering the journey A takes 15 minutes longer than B, the total distance of the journey is
  1. ক
    ক) 46 km
  2. খ
    খ) 48 km
  3. গ
    গ) 50 km
  4. ঘ
    ঘ) 52 km
সঠিক উত্তর: গ
গ) 50 km
উত্তর
সঠিক উত্তর: গ
গ) 50 km
গ
ব্যাখ্যা
Let the distance be ‘x’ km
x/40 – x/50 = 15/60
⇒ (5x – 4x)/200 = 1/4
⇒ x = 200/4
⇒ x = 50 km
∴ Distance of the journey = 50 km
১,০৮৯.
The speed of three cars is in the ratio of 2 : 3 : 4. The ratio of the times taken by these cars to travel the same distance is -
  1. ক
    2 : 3 : 4
  2. খ
    4 : 3 : 2
  3. গ
    4 : 3 : 6
  4. ঘ
    6 : 4 : 3
সঠিক উত্তর: ঘ
6 : 4 : 3
উত্তর
সঠিক উত্তর: ঘ
6 : 4 : 3
ঘ
ব্যাখ্যা
Question: The speed of three cars is in the ratio of 2 : 3 : 4. The ratio of the times taken by these cars to travel the same distance is-

Solution:
Speed is always inversely proportional to time,
⇒ s ∝ (1/t)

∴ Ratio of times takes = 1/2 : 1/3 : 1/4
= (1/2) × 12 : (1/3) × 12 : (1/4) ×12
= 6 : 4 : 3
১,০৯০.
A train crosses two bridges of 400 m and 160 m in 110 sec and 60 sec respectively. The length of the train is:
  1. ক
    ক) 148 m
  2. খ
    খ) 138 m
  3. গ
    গ) 118 m
  4. ঘ
    ঘ) 128 m
সঠিক উত্তর: ঘ
ঘ) 128 m
উত্তর
সঠিক উত্তর: ঘ
ঘ) 128 m
ঘ
ব্যাখ্যা
Let the length of the train be x m.
The train passes a bridge of length 400 m in 110 sec.
Speed of the train = (x + 400)/110...........(1)
The train passes another bridge of length 160 m in 60 sec.
Speed of the train = (x + 160)/60..............(2)

Equating equation (1) and (2),
⇒ (x + 400)/110 = (x + 160)/60
⇒ (x + 400) × 60 = (x + 160) × 110
⇒ (60x + 24000) = (110x + 17600)
⇒ 110x – 60x = 24000 – 17600
⇒ 50x = 6400
⇒ x = 6400/50
⇒ x = 128 m
১,০৯১.
Two runners start running together for a certain distance. One runs at 8 km/h and the other at 5 km/h. The faster runner arrives one and half an hour before the slower runner. What is the distance?
  1. ক
    22 km
  2. খ
    28 km
  3. গ
    20 km
  4. ঘ
    18 km
সঠিক উত্তর: গ
20 km
উত্তর
সঠিক উত্তর: গ
20 km
গ
ব্যাখ্যা

Question: Two runners start running together for a certain distance. One runs at 8 km/h and the other at 5 km/h. The faster runner arrives one and half an hour before the slower runner. What is the distance?

Solution:
Given that,
Speed of first runner v1 = 8 km/h
Speed of second runner v2 = 5 km/h
First runner arrives 1.5 hours before the second.
Let the distance be d km.

We know,
Time = Distance​/Speed
∴ t1 = d/8 and t2 = d/5
And Difference in time, t2 - t1 = 1.5 hours

ATQ,
(d/5) - (d/8) = 1.5
⇒ (8d - 5d)/40 = 3/2
⇒ 3d = 60
∴ d = 20

So the distance is 20 km.

১,০৯২.
A train passes a platform in 40 sec and a woman standing on the platform in 30 sec. If the speed of the train is 108 km/hr, what is the length of the platform?
  1. ক
    ক) 100 m
  2. খ
    খ) 300 m
  3. গ
    গ) 900 m
  4. ঘ
    ঘ) 1020 m
সঠিক উত্তর: খ
খ) 300 m
উত্তর
সঠিক উত্তর: খ
খ) 300 m
খ
ব্যাখ্যা

A train passes a platform in 40 sec and a woman standing on the platform in 30 sec. If the speed of the train is 108 km/hr, what is the length of the platform?
Speed of the train = {108×(5/18)} m/sec = 30 m/sec
Length of the train = (30×30) m = 900 m
Let the length of the platform be x meters
Then, (x+900)/30 = 40
⇒ x + 900 = 1200
⇒ x = 300 m

১,০৯৩.
A train is moving at a speed of 132 km/hr. If the length of the train is 110 meters, how long it will take to cross a railway platform 165 meter long?
  1. ক
    7.5 seconds
  2. খ
    8.5 seconds
  3. গ
    9.5 seconds
  4. ঘ
    10.5 seconds
  5. ঙ
    11.5 seconds
সঠিক উত্তর: ক
7.5 seconds
উত্তর
সঠিক উত্তর: ক
7.5 seconds
ক
ব্যাখ্যা
Speed = 132 km/hr = 132 × 5/18 m/s = 110/3 m/s
time = distance/speed = (110 + 165)/(110/3) = 7.5 seconds
১,০৯৪.
The angle between the minute hand and the hour hand of a clock when the time is 4 : 40, is-
  1. ক
    80°
  2. খ
    100°
  3. গ
    110°
  4. ঘ
    120°
সঠিক উত্তর: খ
100°
উত্তর
সঠিক উত্তর: খ
100°
খ
ব্যাখ্যা
Question: The angle between the minute hand and the hour hand of a clock when the time is 4 : 40, is-

Solution:
Angle = |(11M – 60H)/2|°
= |{(11 × 40) - (60 × 4)}/2|°
= |(440 - 240)/2|°
= |200/2|°
= 100°
১,০৯৫.
A train 200 meters long takes 50 seconds to cross a 300-meter-long bridge. How much time will the train take to cross a 150-meter-long platform?
  1. ক
    18 seconds
  2. খ
    24 seconds
  3. গ
    35 seconds
  4. ঘ
    42 seconds
সঠিক উত্তর: গ
35 seconds
উত্তর
সঠিক উত্তর: গ
35 seconds
গ
ব্যাখ্যা

Question: A train 200 meters long takes 50 seconds to cross a 300-meter-long bridge. How much time will the train take to cross a 150-meter-long platform?

Solution:
Length of train = 200 m
Length of bridge = 300 m
∴ Total distance to cross bridge = 200 + 300 = 500 m

Time taken = 50 seconds

∴ Speed of train = Total distance/Time
= 500/50
= 10 m/s

Length of platform = 150 m
∴ Total distance to cross platform = 200 + 150 = 350 m

∴ Time taken = Total distance/Speed
= 350/10
= 35 seconds

১,০৯৬.
Dhaka and Khulna apart from each other 760 km. A train starts from Dhaka at 8 am and travels towards Khulna at speed 100 km/h. Another train starts from Khulna at 10 am and travels towards Dhaka at speed 40 km/h. At what time both will meet?
  1. ক
    2 pm
  2. খ
    3 pm
  3. গ
    1 pm
  4. ঘ
    4 pm
সঠিক উত্তর: ক
2 pm
উত্তর
সঠিক উত্তর: ক
2 pm
ক
ব্যাখ্যা
Question: Dhaka and Khulna apart from each other 760 km. A train starts from Dhaka at 8 am and travels towards Khulna at speed 100 km/h. Another train starts from Khulna at 10 am and travels towards Dhaka at speed 40 km/h. At what time both will meet?

Solution:
Total distance between D and K = 760 km
A travels 2 hour before B so it travels = 100 × 2
= 200 km
Now the remaining distance D and K = 760 - 200
= 560 km
Relative speed = (100 + 40) km/h
= 140 km/h

Time = 560/140
= 4 hour

So, the time when they meet = 10 am + 4 hour
= 2 pm
১,০৯৭.
Shipon leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after train had departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train’s departure. The distance (in km) from his home to the railway station is - 
  1. ক
    ক) 10 km
  2. খ
    খ) 15 km
  3. গ
    গ) 20 km
  4. ঘ
    ঘ) 25 km
সঠিক উত্তর: গ
গ) 20 km
উত্তর
সঠিক উত্তর: গ
গ) 20 km
গ
ব্যাখ্যা
Question: Shipon leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after train had departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train’s departure. The distance (in km) from his home to the railway station is - 

Solution: 
ধরি, রেলস্টেশন থেকে বাসার দূরত্ব x কিমি 
শিপন ১২ কিমি/ঘণ্টা বেগে গেলে ট্রেন ছাড়ার ১০ মিনিট পরে পৌঁছায়। 
যদি সে ১৫ কিমি/ঘন্টা বেগে যেত তবে ট্রেন ছাড়ার ১০ মিনিট আগে পৌঁছাত। অর্থাৎ, ২০ মিনিট সময় কম লাগত।
২০ মিনিট = ২০/৬০ ঘণ্টা 
= ১/৩ ঘণ্টা 

(x/12) - (x/15) = 1/3
⇒ (5x - 4x)/60 = 1/3
∴ x = 60/3
= 20 km

অতএব, দূরত্ব ২০ কিমি। 
১,০৯৮.
An aeroplane covers a certain distance at a speed of 260 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of:
  1. ক
    ক) 720 km/hr
  2. খ
    খ) 740 km/hr
  3. গ
    গ) 760 km/hr
  4. ঘ
    ঘ) 780 km/hr
সঠিক উত্তর: ঘ
ঘ) 780 km/hr
উত্তর
সঠিক উত্তর: ঘ
ঘ) 780 km/hr
ঘ
ব্যাখ্যা
Question: An aeroplane covers a certain distance at a speed of 260 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of:

Solution: 
Distance = (260 × 5) = 1300 km.
Speed = Distance/Time


Speed = 1300/(5/3) km/hr.
           = 1300 × (3/5) km/hr.
           = 780 km/hr.
১,০৯৯.
A motorist can go downstream at 18 km/hr and upstream at 10 km/hr. Find the speed of the stream and the speed of the motorist in still waters.
  1. ক
    ক) Motorist = 8 km/hr ; Stream = 28 km/hr
  2. খ
    খ) Motorist = 10 km/hr ; Stream = 5 km/hr
  3. গ
    গ) Motorist = 14 km/hr ; Stream = 4 km/hr
  4. ঘ
    ঘ) Motorist = 28 km/hr ; Stream = 8 km/hr
সঠিক উত্তর: গ
গ) Motorist = 14 km/hr ; Stream = 4 km/hr
উত্তর
সঠিক উত্তর: গ
গ) Motorist = 14 km/hr ; Stream = 4 km/hr
গ
ব্যাখ্যা

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

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

X + Y = 18 km/hr and X - Y = 10 km/hr
Adding them we get,
X + Y + X - Y = 28 km/hr

∴ X = 14 km/hr = Speed of Motorist

Y = 18 - 14 = 4 km/hr = Speed of stream

১,১০০.
Two stations A and B are on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 Kmph. Another train starts from B at 8 a.m. and travel towards A at a speed of 25 kmph. If they meet at 10 a.m., what is the distance between two stations A and B?
  1. ক
    90 km
  2. খ
    100 km
  3. গ
    110 km
  4. ঘ
    150 km
সঠিক উত্তর: গ
110 km
উত্তর
সঠিক উত্তর: গ
110 km
গ
ব্যাখ্যা
Question: Two stations A and B are on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 Kmph. Another train starts from B at 8 a.m. and travel towards A at a speed of 25 kmph. If they meet at 10 a.m., what is the distance between two stations A and B?

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

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

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