Time and Speed - Train and Boat

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

১.

A train 125 m long passes a person, running at 8 km/hr in the same direction in which the train is going in 25 seconds. The speed of the train is :

ক
ক) 22
খ
খ) 36
গ
গ) 30
ঘ
ঘ) 26

ব্যাখ্যা

Speed of the train relative to Person
= (125/25) m/s.
= 5 m/s.
= 5 × (18/5) km/hr
= 18 km/hr

Let the speed of the train be x km/hr.
then, relative speed = (x - 8) km/hr.

So, (x - 8) = 18
⇒ x = 26 km/hr.

২.

In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water(in km/hr) is

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

ব্যাখ্যা

Let
speed of boat and stream be x km/hr and y km/hr.
⇒ Downstream speed = (x + y) km/hr
⇒ Upstream speed = (x - y) km/hr
According to the question
(x + y) = 11 km/hr ----(i)
(x - y) = 5 km/hr ----(ii)

Add equation (i) and equation (ii)
2x = 16
x = 8

∴ Speed of the boat is 8 km/hr in still water.

৩.

The distance between two places A and B is 370 km. the 1st car departs from place A to B, at a speed of 80 kmph at 10 am and 2nd car departs from place B to A at a speed of 50 kmph at 1 pm. At what time both cars meet each other?

ক
1:00 pm
খ
1:30 pm
গ
2:00 pm
ঘ
2:30 pm

ব্যাখ্যা

Question: The distance between two places A and B is 370 km. the 1st car departs from place A to B, at a speed of 80 kmph at 10 am and 2nd car departs from place B to A at a speed of 50 kmph at 1 pm. At what time both cars meet each other?

Solution:
Total distance = 370 km
Now, the distance covered by first car in (10 am to 1 pm =) 3 hours
= 80 × 3
= 240 km

Remaining distance = 370 - 240 = 130 km
Relative speed = 80 + 50 = 130 kmph
Now, they cover 130 km in (130/130) = 1/1 hrs = 60 mins

So, they meet 60 mins after 1 pm.
So, requred answer = 2:00 pm.

৪.

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

ক
6 km
খ
8 km
গ
12 km
ঘ
10 km

ব্যাখ্যা

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

Solution:
Let the distance from home to office = d km

Time taken at 4 km/h = d/4 hours
And time taken at 6 km/h = d/6 hours

The difference between these two times = late time + early time = 20 min + 10 min = 30 min = 1/2 hours

ATQ,
(d/4) - (d/6) = 1/2
⇒ (3d - 2d)/12 = 1/2
⇒ d = 12/2
∴ d = 6 km

So the distance from home to office is 6 km.

৫.

A person crosses a 450 meters long street in 2.5 minutes. What is his speed in kilometers per hour?

ক
12.2
খ
10.8
গ
11.4
ঘ
None of these

ব্যাখ্যা

Speed = 450 meters / 2.5 minutes
= (450 × 60)/(2.5 × 1000) km/hr
= 10.8 km/hr

৬.

P does one-third as much work as Q in one-fourth of the time. If together they take 24 days to complete a work, how much time shall Q alone take to do it?

ক
42 days
খ
48 days
গ
56 days
ঘ
62 days

ব্যাখ্যা

Question: P does one-third as much work as Q in one-fourth of the time. If together they take 24 days to complete a work, how much time shall Q alone take to do it?

Solution:
Let Q takes x days to do the work.
P takes 1/4 of x time to do 1/3 of the work.
∴ the work will be done by P in (x/4) × 3 days
= 3x/4

ATQ,
(1/x) + (4/3x) = 1/24
⇒ 7/3x = 1/24
⇒ x = 56
∴ Q alone will take 56 days

৭.

A train passes a station platform in 36 seconds and a man standing on the platform in 52/3 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

ক
ক) 300 meters
খ
খ) 280 meters
গ
গ) 250 meters
ঘ
ঘ) 240 meters

ব্যাখ্যা

Question: A train passes a station platform in 36 seconds and a man standing on the platform in 52/3 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Solution:
Speed = 54 km/hr = (54 × 1000)/3600 m/s
= 15 m/s

Length of the train = 15 × (52/3) m = 260 m.

Let,
The length of the platform be x meters
∴ (260 + x)/36 = 15
⇒ 260 + x = 540
⇒ x = 540 - 260
∴ x = 280

∴ The length of the platform 280 meters

৮.

The ratio between the speeds of two trains is 5 : 8. If the second train runs 600 km in 5 hours, then the speed of the first train is -

ক
100 kmph
খ
95 kmph
গ
80 kmph
ঘ
75 kmph

ব্যাখ্যা

Question: The ratio between the speeds of two trains is 5 : 8. If the second train runs 600 km in 5 hours, then the speed of the first train is -

Solution:
Let the speed of the trains are 5x and 8x

the speed of the second train = 600/5 kmph = 120 kmph

∴ 8x = 120
x = 15

∴ speed of first train = 5x = 75 kmph

৯.

A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?

ক
100 m
খ
150 m
গ
190 m
ঘ
200 m
ঙ
None of these

ব্যাখ্যা

Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?

Solution:
Relative speed of the thief and policeman = (11 - 10) km/hr = 1 km/hr
Distance covered in 6 minutes = (1/60) × 6 km = 1/10 km = 100 m
Therefore, Distance between the thief and policeman = (200 - 100) m = 100 m.

১০.

Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide?

ক
ক) 1/12
খ
খ) 1/6
গ
গ) 1/4
ঘ
ঘ) 1/2

ব্যাখ্যা

Notice that the distance between the two boats one minute before they collide is equal to the total distance traveled by the two boats in one minute.

In 1 minute, the boat with speed of 5 km/hr will have traveled 5 x 1/60 = 5/60 km.
Similarly, the boat with speed of 10 km/hr will have traveled 10 x 1/60 = 10/60 km in 1 minute.
Therefore, 1 minute before they collide, they are 5/60 + 10/60 = 15/60 = 1/4 km apart.

১১.

A plane traveling at 600 miles per hour is heading for Chittagong airport. At 3.58 pm it was 30 miles from the airport. At what time it will arrive at the airport?

ক
4.01 pm
খ
4.02 pm
গ
4.18 pm
ঘ
4.20 pm

ব্যাখ্যা

Question: A plane traveling at 600 miles per hour is heading for Chittagong airport. At 3.58 pm it was 30 miles from the airport. At what time it will arrive at the airport?

Solution:
প্লেনটি ৬০০ মাইল অতিক্রম করে ৬০ মিনিটে
প্লেনটি ১ মাইল অতিক্রম করে ৬০/৬০০ মিনিটে
প্লেনটি ৩০ মাইল অতিক্রম করে (৬০ × ৩০)/৬০০ মিনিটে
= ৩ মিনিটে

প্লেনটি বিমানবন্দরে পৌঁছাতে ৩ মিনিট সময় নিবে।
যদি বিকাল ৩ : ৫৮ এ প্লেনটি ৩০ মাইল দূরে থাকে, তাহলে ৩ মিনিট যোগ করলে পৌঁছানোর সময় হবে:
৩ : ৫৮ বিকাল + ৩ মিনিট = ৪ : ০১ বিকাল

১২.

Excluding stoppages, the speed of a train is 80 kmph, and including stoppages, it is 64 kmph. For how many minutes does the train stop per hour?

ক
12 minutes
খ
15 minutes
গ
22 minutes
ঘ
16 minutes

ব্যাখ্যা

Question: Excluding stoppages, the speed of a train is 80 kmph, and including stoppages, it is 64 kmph. For how many minutes does the train stop per hour?

Solution:
Excluding stoppages speed = 80 kmph
Including stoppages speed = 64 kmph

Loss in distance per hour due to stoppages
= (80 - 64) km
= 16 km

Time taken to cover 16 km at 80 kmph
= (16/80) × 60 minutes
= 12 minutes

১৩.

A train running at the speed of 84 km/hr passes a man walking in opposite direction at the speed of 6 km/hr in 4 seconds. What is the length of train (in meter)?

ক
130 meters
খ
150 meters
গ
90 meters
ঘ
100 meters

ব্যাখ্যা

Question: A train running at the speed of 84 km/hr passes a man walking in opposite direction at the speed of 6 km/hr in 4 seconds. What is the length of train (in meter)?

Solution:
Given that,
Train speed = 84 km/hr
Man speed = 6 km/hr (opposite direction)
∴ Relative speed = 84 + 6 = 90 km/hr
= 90 × (5/18) = 25 m/s

And,
Time taken to pass the man,
Given = 4 seconds

∴ Length = Relative speed × Time = 25 × 4 = 100 m

So the length of the train is 100 meters.

১৪.

A 280 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

ক
ক) 220 m
খ
খ) 240 m
গ
গ) 260 m
ঘ
ঘ) 210 m

ব্যাখ্যা

Relative speed = (120 + 80) km/hr
= 200 km/hr
= 200 ×(5/18) m/sec
= 500/9 m/sec

Let the length of the other train be x metres.
Now
(x + 280)/9 = 500/9
x + 280 = 500
x = 500 - 280
x = 220

১৫.

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

ক
40 m
খ
50 m
গ
45 m
ঘ
55 m

ব্যাখ্যা

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

Solution:
Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 - 36) km/hr
= 10 × (5/18) m/sec
= 25/9 m/sec

ATQ,
2x/36 = 25/9
⇒ 18x = 25 × 36
⇒ x = (25 × 36)/18
= 50

১৬.

A truck travels at 96 km/h. How much distance will it cover in 75 minutes?

ক
118 km
খ
120 km
গ
124 km
ঘ
122 km

ব্যাখ্যা

Question: A truck travels at 96 km/h. How much distance will it cover in 75 minutes?

Solution:
Given that,
Speed = 96 km/h
Time = 75 minutes = 75/60 hours = 5/4 hours

We know,
Distance = Speed × Time
= 96 × (5/4)
= 96 × 1.25
= 120 km

So the truck will cover 120 km in 75 minutes.

১৭.

A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?

ক
ক) 180
খ
খ) 175
গ
গ) 190
ঘ
ঘ) 185
ঙ
ঙ) 200

ব্যাখ্যা

Speed = 40 km/hr = (40 × 5/18) m/s = 100/9 m/s
Time = 18 seconds
Distance Covered = 100/9 × 18 = 200 m
Therefore,
Length of the train = 200 m

১৮.

In a boat race, a person rows a boat 6 km upstream and returns to the starting point in 4 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.

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

ব্যাখ্যা

Question: In a boat race, a person rows a boat 6 km upstream and returns to the starting point in 4 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.

Solution:
Let the speed of the boat in still water be B km/hr
⇒ Speed upstream = (B - 2) km/hr
⇒ Speed downstream = (B + 2) km / hr

We know that Time = Distance / Speed
⇒ 6/(B - 2) + 6/(B + 2) = 4
⇒ 6B + 12 + 6B - 12 = 4(B - 2)(B + 2)
⇒ 12B = 4(B - 2)(B + 2)
⇒ 3B = B² - 4
⇒ B² - 3B - 4 = 0
⇒ (B + 1) (B - 4) = 0
⇒ B = 4 km/hr (Speed cannot be negative)

১৯.

A bike travels at a speed twice as fast as walking. A person spends the same amount of time walking and riding the bike, covering a total distance of 180 km. How many kilometers does he walk?

ক
120 km
খ
80 km
গ
90 km
ঘ
60 km

ব্যাখ্যা

Question: A bike travels at a speed twice as fast as walking. A person spends the same amount of time walking and riding the bike, covering a total distance of 180 km. How many kilometers does he walk?

Solution:
Let the walking speed be = x km/h.
Then the bike speed is = 2x km/h ; [since the bike is 2 times faster than walking]
Total distance covered = 180 km.

Let the distance walked = d km.
Then the distance covered by bike = (180 - d) km.

We know,
Time = distance/speed
⇒ d/x = (180 - d)/2x
⇒ d = (180 - d)/2
⇒ 2d = 180 - d
⇒ 3d = 180
⇒ d = 180/3
∴ d = 60

So, the person covers 60 km by walking.

২০.

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

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

ব্যাখ্যা

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

Solution:
Let the speed of the stream be x km/h and both the boats meet after t hour.

A's speed is = 12 + x
B's speed is = 15 - x

According to the question,
(12 + x) × t + (15 - x) × t = 108
Or, 12t + 15t = 108
Or, 27t = 108
∴ t = 4 hours

২১.

If 60 men can complete a job in 50 days, how many extra men need to be hired to finish the same work 10 days earlier?

ক
10 men
খ
15 men
গ
12 men
ঘ
8 men

ব্যাখ্যা

Question: If 60 men can complete a job in 50 days, how many extra men need to be hired to finish the same work 10 days earlier?

Solution:
Let the total work = 60 × 50 = 3000 man-days
New time to finish work = 50 - 10 = 40 days

Number of men required = Total work ÷ New time
= 3000 ÷ 40
= 75 men

Extra men needed = 75 - 60 = 15 men

২২.

Two trains of equal length are moving in same direction on parallel tracks at speed of 92 km/hr and 72 km/hr respectively. The faster train crosses the slower train in 18 seconds. Find the length of each train.

ক
65 meters
খ
60 meters
গ
55 meters
ঘ
50 meters

ব্যাখ্যা

Question: Two trains of equal length are moving in same direction on parallel tracks at speed of 92 km/hr and 72 km/hr respectively. The faster train crosses the slower train in 18 seconds. Find the length of each train.

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 x m each.

So the distance to be covered = 2x.
Now the trains are running int he same direction.
∴ Their relative speed = (92 - 72) km/hr. = 20 km/hr. = 20 × (5/18) km/hr. = (50/9) m/sec.

So, the time taken by the trains to cove 2x m distance
= 2x ÷ (50/9) sec.

∴ By the given conditions,
2x ÷ (50/9) = 18
⇒ 2x × (9/50) = 18
⇒ 2x = (18 × 50)/9
⇒ 2x = 100
∴ x = 50

So the length of each train = 50 m.

২৩.

Due to bad weather, a car reduced its speed by 15 km/hr and reached a destination 300 km away 1 hour late. What was the car's original speed?

ক
60 km/hr
খ
65 km/hr
গ
70 km/hr
ঘ
75 km/hr

ব্যাখ্যা

Question: Due to bad weather, a car reduced its speed by 15 km/hr and reached a destination 300 km away 1 hour late. What was the car's original speed?

Solution:
ধরি,
গাড়িটির আসল গতিবেগ ছিল S কিমি/ঘন্টা
এবং আসল সময় ছিল T ঘন্টা।

আমরা জানি, সময় = দূরত্ব/গতিবেগ
∴ T = 300/S

গতিবেগ 15 কিমি/ঘন্টা কমালে,
নতুন গতিবেগ হয় (S - 15) কিমি/ঘন্টা।

গন্তব্যে পৌঁছাতে 1 ঘন্টা বেশি লাগে,
অর্থাৎ নতুন সময় হয় (T + 1) ঘন্টা।
সুতরাং, (T + 1) = 300/(S - 15)

এখন,
(T + 1) - T = 300/(S - 15) - 300/S
⇒ 1 = 300 × {1/(S - 15) - 1/S}
⇒ 1 = 300 × {(S - (S - 15)}/{S(S - 15)}
⇒ 1 = 300 × 15/(S² - 15S)
⇒ S² - 15S = 4500
⇒ S² - 15S - 4500 = 0
⇒ (S - 75)(S + 60) = 0

যেহেতু গতিবেগ ঋণাত্মক হতে পারে না, তাই S = 75 কিমি/ঘন্টা।
সুতরাং, গাড়িটির আসল গতিবেগ ছিল 75 কিমি/ঘন্টা।

২৪.

The ratio of the speed of boat in still water to the speed of stream is 16 : 5. A boat goes 16.5 km in 45 minute upstream, find the time taken by boat to cover the distance of 17.5 km downstream.

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

ব্যাখ্যা

Let, speed of boat in still water = 16x, speed of stream = 5x
Upstream speed = 16x – 5x = 11x
S = D/t
Or, 11x = 16.5 × 60/45 = 22
Or, x = 2
So, speed of boat in still water = 32 km/h, speed of stream = 10 km/h
Downstream speed = 32 + 10 = 42 km/h
Distance = 17.5 km
Required time = 17.5 / 42 = 5/12 hour = 5 × 60/12 = 25 minutes

২৫.

A driver of an auto rickshaw sees a lorry 60 meters ahead of him. After 30 seconds the lorry is 90 meters behind. If the speed of the auto rickshaw is 38 km/h, then what is the speed of the lorry?

ক
ক) 23km/h
খ
খ) 20km/h
গ
গ) 25km/h
ঘ
ঘ) 18km/h

ব্যাখ্যা

Total distance is 60 + 90= 150 meters.
Time taken is 30 seconds.
Relative 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

২৬.

A and B go cycling in the same direction with speeds of 6 km/hr and 12 km/hr. A car from behind passes them in 9 and 10 seconds respectively. What is the speed of the car?

ক
ক) 22 km/hr
খ
খ) 33 km/hr
গ
গ) 66 km/hr
ঘ
ঘ) 44 km/hr

ব্যাখ্যা

আমরা জানি,
অতিক্রান্ত দূরত্ব = গতি × সময়

এখানে
গাড়ির আপেক্ষিক বেগ যথাক্রমে= (x - 6) এবং (x - 12) kmph
গাড়ি কর্তৃক অতিক্রান্ত দূরত্ব = (x - 6) × 9 এবং (x - 12) × 10 km
প্রশ্নমতে
(x - 6) × 9 = (x - 12) × 10
9x - 54 = 10x - 120
10x - 9x = 120 - 54
x = 66

২৭.

In one hour, a boat goes 13 km along the stream and 5 km against the stream. What is the speed of the stream?

ক
12 km/h
খ
11 km/h
গ
9 km/h
ঘ
6 km/h
ঙ
4 km/h

ব্যাখ্যা

Question: In one hour, a boat goes 13 km along the stream and 5 km against the stream. What is the speed of the stream?

Solution:
Let x be the boat speed.
and y be the stream speed.

Down stream speed,
x + y = 13 ............................. (i)
Upper stream speed,
x - y = 5 ................................ (ii)

Now (i) + (ii); we get,
x + y + x - y =13 + 5
⇒ 2x = 18
⇒ x = 9

From (i),
⇒ 9 + y = 13
⇒ y = 13 - 9
⇒ y = 4

∴ The speed of the stream is 4 km/h.

২৮.

A train 120 meters long is traveling at a speed of 60 km/h. The time in which it will pass a passersby, walking at 6 km/h in the same direction is -

ক
8 sec
খ
4 sec
গ
12 sec
ঘ
16 sec

ব্যাখ্যা

Question: A train 120 meters long is traveling at a speed of 60 km/h. The time in which it will pass a passersby, walking at 6 km/h in the same direction is -

Solution:
Speed of train relative to man = (60 - 6)km/hr
= 54km/hr
= (54 × 1000)/3600 m/sec
= (54 × 10)/36 m/sec
= 15 m/sec

∴ Time taken to pass the man = (120/15) sec
= 8 sec

২৯.

Tofail drives first 120 km in 2 hrs and next 180 km in next 4 hrs. What is his average speed for the entire trip in km per hour?

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

ব্যাখ্যা

Question: Tofail drives first 120 km in 2 hrs and next 180 km in next 4 hrs. What is his average speed for the entire trip in km per hour?

Solution:
Total Distance travelled = 120 + 180 = 300 km.
Total Time taken = 2 + 4 = 6 hrs.

∴ Average Speed = Total Distance Travelled/Total Time Taken
= 300/6 km/hr.
= 50 km/hr.

৩০.

Two trains starting at the same time from two-stations 250 km apart and going in opposite directions, cross each other at a distance of 140 km from one of them. The ratio of their speeds is-

ক
11 : 15
খ
13 : 17
গ
14 : 11
ঘ
13 : 9

ব্যাখ্যা

Question: Two trains starting at the same time from two-stations 250 km apart and going in opposite directions, cross each other at a distance of 140 km from one of them. The ratio of their speeds is -

Solution:
In the same time, they cover 140 km and 110 km respectively.
Therefore, the ratio of their speeds = 140 : 110
= 14 : 11

৩১.

If a man can swim at 8 km/hr in still water and the river flows at 2 km/hr, taking 80 minutes for a round trip, what is the distance to the location?

ক
3 km
খ
4 km
গ
5 km
ঘ
7 km

ব্যাখ্যা

Question: If a man can swim at 8 km/hr in still water and the river flows at 2 km/hr, taking 80 minutes for a round trip, what is the distance to the location?

Solution:
Let the place be p km far.

Speed downstream = 8 + 2 = 10 km/hr

Speed upstream = 8 - 2 = 6 km/hr

As per the question;
p/6 + p/10 = 80/60
⇒ (5p + 3p)/30 = 4/3
⇒ 24p = 120
∴ p = 120/24 = 5 km

৩২.

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

ক
ক) 100 km
খ
খ) 120 km
গ
গ) 60 km
ঘ
ঘ) 80 km

ব্যাখ্যা

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

Solution:
ধরি,
A থেকে B এর দূরত্ব = x কি.মি.
প্রশ্নমতে,
(x/40) + (x/30) + 1 = 8
⇒ (x/40) + (x/30) = 8 - 1
⇒ (4x + 3x)/120 = 7
⇒ 7x/120 = 7
⇒ 7x = 7 × 120
⇒ x = (7 × 120)/7
x = 120

৩৩.

Two trains passing towards same direction with the speed of 72km/h and 108km/h. The length of one train is 200m and the overtaking takes 1 minute. How long is the another train?

ক
300m
খ
400m
গ
500m
ঘ
600m

ব্যাখ্যা

Question: Two trains passing towards same direction with the speed of 72km/h and 108km/h. The length of one train is 200m and the overtaking takes 1 minute. How long is the another train?

Solution:
hints: kmph/3.6 = mps
1st train speed = 72km/h
= 20 m/s
second train speed = 108 km/h
= 30m/s

as moving towards same direction,
resultant speed = 30 - 20 = 10m/s
total distance = the length of two trains.
total time = 1 minute = 60s

∴ total distance covered is = speed × time
= 10 × 60 = 600m

length of the second train is = 600 - 200
= 400m

৩৪.

The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:

ক
ক) 1.2 km
খ
খ) 3.6 km
গ
গ) 1.8 km
ঘ
ঘ) 2.4 km

ব্যাখ্যা

The speed of a boat in still water=15km/hr
Rate of current =3km/hr
Speed in downstream=15+3=18km/hr

Time given=12min= 12/60 hr= 1/5 hr
Distance travelled= Speed×Time=18× 1/5 =3.6km

৩৫.

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

ক
0.5 km/hr
খ
1 km/hr
গ
1.8 km/hr
ঘ
2 km/hr

ব্যাখ্যা

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

Solution:
let, rate of stream y and rate of rafsan is x km/hr

ATQ,
4/(x + y) = 3/(x - y)
⇒ 4x - 4y = 3x + 3y
⇒ x = 7y

48/(x + y) + 48/(x - y) = 14
⇒ 1/(7y + y) + 1/(7y - y) = 14/48
⇒ (1/8y) + (1/6y) = 14/48
⇒ 7/24y = 14/48
⇒ y = 1 km/hr

৩৬.

A 220 meters long train running at the speed of 108 kmph crosses another train running in opposite direction at the speed of 90 kmph in 9 seconds. What is the length of the other train?

ক
275 meters
খ
250 meters
গ
225 meters
ঘ
210 meters

ব্যাখ্যা

Question: A 220 meters long train running at the speed of 108 kmph crosses another train running in opposite direction at the speed of 90 kmph in 9 seconds. What is the length of the other train?

Solution:
Relative speed =(108 + 90) km/h
= (198 × 5/18) m/sec
= 55 m/sec

Let,
the length of the other train be x metres.
Then,
(x + 220)/9 = 55
⇒ x + 220 = 55 × 9
⇒ x = 495 - 220
∴ x = 275

৩৭.

An aeroplane covers a certain distance at a speed of 250 kmph in 6 hours. To cover the same distance in 100 minutes, it must travel at a speed of-

ক
900 km/hr
খ
700 km/hr
গ
800 km/hr
ঘ
950 km/hr

ব্যাখ্যা

Question: An aeroplane covers a certain distance at a speed of 250 kmph in 6 hours. To cover the same distance in 100 minutes, it must travel at a speed of-

Solution:
Total Distance = (250 × 6) = 1500 km.
Time 100 minutes = 100/60 hr
= 5/3 hr

We know that,
Speed = Distance/Time
∴ Required speed = 1500/(5/3) km/hr
= 900 km/hr.

৩৮.

It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is-

ক
2 : 3
খ
3 : 4
গ
4 : 5
ঘ
3 : 5

ব্যাখ্যা

Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is-

Solution:
Let, Speed of train and car is T and C respectively

ATQ,
(120/T) + (600 - 120)/C = 8 hours or 480 minutes
⇒ (120/T) + (600 - 120)/C = 480
⇒ (120/T) + (480/C) = 480
⇒ (1/T) + (4/C) = 4 ........... (1)

Again, (200/T) + (600 - 200)/C = 480 + 20
⇒ (2/T) + (4/C) = 500
⇒ (2/T) + (4/C) = 5 ............. (2)

Now, (2) - (1) ⇒
(2/T) - (1/T) = 1
⇒ 1/T = 1
∴ T = 1

from, (1) ⇒ (1/T) + (4/C) = 4
⇒ 1 + (4/C) = 4
⇒ 4/C = 3
∴ C = 4/3

So, the ratio of the speed of the train to that of the cars is = 1 : (4/3)
= 3 : 4

৩৯.

Two boats, travelling at 5 km/h and 10 km/h, head directly towards each other. They begin at a distance of 20 km from each other. How far apart are they (in km) one minute before they collide?

ক
1/4 km
খ
1/6 km
গ
1/3 km
ঘ
4/3 km
ঙ
None of the above

ব্যাখ্যা

Question: Two boats, travelling at 5 km/h and 10 km/h, head directly towards each other. They begin at a distance of 20 km from each other. How far apart are they (in km) one minute before they collide?
(৫ কিমি/ঘণ্টা এবং ১০ কিমি/ঘণ্টা বেগে চলমান দুটি নৌকা পরস্পরের দিকে মুখোমুখি যাত্রা শুরু করে। তারা ২০ কিমি দূরত্ব থেকে এগোতে শুরু করে। সংঘর্ষের এক মিনিট পূর্বে তাদের মধ্যে কত কিলোমিটার দূরত্ব ছিল?)

Solution:
শেষ মুহূর্তে সংঘর্ষের আগে, দুইটি নৌকা যথাক্রমে দূরত্ব অতিক্রম করে 5/60 km and 10/60 km.

যেহেতু তারা একে অপরের দিকে অগ্রসর হচ্ছে, তাই 1 মিনিটে আপেক্ষিকভাবে অতিক্রান্ত হচ্ছে
1/12 + 1/6
= 1/4 km

৪০.

A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is-

ক
35.55 km/hr
খ
36 km/hr
গ
71.11 km/hr
ঘ
71 km/hr

ব্যাখ্যা

Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is-

Solution:
Total time taken = (160/64 + 160/80) hrs
= (5/2 + 2) hrs
= (5 + 4)/2 hrs
= 9/2 hrs.

Average speed = 320 × (2/9) km.hr
= 71.11 km/hr.

৪১.

A man rows downstream at 32 km/h and rows upstream at 22 km/h. At what speed can he row in still water?

ক
27 km/h
খ
5 km/h
গ
54 km/h
ঘ
15 km/h

ব্যাখ্যা

Question: A man rows downstream at 32 km/h and rows upstream at 22 km/h. At what speed can he row in still water?

Solution:
Given,
Man rows downstream = 32 km/h
Man rows upstream = 22 km/h
We know that,
Speed in still water = (Downstream speed + Upstream speed) ÷ 2
= (32 + 22) ÷ 2
= 54 ÷ 2
= 27 km/h

৪২.

For a motorboat that covers a certain distance downstream in 2 hours & returns in 3 hours, what would be its speed in still water if the speed of stream is 6 km/hr?

ক
ক) 9 km/hr
খ
খ) 15 km/hr
গ
গ) 30 km/hr
ঘ
ঘ) 36 km/hr

ব্যাখ্যা

Hint: If a boat moves to a certain distance downstream in 't1 ' hours & returns the same distance upstream in time 't2' hours, then
Speed of boat in still water = y{(t2+t1)/(t2–t1)} km/hr.
With the given parameters,
y = 6 km/hr, t1 = 3 hrs, t2 = 2 hrs
We can find, Speed of boat in still water
(x) = 6{(3+2)/(3–2)}= 30 km/hr

৪৩.

A tap can fill a tank in 30 minutes and another tap can fill the same tank in 60 minutes. lf both the taps are opened simultaneously when the tank is half empty, in how many minutes will the tank be full?

ক
ক) 7 minutes
খ
খ) 10 minutes
গ
গ) 18 minutes
ঘ
ঘ) 20 minutes
ঙ
ঙ) 15 minutes

ব্যাখ্যা

Tap A can fill the tank in 30 minutes. Therefore, it fills 1/30th of the tank every minute.
Tap B can fill the tank in 60 minutes. Therefore, it fills 1/60th of the tank every minute.
Together, the two taps will fill
1/30 + 1/60
= (2 + 1)/60
= 3/60
= 1/20th of the tank every minute.

Therefore, when both the taps are opened simultaneously, they will fill the tank in 20 minutes. As the tank is already half full, they need to fill only half the tank.
Therefore, the tank will overflow 10 minutes after both the taps are opened.

৪৪.

A car running at a speed of 140 km/hr reached its destination in 2 hours. If the car wants to reach at its destination in 1 hour, at what speed it needs to travel?

ক
300 km/hr
খ
280 km/hr
গ
250 km/hr
ঘ
240 km/hr

ব্যাখ্যা

Question: A car running at a speed of 140 km/hr reached its destination in 2 hours. If the car wants to reach at its destination in 1 hour, at what speed it needs to travel?

Solution:
Distance to be covered = Speed × Time = 140 × 2 = 280 km

Time = 1 hour

Required Speed = 280/1 = 280 km/hr

৪৫.

A car travels first half distance between two places with a speed of 40 km/hr and rest of the half distance with a speed of 60 km/hr. The average speed of the car is-

ক
ক) 48 km/hr
খ
খ) 37 km/hr
গ
গ) 44 km/hr
ঘ
ঘ) 45 km/hr

ব্যাখ্যা

Here, 2xy/(x+y) = (2×40×60)/(40+60) = 48

৪৬.

If a train of length 120 meters, crosses a tree in 6 seconds, then the time taken to covers 24 km by the train is: (in minutes)

ক
12
খ
20
গ
11
ঘ
14

ব্যাখ্যা

Length of the train = 120 m
Time taken to cross the tree = 6 seconds.
According to the question,
The time taken by the train to cover 120 m is 6 seconds.
Speed of the train = distance/time
= 120/6 m/s.
= 20 m/s.
Time taken to cover 24 km (24000 m) = 24000/20 seconds
= 1200 seconds
Since, 60 seconds = 1 minute
Then,
1200 seconds = 1200/60 minutes.
= 20 minutes.
Hence, the answer is 20 minutes.

৪৭.

Two trains of equal length are running on parallel lines in the same direction at 65 km/hr and 80 km/hr. The faster train passes the slower train in 48 seconds. The length of each train is:

ক
80 m
খ
100 m
গ
120 m
ঘ
150 m

ব্যাখ্যা

Question: Two trains of equal length are running on parallel lines in the same direction at 65 km/hr and 80 km/hr. The faster train passes the slower train in 48 seconds. The length of each train is:

Solution:
যেহেতু ট্রেন দুটি একই দিকে চলছে, তাই তাদের আপেক্ষিক গতিবেগ হবে তাদের গতিবেগের পার্থক্য।
আপেক্ষিক গতিবেগ = (80 - 65) কিমি/ঘন্টা
= 15 কিমি/ঘন্টা
= 15 × (5/18) মিটার/সেকেন্ড
= 75/18 মিটার/সেকেন্ড
= 25/6 মিটার/সেকেন্ড

ধরি, প্রতিটি ট্রেনের দৈর্ঘ্য x মিটার।
যখন দ্রুতগামী ট্রেনটি ধীরগামী ট্রেনটিকে অতিক্রম করে, তখন মোট অতিক্রান্ত দূরত্ব হয় উভয় ট্রেনের দৈর্ঘ্যের যোগফল।
∴ মোট অতিক্রান্ত দূরত্ব = (x + x) মিটার = 2x মিটার

এখন,
দূরত্ব = গতিবেগ × সময়
2x = (25/6) × 48
2x = 25 × 8
2x = 200
x = 100 মিটার

সুতরাং, প্রতিটি ট্রেনের দৈর্ঘ্য হলো 100 মিটার।

৪৮.

A man can row 6 km/hr in still water. It 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 _____

ক
ক) 30 km
খ
খ) 24 km
গ
গ) 20 km
ঘ
ঘ) 32 km

ব্যাখ্যা

Question: A man can row 6 km/hr in still water. It 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 _____

Solution:
ধরি,
দূরত্ব = x কি.মি.

প্রশ্নমতে,
x/(6 - 2) - x/(6 + 2) = 3
⇒ x/4 - x/8 = 3
⇒ (2x - x)/8 = 3
⇒ x/8 = 3
∴ x = 24

∴ নির্ণেয় দূরত্ব 24 কি.মি.

৪৯.

The speed of a boat in still water is 5 km/hr. If the speed of the boat against the stream is 3 km/hr, what is the speed of the stream?

ক
1.5 km/hr
খ
2 km/hr
গ
2.5 km/hr
ঘ
1 km/hr

ব্যাখ্যা

Question: The speed of a boat in still water is 5 km/hr. If the speed of the boat against the stream is 3 km/hr, what is the speed of the stream?

Solution:
Let the speed of stream = X km/hr

Speed of boat = 5 km/hr
Speed upstream = 3km/hr

Apply formula:
Speed upstream = speed of boat - speed of stream
3 = 5 - X
∴ X = 5 - 3 = 2 km/hr

৫০.

The ratio between the speeds of two trains is 8 : 9. If the second train runs 432 km in 4 hours, then the speed of the first train is:

ক
ক) 84 km/hr.
খ
খ) 72 km/hr.
গ
গ) 96 km/hr.
ঘ
ঘ) 92 km/hr.

ব্যাখ্যা

Let the speed of two trains be 8x and 9x km/hr.
It is given that the second train runs 432 km in 4 hours,

We have,
9x = 432/4
9x= 108
x = 108/9
x = 12

The speed of the first train is = 8 × 12 = 96 km/hr.

৫১.

A man on tour travels first 180 km at 96 km/hr and the next 180 km at 80 km/hr. The average speed for the first 360 km of the tour is:

ক
ক) 970/11 km/hr.
খ
খ) 950/11 km/hr.
গ
গ) 810/11 km/hr.
ঘ
ঘ) 960/11 km/hr.

ব্যাখ্যা

Question: A man on tour travels first 180 km at 96 km/hr and the next 180 km at 80 km/hr. The average speed for the first 360 km of the tour is:

Solution:
Total time taken = (180/96) + (180/80)
= (900 + 1080)/480
= 1980/480
= 99/24

Average speed = 360/(99/24) km/hr.
= (360 × 24)/99
= 960/11 km/hr.

৫২.

A boat goes 6 km upstream in 24 minutes. The speed of the stream is 3 km/hr. The speed of boat in still water is

ক
12 km/hr
খ
14 km/hr
গ
16 km/hr
ঘ
18 km/hr

ব্যাখ্যা

Question: A boat goes 6 km upstream in 24 minutes. The speed of the stream is 3 km/hr. The speed of boat in still water is

Solution:
The speed upstream is 6/24 km/min
= (6 × 60)/24 km/hr
= 15 km/hr

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

Here, x - 3 = 15
⇒ x = 15 + 3
∴ x = 18

∴ The speed of the boat in still water is 18 km/hr

৫৩.

The speed of a boat in still water is 6 km/h. The time it takes to travel downstream is half the time it takes to travel upstream. What is the speed of the stream?

ক
1 km/h
খ
2 km/h
গ
3 km/h
ঘ
4 km/h

ব্যাখ্যা

Question: The speed of a boat in still water is 6 km/h. The time it takes to travel downstream is half the time it takes to travel upstream. What is the speed of the stream?

Solution:
Let the speed of the current be = x km/h

Then,
Downstream speed = (6 + x) km/h
Upstream speed = (6 − x) km/h

According to the question:
(6 + x) = 2(6 − x)
⇒ 6 + x = 12 - 2x
⇒ 2x + x = 12 - 6
⇒ 3x = 6
⇒ x = 6/3
⇒ x = 2

∴ The speed of the current = 2 km/h

৫৪.

The speed of a boat in standing water is 9 kmph, and the speed of the stream is 1.5 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-

ক
10 h
খ
14 h
গ
18 h
ঘ
24 h
ঙ
25 h

ব্যাখ্যা

Question: The speed of a boat in standing water is 9 kmph, and the speed of the stream is 1.5 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 upstream = (9 - 1.5) kmph
= 7.5 kmph
Speed downstream = (9 + 1.5) kmph
=10.5 kmph
∴ Total time taken = (105/7.5) + (105/10.5)
= 14 + 10
= 24 h

৫৫.

A man's speed with the current is 18 km/hr and the speed of the current is 3.6 km/hr. The man's speed against the current is:

ক
ক) 10.5 km/hr
খ
খ) 10.8 km/hr
গ
গ) 11.2 km/hr
ঘ
ঘ) 12.4 km/hr

ব্যাখ্যা

Question: A man's speed with the current is 18 km/hr and the speed of the current is 3.6 km/hr. The man's speed against the current is:

Solution:
Man's rate in still water = (18 - 3.6) km/hr = 14.4 km/hr

∴ Man's rate against the current = (14.4 - 3.6) km/hr = 10.8 km/hr.

৫৬.

A 250 meters long train crosses a bridge 750 meters long in 20 seconds and crosses a platform in 16 seconds. Find the length of the platform.

ক
ক) 500 m
খ
খ) 550 m
গ
গ) 580 m
ঘ
ঘ) 590 m

ব্যাখ্যা

Let the length of the platform be x

The speed of the train = (750 + 250)/20
= 1000/20
= 50 m/sec
Now, Again according to the question
The train crosses the platform in 16 seconds
250 + x = 50 × 16
⇒ x = 800 - 250
⇒ x = 550 m

∴ The length of the platform is 550 m.

৫৭.

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

ক
50 km
খ
56 km
গ
70 km
ঘ
80 km

ব্যাখ্যা

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

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

সে মোট হাটে = ২০/৪ ঘণ্টা = ৫ ঘণ্টা

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

৫৮.

2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days . In how many days can 2 men and 1 boy do the work?

ক
ক) 15
খ
খ) 18.5
গ
গ) 12.5
ঘ
ঘ) 10.5
ঙ
ঙ) 16

ব্যাখ্যা

• 2 men and 3 boys can do a piece of work in 10 days.
Thus, 20 men and 30 boys can do a piece of work in 1 day......(i)

• 3 men and 2 boys can do the same work in 8 days.
Thus, 24 men and 16 boys can do the same work in 1 day....(ii)

• Equating (i) and (ii) we get -
o 20 men + 30 boys = 24 men + 16 boys
o 4 men = 14 boys
o 2 men = 7 boys

• Substituting this in equation (i) we get

10 boys can do a piece of work in 10 days.
But we need to find out in how many days 2 men and 1 boy can do the work, which is equivalent to 8 boys.

8 boys can do the same work in (10 × 10/8) = 12.5 days.

৫৯.

A truck cover a distance of 480 meters in 1 min whereas a bus covers a distance of 54 km in 45 min. The ratio of their speed-

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

ব্যাখ্যা

Question: A truck cover a distance of 480 meters in 1 min whereas a bus covers a distance of 54 km in 45 min. The ratio of their speed-

Solution:
Speed of truck = 480/60 = 8 m/s
speed of bus = (54 × 1000)/(45 × 60) = 20 m/s

Ratio = 8 : 20 = 2 : 5

৬০.

The speed of a boat in still water in 12 km/h and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is-

ক
5 km
খ
6 km
গ
3 km
ঘ
4 km

ব্যাখ্যা

Question: The speed of a boat in still water in 12 km/h and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is-

Solution:
Speed downstream
= (12 + 3) kmph
= 15 kmph

Distance travelled = (15 × 24/60) km
= 6 km

৬১.

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

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

ব্যাখ্যা

Speed of the first train = 48 km/hr.
Let the length of the first train = 2x metre.

Speed of the second train = 42 km/hr.
Let the length of the second train = x metre.

Distance = (2x + x) = 3x metre.
Time = 12 seconds

Relative speed = 48 + 42 = 90 km/hr.
= 90 × (5/18) = 25 m/s.
3x = 25 × 12
⇒ x = 100 metre.

Length of the first train = 200
Time is taken to cross the platform = 45 seconds.
Speed of first train = 48 km/hr
= 48 × (5/18)
= 40/3 m/s.

Let the length of the platform = y metre.
Distance = 200 + y metre.
⇒ 200 + y = 45 × (40/3)
⇒ 200 + y = 600
⇒ y = 400 metre.

৬২.

A man sitting in a train is counting the pillars of electricity. The distance between two pillars is 60 meters and the speed of the train is 36 km/hr. In 5 hours, how many pillars will be count?

ক
3000
খ
3001
গ
3006
ঘ
3010

ব্যাখ্যা

Question: A man sitting in a train is counting the pillars of electricity. The distance between two pillars is 60 meters and the speed of the train is 36 km/hr. In 5 hours, how many pillars will be count?

Solution:
Distance covered by the train in 5 hours = (36 × 5) km
= (180 km × 1000)
= 180000 m

∴ Number of pillars counted by man = {(180000/60) + 1}
= (3000 + 1)
= 3001

[ Since the man start counting with pillar and end with pillar so 1 is added]

৬৩.

A train is moving at a speed of 132 km/h. If the length of the train is 110 metres, how long will it take to cross a railway platform, 165 metres long?

ক
8.5 s
খ
5.5 s
গ
10.5 s
ঘ
7.5 s
ঙ
None

ব্যাখ্যা

Question: A train is moving at a speed of 132 km/h. If the length of the train is 110 metres, how long will it take to cross a railway platform, 165 metres long?

Solution:
Speed of the train = 132 km/h = 132 × (5/18) m/s
Distance = (110 + 165) = 275 m

Time required to cross the railway platform = (275 × 18)/(132 × 5)
= 7.5 s

৬৪.

A man can row 34/3 kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. The speed of the current is:

ক
ক) 17/3 km/hr.
খ
খ) 34/3 km/hr.
গ
গ) 28/3 km/hr.
ঘ
ঘ) 11/3 km/hr.

ব্যাখ্যা

Let speed upstream be x kmph
Then speed downstream = 3x kmph
Speed in still water = (1/2)(3x + x)kmph
=2x kmph

Now
2x = 34/3
x = (34/3) × 2
x = 17/3

So Speed upstream = 17/3 km/hr
Speed downstream = 17 km/hr

Hence speed of the current =(1/2){17 - (17/3)} km/hr.
= (1/2)(51 - 17)/3 km/hr.
= (1/2)(34/3) km/hr.
= 17/3 km/hr.

৬৫.

How long will it take to row 20 km upstream if one can row 10 km in 10 minutes in still water and the same distance in 8 minutes with the stream?

ক
12 min
খ
13.33 min
গ
24 min
ঘ
26.67 min
ঙ
27 min

ব্যাখ্যা

Question: How long will it take to row 20 km upstream if one can row 10 km in 10 minutes in still water and the same distance in 8 minutes with the stream?

Solution:
Let x be the speed of man in still water
and y be the speed of stream.
∴ Speed of man (x) = 60 km/hr
and speed of downstream = 75 km/hr.
∴ Speed of stream = 15 km/hr.

Hence upstream speed = 60 - 15 = 45 km/hr.

So time taken to cover 20 km = (20/45) × 60 min = 26.67min.

৬৬.

Two friends, Rina and Mina, start walking from the same point on a circular track in opposite directions at 7:00 AM. Rina walks at 1.5 rounds per hour, Mina walks at 2.5 rounds per hour. By what time will they have crossed each other 6 times?

ক
7 : 50 AM
খ
8 : 10 AM
গ
8 : 20 AM
ঘ
8 : 30 AM
ঙ
9 : 00 AM

ব্যাখ্যা

Question: Two friends, Rina and Mina, start walking from the same point on a circular track in opposite directions at 7:00 AM. Rina walks at 1.5 rounds per hour, Mina walks at 2.5 rounds per hour. By what time will they have crossed each other 6 times?

Solution:
Given,
Rina's speed = 1.5 rounds/hour
Mina's speed = 2.5 rounds/hour
Starting time = 7:00 AM

Since they walk in opposite directions,
Relative speed = (1.5 + 2.5) = 4 rounds/hour

∴ Time to meet 6 times = 6/4 = 1.5 hours = 1 hour 30 minutes

∴ They have crossed each other 6 times = (7 : 00 AM + 1 hour 30 minutes)
= 8 : 30 AM

৬৭.

At 8 am two trains started traveling towards each other from stations 300 Km apart. They passed each other at 12 noon. the same day. If the average speed of the faster train was 9 km more than that of the slower train, then what is the speed of the faster train in km/hr?

ক
ক) 40
খ
খ) 42
গ
গ) 45
ঘ
ঘ) None

ব্যাখ্যা

Question: At 8 am two trains started traveling towards each other from stations 300 Km apart. They passed each other at 12 noon. the same day. If the average speed of the faster train was 9 km more than that of the slower train, then what is the speed of the faster train in km/hr?

Solution:
ধরি
দ্রুতগতির ট্রেন এর গতিবেগ = x কি.মি./ঘণ্টা
ধীরগতির ট্রেন এর গতিবেগ =y কি.মি./ঘণ্টা

যাত্রার মোট সময় = 12 - 8 = 4 ঘণ্টা
এখানে
x + y = 300/4 = 75...............(1)
আবার
x - y = 9 .................(2)

(1) + (2) ⇒
x + y + x - y = 75 + 9
2x = 84
x = 42 কি.মি./ঘণ্টা

৬৮.

A bike rider increases his speed by 1 km after every 30 minutes. If the distance travelled in the 1st 30 minutes was 30 km then what was the total distance travelled in 6 hours?

ক
426 km
খ
213 km
গ
639 km
ঘ
none of these

ব্যাখ্যা

Given that,
Distance travelled in 1st 30 minutes = 30 km
Speed of the bike increases by 1 km after every 30 minutes
Distance travelled in 2^nd 30 minutes = 31 km
Distance travelled in 3^rd 30 minutes = 32km
6 hours contains 12 thirty minutes.
Total Distance Travelled = [30 + 31 + 32 + ... (12 terms)]
This is an Arithmetic Progression(AP) with
first term a = 35, number of terms n = 12 and common difference d = 1
Sum of the first n terms of an Arithmetic Progression(AP),
Sn = (n/2)[2a + (n-1)d]
where n =number of terms
Here, [30 + 31 + 32 +... (12 terms)]
S₁₂ = (12/2)[2 × 30 + (12-1)1]
= 6[60 + 11]
= 6 × 71
= 426
Hence, the total distance travelled = 426 km.

৬৯.

A rowing team rows a boat and covers a distance of 18 km in 6 hours while going upstream. When they go downstream, they cover a distance of 30 km in 5 hours. Find the speed of the boat in still water?

ক
ক) 4.5 km/h
খ
খ) 3.5 km/h
গ
গ) 2.5 km/h
ঘ
ঘ) 5.5 km/h

ব্যাখ্যা

The boat covers 15 km upstream in 5 hours and 24 km downstream in 4 hours
According to the question,
Downstream speed = 30/5 = 6 km/h
Upstream speed = 18/6 = 3 km/h

∴ Speed of the Boat in still water = 1/2 × (6 + 3) = 4.5 km/h

৭০.

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is-

ক
65.5 km/hr
খ
70 km/hr
গ
75 km/hr
ঘ
84 km/hr
ঙ
87.5 km/hr

ব্যাখ্যা

Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is-

Solution:
Let the speed of two trains be 7x and 8x km/hr.
Then,
8x = (400/4) = 100
∴ x = 100/8 = 12.5

Speed of first train = (7 × 12.5) km/hr = 87.5 km/hr.

৭১.

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

ক
ক) 20 sec
খ
খ) 22 sec
গ
গ) 23 sec
ঘ
ঘ) 24 sec

ব্যাখ্যা

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

Solution:
ট্রেন + ব্রিজের মোট দূরত্ব = ১৫০ + ৫০০ = ৬৫০ মি
ট্রেন + প্লাটফর্ম = ১৫০ + ৩৭০ = ৫২০ মি

৬৫০ মি অতিক্রম করে ৩০ সেকেন্ডে
১ মি অতিক্রম করে ৩০/৬৫০ সেকেন্ডে
৫২০ মি অতিক্রম করে (৩০ × ৫২০)/৬৫০ সেকেন্ডে
= ২৪ সেকেন্ডে

৭২.

How long will a boy take to run round a square field of side 35 meters, If he runs at the rate of 9 km/hr?

ক
56 sec
খ
54 sec
গ
52 sec
ঘ
50 sec
ঙ
55 sec

ব্যাখ্যা

Question: How long will a boy take to run round a square field of side 35 meters, If he runs at the rate of 9 km/hr?

Solution:
Speed = 9 km/hr = 9 × (5/18) m/sec = 5/2 m/sec

Distance = (35 × 4) m = 140 m.

Time taken = 140 × (2/5) sec= 56 sec

৭৩.

A truck travels the first 120 km at an average speed of 60 km/h and the next 120 km at an average speed of 40 km/h. What is its average speed for the entire journey in km per hour?

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

ব্যাখ্যা

Question: A truck travels the first 120 km at an average speed of 60 km/h and the next 120 km at an average speed of 40 km/h. What is its average speed for the entire journey in km per hour?

Solution:
প্রথম অংশের জন্য সময়:
সময় = দূরত্ব/গতিবেগ
= 120 কিমি / 60 কিমি/ঘন্টা
= 2 ঘন্টা

দ্বিতীয় অংশের জন্য সময়:
সময় = দূরত্ব/গতিবেগ
= 120 কিমি / 40 কিমি/ঘন্টা
= 3 ঘন্টা

মোট অতিক্রান্ত দূরত্ব = (120 + 120) কিমি = 240 কিমি
মোট সময় = (2 + 3) ঘন্টা = 5 ঘন্টা

গড় গতিবেগ = মোট অতিক্রান্ত দূরত্ব/মোট সময়
= 240 কিমি/5 ঘন্টা
= 48 কিমি/ঘন্টা

∴ পুরো যাত্রায় ট্রাকটির গড় গতিবেগ ছিল 48 কিমি/ঘন্টা।

৭৪.

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

ক
ক) 63 sec
খ
খ) 69 sec
গ
গ) 89 sec
ঘ
ঘ) 91 sec

ব্যাখ্যা

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

Solution:
Speed = 240/24 = 10 m/s

∴ Required time = (240 + 650) / 10 = 89 sec

৭৫.

A covers a certain distance in 3 hours with a constant speed of 60 km/h. What should be the speed of B to cover the same distance in 2 hours 30 minutes?

ক
ক) 78 km/h
খ
খ) 71 km/h
গ
গ) 72 km/h
ঘ
ঘ) 79 km/h

ব্যাখ্যা

A's time = 3 hours
A's speed = 60 km/h

B's time = 2 hours 30 minutes

Speed = Distance/time

D = 60 × 3 = 180 km

B's speed = 180/2.5
⇒ B's speed = 72 km/h
∴ B's speed is 72 km/h

৭৬.

The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. Time in which A reach the destination?

ক
4/5 hr
খ
4/3 hr
গ
5/3 hr
ঘ
5/4 hr

ব্যাখ্যা

Question: The speed of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. Time in which A reach the destination?
Solution:
here, ratio of speed is 3 : 4
as the ratio of time is inversly proportional to speed,
ratio of time = 4 : 3

ATQ,
4x - 3x = 20 min
x = 20 min = 1/3 hr

A takes total time of = 4 × 1/3 = 4/3 hr

৭৭.

From P and Q, two trains start moving towards each other at the same time. Their speeds are 120 km/h and 100 km/h, respectively. When the two trains meet each other, one train has covered 40 km more than the other train. Find the distance between P and Q?

ক
380 km
খ
440 km
গ
520 km
ঘ
400 km

ব্যাখ্যা

Question: From P and Q, two trains start moving towards each other at the same time. Their speeds are 120 km/h and 100 km/h, respectively. When the two trains meet each other, one train has covered 40 km more than other train. Find the distance between P and Q?

Solution:
Speeds are in the ratio 120 : 100 = 6 : 5
So distances covered in the same time are also in the ratio 6 : 5

Let distances be 6k and 5k.

∴ Difference = 6k - 5k = 40
∴ k = 40

∴ Total distance = 6k + 5k = 11k = 11 × 40 = 440 km

So the distance between P and Q is 440 km.

৭৮.

A train runs at the speed of 72 km/hr and crosses a 320 m long platform in 30 seconds. What is the length of the train?

ক
ক) 285 meters
খ
খ) 280 meters
গ
গ) 275 meters
ঘ
ঘ) 270 meters

ব্যাখ্যা

Question: A train runs at the speed of 72 km/hr and crosses a 320 m long platform in 30 seconds. What is the length of the train?

Solution:

Speed = (72 × 1000)/3600 m/sec = 20 m/sec
Time = 30 sec
Let the length of the train be x meters.

Now,
(x + 320)/30 = 20
⇒ x + 320 = 600
⇒ x = 600 - 320
∴ x = 280

∴ The length of the train is 280 meters.

৭৯.

Two trains, each 200 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the slower train is:

ক
ক) 60 km/hr
খ
খ) 30 km/hr
গ
গ) 40 km/hr
ঘ
ঘ) 70 km/hr

ব্যাখ্যা

Let the speed of the slower train be x m/sec.
Then, speed of the faster train = 2x m/sec.
Relative speed = (x + 2x) m/sec = 3x m/sec.

(200 + 200)/8= 3x
400/8 = 3x
x = (400/(3 × 8)
x = 50/3

Speed of the slower train = (50/3) × (18/5)
= 60 km/hr

৮০.

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

ক
200m
খ
300m
গ
600m
ঘ
700m

ব্যাখ্যা

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

Solution:
Let the length of the train be x meters
Then, length of the platform = (2x) meters

∴ Speed of the train = {72 × (5/18)} m/sec
= 20 m/sec

∴(x+2x)/20 = 45
⇒ 3x = 45 × 20
⇒ 3x = 900
⇒ x = 900/3 = 300

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

৮১.

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

ক
ক) 80 sec
খ
খ) 89 sec
গ
গ) 90 sec
ঘ
ঘ) 95 sec

ব্যাখ্যা

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

Solution:
ট্রেনটির মোট অতিক্রম করতে হবে = (240 + 650) মিটার = 890 মিটার

ট্রেনটি 240 মিটার অতিক্রম করতে সময় লাগে 24 সেকেন্ড
ট্রেনটি 1 মিটার অতিক্রম করতে সময় লাগে 24/240 সেকেন্ড
ট্রেনটি 890 মিটার অতিক্রম করতে সময় লাগে (24 × 890)/240 সেকেন্ড
= 89 সেকেন্ড

৮২.

Rizvi and Amin start simultaneously from a place A towards B 60 km apart. Rizvi's speed is 4km/h less than that of Amin. Amin, after reaching B, turns back and meets Rizvi at a place 12 km away from B. Rizvi's speed is -

ক
ক) 12 km/hr
খ
খ) 10 km/hr
গ
গ) 8 km/hr
ঘ
ঘ) 6 km/hr

ব্যাখ্যা

Let the speed of Rizvi be x kmph;
Hence, Amin's speed = (x + 4) kmph;
Distance covered by Amin = 60 + 12 = 72 km;
Distance covered by Rizvi = 60 - 12 = 48 km.

According to question,
⇒ 72/(x + 4) = 48/x
⇒ 3/(x + 4) = 2/x
⇒ 3x = 2x + 8
⇒ x = 8 kmph.

৮৩.

A boat runs at 22 km hour along the stream and 10 km per hour against the stream. Find the ratio of the speed of the boat in still water to that of the speed of the stream.

ক
ক) 2 : 3
খ
খ) 5 : 3
গ
গ) 7 : 3
ঘ
ঘ) 8 : 3

ব্যাখ্যা

ধরি
নৌকার বেগ = x কি.মি./ঘণ্টা
স্রোতের বেগ = y কি.মি./ঘণ্টা

x + y = ২২........... (১)
x - y =১০ ..............(২)
(১)নং ও (২) নং যোগ করে পাই
২x = ৩২
বা, x = ৩২/২
∴ x = ১৬
(১)নং হতে (২) নং বিয়োগ করে পাই
২y = ১২
বা, y = ১২/২
∴ y =৬

নির্ণেয় অনুপাত = ১৬ : ৬
= ৮ : ৩

৮৪.

A man travelled a certain distance by train at the rate of 25 kmph. and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, the distance was?

ক
10 km
খ
15 km
গ
20 km
ঘ
25 km

ব্যাখ্যা

Question: A man travelled a certain distance by train at the rate of 25 kmph. and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, the distance was?

Solution:
Let, the distance be = x km
∴Total time = 5 hours 48 minutes
= {5 + (48/60)}
= {5 + (4/5)} hours
= 29/5 hours

ATQ,
(x/25) + (x/4) = 29/5
⇒ (4x + 25x)/100 = 29/5
⇒29x/100 = 29/5
⇒ 5 × 29x = 29 × 100
⇒ x = (29 × 100)/(5 × 29)
⇒ x = 20 km

৮৫.

A man walk at a speed of 9 km/h. After every kilometer, he takes a rest of 4 minutes. How much time will he take to cover a distance of 6 km?

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

ব্যাখ্যা

Question: A man walk at a speed of 9 km/h. After every kilometer, he takes a rest of 4 minutes. How much time will he take to cover a distance of 6 km?

Solution:
Given,
Distance = 6 km
Speed = 9 km/h

∴ The man needs time = (Distance ÷ Speed)
= (6 ÷ 9) hours
= 2/3 hours
= (2/3 × 60) minutes
= 40 minutes

He will also rest 4 times after 1000, 2000, 3000, 4000 and 5000 meters
Total resting time = 4 × 5
= 20 minutes.

Total time = (40+ 20) minutes
= 60 minutes
= 1 hour

৮৬.

In a kilometer race, A beats B by 100 meters. B beats C by 100 meters. By how much meters does A beat C in the same race ?

ক
ক) 200 meters
খ
খ) 180 meters
গ
গ) 190 meters
ঘ
ঘ) 210 meters

ব্যাখ্যা

While A covers 1000 meters, B can cover 900 meters

While B covers 1000 meters, C can cover 900 meters

Let's assume that all three of them are running the same race.
So when B runs 900 meters,
C can run 900 × (9/10)
= 810

So A can beat C by = 1000 - 810 = 190 meters.

৮৭.

A monkey tries to ascend a greased pole which has a height of 14 m. He ascends 2 m in first two minutes and slips 1 m in the very next minute. If he continues to ascend in this fashion, how long does he take to reach the top of the pole?

ক
ক) 26 min
খ
খ) 24 min
গ
গ) 22 min
ঘ
ঘ) 25 min

ব্যাখ্যা

In every two minutes he is able to ascend 1 m.
In this fashion he ascends up to 12 m because when he reaches at the top he does not slip down.
Thus, up to 12 m he takes 12×2=24 min. and for the last 2 m he takes 1 m.
Therefore, total time taken by him is 24+1 = 25 min to reach the top.

৮৮.

A car is driven at the speed of 100 km/hr and stops for 10 minutes at the end of every 150 km. To cover a distance of 1000 km, it will take.

ক
ক) 11 hours
খ
খ) 9 hours
গ
গ) 10 hours
ঘ
ঘ) 12 hours

ব্যাখ্যা

Time taken to cover 150 km = (1 hr 30 min + 10 min) = 1 hr 40 min = 1(2/3) hr = 5/3 hr
Time taken to cover (150×6) i.e., 900 km = (5/3)×6 hrs = 10 hrs.
Remaining 100 km is covered in 1 hour.
Total time taken = (10+1) hrs = 11 hrs.

৮৯.

Salman is traveling in a constant velocity. The time ratio that he needs to pass the distances of 300 km and 500 km is:

ক
3 : 5
খ
5 : 3
গ
2 : 3
ঘ
3 : 2

ব্যাখ্যা

Question: Salman is traveling in a constant velocity. The time ratio that he needs to pass the distances of 300 km and 500 km is:

Solution:
if the velocity or speed remain the same,
time is proportional to distance.

∴ t₁ : t₂ = 300 : 500
t₁ : t₂ = 3 : 5

৯০.

Shafiq performs 6/15 of the total journey by rail 8/20 by train and the remaining 12 km on foot, his total journey is:

ক
ক) 50 km
খ
খ) 65 km
গ
গ) 60 km
ঘ
ঘ) 45 km

ব্যাখ্যা

Question: Shafiq performs 6/15 of the total journey by rail 8/20 by train and the remaining 12 km on foot, his total journey is:

Solution:
Let, the total journey be x km.

ATQ,
∴ (6x/15) + (8x/20) + 12 = x
or, (24x + 24x + 720)/60 = x
or, 24x + 24x + 720 = 60x
or, 60x - 48x = 720
or, 12x = 720
or, x = 60

∴ Total journey = 60 km.

৯১.

A train takes 50 sec to cross a boy travelling at 6 km/h in the opposite direction to it. Another train which is half as long as and 25% faster take 30 sec to cross the stationary pole. Find the approximate length of the second train.

ক
ক) 100 m
খ
খ) 125 m
গ
গ) 190 m
ঘ
ঘ) 148 m

ব্যাখ্যা

Question: A train takes 50 sec to cross a boy travelling at 6 km/h in the opposite direction to it. Another train which is half as long as and 25% faster take 30 sec to cross the stationary pole. Find the approximate length of the second train.

Solution:
Let m be the length of the first train.
Let r be the speed of the first train in meters per second.

then m=50(r+5/3m/s).

Let n be the length of the second train.
Since the second train is half as long as the first train
we know that n=1/2m.

Let 1.25r be the speed of the second train.
The length of the second train is n = 30 ×1.25r

Since n=1/2m

we can substitute to make 1/2m=30 × 1.25r.
Or m = 2 × 30 × 1.25r = 75r.
m =75r.

We can now combine the 2 equations:
50(r+5/3) = 75r
50r+250/3=75r
150r+250=225r
75r=250
r =10/3.

m =75r = 75 × 10/3 = 250 meters.

The second train is 125 meters long.

৯২.

A train reaches from A to B in 5 hours travelling at a speed of 60 km/hr. If its speed is increased by 15 km/hr, then the time of journey is reduced by-

ক
30 minutes
খ
45 minutes
গ
1 hour
ঘ
1.5 hour

ব্যাখ্যা

Question: A train reaches from A to B in 5 hours travelling at a speed of 60 km/hr. If its speed is increased by 15 km/hr, then the time of journey is reduced by-

Solution:
Total distance = speed × time
= 60 × 5 = 300 km

If speed increased then new speed = 60 + 15 = 75 km/hr

New time = Total distance/speed
= 300/75
= 4 hour

Time reduced by 5 - 4 = 1 hour

৯৩.

Two buses start from a bus terminal with a speed of 20 km/h at an interval of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at an interval of 8 minutes?

ক
ক) 3 kmph
খ
খ) 4 kmph
গ
গ) 5 kmph
ঘ
ঘ) 7 kmph

ব্যাখ্যা

Let, Speed of the man is x Kmph.
Distance covered in 10 minutes at 20 kmph = distance covered in 8 minutes at (20 + x) kmph.
⇒ 20 × (10/60) = 8/60 × (20 + x)
⇒ 200 = 160 + 8x
⇒ 8x = 40
Hence, x = 5 kmph.

৯৪.

Excluding stoppages, a train travels at 72 km/h and including stoppages, its average speed is 60 km/h. For how many minutes does the train stop per hour?

ক
12 minutes
খ
10 minutes
গ
8 minutes
ঘ
5 minutes

ব্যাখ্যা

Question: Excluding stoppages, a train travels at 72 km/h and including stoppages, its average speed is 60 km/h. For how many minutes does the train stop per hour?

Solution:
At its moving speed of 72 km/h, the time required to cover 60 km is:
∴ Time moving = distance/speed
= 60 km/72 km/h
= 60/72 hours
= 5/6 hours
= (5/6) × 60 minutes
= 50 minutes

We know,
1 hour = 60 minutes

∴ Stopping time = 60 - 50 = 10 minutes

∴ The train stops for 10 minutes per hour.

৯৫.

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

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

ব্যাখ্যা

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

Solution:
মোটরযানের বেগ ২৬ কিমি/ঘণ্টা

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

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

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

৯৬.

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 these two cities is 330km then at what time will they meet?

ক
ক) 4:00 pm
খ
খ) 5:00 pm
গ
গ) 5:30 pm
ঘ
ঘ) 6:00 pm

ব্যাখ্যা

Question: 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 these two cities is 330km then at what time will they meet?

Solution:
ধরি
ট্রেন দুটি ১PM এর x ঘণ্টা পর মিলিত হয়।

প্রথম ট্রেনটির অতিক্রান্ত দূরত্ব = 75(x - 1)
দ্বিতীয় ট্রেনটির অতিক্রান্ত দূরত্ব = 60x

প্রশ্নমতে
75(x - 1) + 60x = 330
75x - 75 + 60x = 330
135x = 330 + 75
135x = 405
x = 405/135
x = 3

ট্রেন দুটি 1PM এর 3 ঘণ্টা পর মিলিত হয়।
4 PM এ পরস্পর মিলিত হবে।

৯৭.

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

ক
6 minutes
খ
8 minutes
গ
12 minutes
ঘ
14 minutes

ব্যাখ্যা

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

Solution:
Ratio of the speed of A, B and C = 6 : 3 : 1
Then, ratio of time taken;
= 1/6 : 1/3 : 1 = 1 : 2 : 6

Hence, time taken by A = 72/6
= 12 minutes.

৯৮.

A train 125 m long passes a person, running at 8 kmph in the same direction in which the train is going in 25 seconds. The speed of the train is:

ক
ক) 22 km/hr.
খ
খ) 36 km/hr.
গ
গ) 30 km/hr.
ঘ
ঘ) 26 km/hr.

ব্যাখ্যা

Speed of the train relative to Person
= (125/25) m/s.
= 5 m/s.

∴ 5 × (18/5) km/hr
= 18 km/hr

Let the speed of the train be x km/hr.
then, relative speed = (x - 8) km/hr.

So, (x - 8) = 18
⇒ x = 26 km/hr.

৯৯.

The average speed of a bus is one-third of the speed of a train. The train covers 1200 km in 16 hours. How much distance will the bus cover in 48 minutes?

ক
ক) 30 km
খ
খ) 25 km
গ
গ) 20 km
ঘ
ঘ) 50 km

ব্যাখ্যা

Question: The average speed of a bus is one-third of the speed of a train. The train covers 1200 km in 16 hours. How much distance will the bus cover in 48 minutes?

Solution:
Speed of the train = (1200/16) km/hr.
= 75 km/hr.

Speed of the bus = (1/3)×75 km/hr.
= 25 km/hr.

Distance covered by the bus in 60 min = 25 km
Distance covered by the bus in 48 min =(25/60) × 48 = 20 km

১০০.

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

ক
ক) 2 km/hr
খ
খ) 2.5 km/hr
গ
গ) 3 km/hr
ঘ
ঘ) 3.5 km/hr
ঙ
ঙ) 4 km/hr

ব্যাখ্যা

Let the speed of the stream be x km/hr
Then speed downstream = (10 + x) km/hr
Speed upstream
= (10−x)km/hr
∴ 26/(10+x) = 14/(10−x)
⇒ 260−26x = 140+14x
⇒ 40x = 120
⇒ x = 3km/hr