Time and Speed - Train and Boat

PrepBank · পাতা ১৫ / ১৫ · ১,৪০১–১,৪৩১ / ১,৪৩৯

১,৪০১.

A train takes 50 seconds to cross a platform 300 meters long and 35 seconds to cross another platform 150 meters long. Find the length of the train.

ক
200 meters
খ
300 meters
গ
400 meters
ঘ
240 meters

ব্যাখ্যা

Question: A train takes 50 seconds to cross a platform 300 meters long and 35 seconds to cross another platform 150 meters long. Find the length of the train.

Solution:
Let the length of the train = x meters

Then,
For the first platform, the distance covered by the train = (x + 300) meters
And,
For the second platform, the distance covered by the train = (x + 150) meters

According to the question,
(x + 300)/50 = (x + 150)/35
⇒ 50(x + 150) = 35(x + 300)
⇒ 50x + 7500 = 35x + 10500
⇒ 50x - 35x = 10500 - 7500
⇒ 15x = 3000
⇒ x = 3000/15
⇒ x = 200

∴ The length of the train is 200 meters

১,৪০২.

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 1.5 hour, at what speed it needs to travel?

ক
186.67 km/hr
খ
240.50 km/hr
গ
210 km/hr
ঘ
280 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 1.5 hour, at what speed it needs to travel?

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

Time = 1.5 hour
∴ Required Speed = 280/1.5 = 186.67 km/hr

১,৪০৩.

An engine pulls four identical carriages. The engine is 2/3the length of a carriage and the total length of the train is 86.8m. Find the length of the engine.

ক
ক) 12.4 m
খ
খ) 12 m
গ
গ) 11.5 m
ঘ
ঘ) 13 m

ব্যাখ্যা

ধরি,
১টি বগির দৈর্ঘ্য = x মিটার
চারটি বগির দৈর্ঘ্য = 4x মিটার

প্রশ্নমতে,
4x + (2/3)x = 86.8
(12x + 2x)/3 = 86.6
14x/3 = 86.6
x = 86.6(3/14)
x = 18.55

ইঞ্জিনের দৈর্ঘ্য = 18.55 × (2/3)
= 12.36 মিটার
= 12.4 মিটার

১,৪০৪.

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

ক
ক) 10 km/hr
খ
খ) 12 km/hr
গ
গ) 16 km/hr
ঘ
ঘ) 18 km/hr

ব্যাখ্যা

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

Speed of the boat in upstream = 22/2.2= (22 × 10)/22 =10km/hr.

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

১,৪০৫.

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:

ক
12 hours
খ
16 hours
গ
18 hours
ঘ
20 hours

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

১,৪০৬.

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

ক
300 kmph
খ
360 kmph
গ
600 kmph
ঘ
720 kmph
ঙ
800 kmph

ব্যাখ্যা

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

Solution:
Distance = (240 × 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr.

∴ Required speed = 1200 × (3/5) km/hr = 720 km/hr.

১,৪০৭.

A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current:

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

ব্যাখ্যা

Speed upstream = 3/(20/60)
= 9 km/hr.
Speed downstream = 3/(18/60)
= 10 km/hr.
Rate of current = (10 - 9)/2
= 1/2 km/hr.

১,৪০৮.

A man rowed 4 miles upstream in 2 hours. If the river current is 1 mile per hour, how long will it take him to return downstream?

ক
3 hour
খ
2 hour
গ
1 hour
ঘ
5 hour
ঙ
None

ব্যাখ্যা

Question: A man rowed 4 miles upstream in 2 hours. If the river current is 1 mile per hour, how long will it take him to return downstream?

Solution:
Let,
the velocity of the boat in still water = x mph
and the velocity of the stream = y mph = 1 mph

In upstream, he covers 4 miles in 2 hours.
∴ Upstream speed = 4 ÷ 2 = 2 mph

ATQ,
x - y = 2
⇒ x - 1 = 2
⇒ x = 3

So, downstream speed = x + y = 3 + 1 = 4 mph

Time to row 4 miles downstream = 4 ÷ 4 = 1 hour

∴ The return trip will take 1 hour.

১,৪০৯.

A cyclist completes a journey in 8 hours. He travels the first half of the journey at the rate of 15 km/hr and the second half at the rate of 25 km/hr. Find the total journey in km.

ক
150 km
খ
180 km
গ
200 km
ঘ
240 km

ব্যাখ্যা

Question: A cyclist completes a journey in 8 hours. He travels the first half of the journey at the rate of 15 km/hr and the second half at the rate of 25 km/hr. Find the total journey in km.

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

প্রথম অর্ধেক যাত্রায়, সময় = দূরত্ব/গতিবেগ
= (D/2)/15 ঘন্টা
= D/30 ঘন্টা

দ্বিতীয় অর্ধেক যাত্রায়, সময় = দূরত্ব/গতিবেগ
= (D/2)/25 ঘন্টা
= D/50 ঘন্টা

প্রশ্নমতে,
D/30 + D/50 = 8
⇒ (5D + 3D)/150 = 8
⇒ 5D + 3D = 8 × 150
⇒ 8D = 1200
⇒ D = 1200/8
⇒ D = 150 কিমি

সুতরাং, মোট যাত্রার দূরত্ব হলো 150 কিমি।

১,৪১০.

A man runs at a speed of 7 km per hour and he increases his speed every hour by 1 km per hour. In how many hours will he cover 19.5 km?

ক
ক) 1(1/4) hours
খ
খ) 2(1/2) hours
গ
গ) 3(1/3) hours
ঘ
ঘ) 3 hours

ব্যাখ্যা

The man starts with 7 kmph
Distance covered in first 1 hour = 7 km
He increases his speed every hour by 1 km.
Speed in 2nd hour = 8 km/hr
Distance covered in 2nd hour = 8 km
Remaining distance = 19.5 - (7 + 8)
19.5 - 15
= 4.5 km
Speed in the third hour = 9 km/hr
Time taken to cover 4.5 km at 9 km/hr
= 4.5/9
= 1/2 hour.
Therefore,
Total time = 1 + 1 + (1/2) hours = 2 (1/2) hours.
Hence, the answer is 2(1/2) hours.

১,৪১১.

A man goes by motor boat a certain distance upstream at 15 km/hr and return the same downstream at 20 kin/hr. The total time taken for the journey was 7 hrs. Find how far did he go.

ক
60 km
খ
50 km
গ
40 km
ঘ
120 km
ঙ
None of above

ব্যাখ্যা

d/20 + d/15 = 7
Therefore, d = 60 km

১,৪১২.

The ratio between the speeds of two trains is 5 : 6. If the second train runs 360 km in 3 hours, then the speed of the first train is:

ক
90 km/hr
খ
95 km/hr
গ
100 km/hr
ঘ
110 km/hr

ব্যাখ্যা

Question: The ratio between the speeds of two trains is 5 : 6. If the second train runs 360 km in 3 hours, then the speed of the first train is:

Solution:
Let,
the speed of first train be 5x
the speed of second train be 6x

ATQ,
6x = 360/3
Or, 6x = 120
Or, x = 120/6
Or, x = 20

∴ Speed of first train = 5x = 5 × 20 = 100 km/hr.

১,৪১৩.

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

ক
ক) 80
খ
খ) 89
গ
গ) 90
ঘ
ঘ) 95

ব্যাখ্যা

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

১,৪১৪.

Two trains, each 100 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 faster train is:

ক
ক) 30 km/hr
খ
খ) 45 km/hr
গ
গ) 60 km/hr
ঘ
ঘ) 75 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.
So,(100 + 100)/8 = 3x
⇒ 24x = 200
⇒ x = 25/3
So, speed of the faster train =50/3 m/sec
= (50/3) x (18/5) km/hr
= 60 km/hr.

১,৪১৫.

A boat covers a certain distance in half an hour downstream with the speed of 20km/hr in still water and the speed of the current is 4km/hr. Then the distance travelled by the boat is:

ক
6km
খ
7km
গ
12km
ঘ
4km

ব্যাখ্যা

Given that,
The speed of a boat in still water is 20 km/hr
The speed of the stream is 4 km/hr.
Then,
The speed downstream = (20 + 4) km/hr
= 24 km/hr
The distance travelled in half an hour = 24 x 1/2
= 12 km
Hence the distance travelled by the boat is 12 km.

১,৪১৬.

A wheel rotates 10 times per minute and moves 20 feet during each rotation, How many feet does the wheel move in 1 hour.

ক
1200
খ
600
গ
12,000
ঘ
None

ব্যাখ্যা

Question: A wheel rotates 10 times per minute and moves 20 feet during each rotation, How many feet does the wheel move in 1 hour.

Solution:
Number of rotation per hour = 10 × 60 = 600 ft
Movement of the wheel per hour = 600 × 20 = 12000 ft

১,৪১৭.

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

ক
ক) 5.2 km/hr
খ
খ) 2.5 km/hr
গ
গ) 3.5 km/hr
ঘ
ঘ) 5.3 km/hr
ঙ
ঙ) None of these

ব্যাখ্যা

Let rate of stream be y km/hr, distance be d km
time upstream = 2 (time downstream)
⇒ d/(7.5 − y) = 2d/(7.5 + y)
⇒ 2( 7.5 − y ) = 7.5 + y
⇒ 15 − 2 y = 7.5 + y
⇒ 3 y = 7.5
⇒ y = 2.5

১,৪১৮.

A train having length 150 m passes a platform of 550 m length. The time taken for it is 56 seconds. In how much time will this train take to pass a platform of 250 m length?

ক
24 seconds
খ
30 seconds
গ
28 seconds
ঘ
32 seconds

ব্যাখ্যা

Question: A train having length 150 m passes a platform of 550 m length. The time taken for it is 56 seconds. In how much time will this train take to pass a platform of 250 m length?

Solution:
We know,
When a train passes a platform, the total distance to be covered is,
Length of train + Length of platform

Case 1:
Distance covered = 150 m + 550 m = 700 m
Time taken = 56 seconds
∴ Speed of the train = Distance/Time
= 700/56
= 12.5 m/s

Case 2:
Length of new platform = 250 m
∴ Total distance to be covered now = 150 + 250 = 400 m
Time taken to pass the new platform = Distance/Speed
= 400m/12.5 m/s
= 32 seconds

So the train will take 32 seconds to pass the platform of 250 m length.

১,৪১৯.

A cyclist moving on a circular track of radius 105 meters completes one revolution in 3 minutes. What is the average speed of cyclist (approx.)?

ক
ক) 330 m/min
খ
খ) 260 m/min
গ
গ) 220 m/min
ঘ
ঘ) 240 m/min

ব্যাখ্যা

Question: A cyclist moving on a circular track of radius 105 meters completes one revolution in 3 minutes. What is the average speed of cyclist (approx.)?

Solution:
Distance covered in one complete revolution
= 2πr
= (2 × 105 × 22)/7
= 660 m

Average speed = 660/3 = 220 m/min

১,৪২০.

A man can row 12 km/hr in still water. If the speed of the current is 4 km/hr, he takes 3 hours more upstream than downstream. What is the distance (in km)?

ক
ক) 48 km
খ
খ) 50 km
গ
গ) 64 km
ঘ
ঘ) 72 km

ব্যাখ্যা

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

Let, The distance is x km
Now
x/8 – x/16 = 3
=(2x - x)/16 = 3
= x/16 = 3
∴ x = 48 km

১,৪২১.

A boy walked 20 minutes at 3km/hr and ran 20 minutes at 15km/hr. The total distance covered by the boy is -

ক
2km
খ
3km
গ
6km
ঘ
8km

ব্যাখ্যা

Question: A boy walked 20 minutes at 3km/hr and ran 20 minutes at 15km/hr. The total distance covered by the boy is -

Solution:
first 20 minutes he covered
= 3 × 20/60 km
= 1km

in the second 20 minutes, he covered
= 15 × 20/60 km
= 5km

total distance = 1 + 5 = 6km

১,৪২২.

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 15 minutes. How long will it take to go 9 km in stationary water?

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

ব্যাখ্যা

Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 15 minutes. How long will it take to go 9 km in stationary water?

Solution:
Rate downstream = (1/15 × 60) km/h
= 4 km/h

Rate upstream = 2 km/h

Speed in still water = (4 + 2)/2 km/h
= 3 km/h

Required time = (9/3) h
= 3 h

১,৪২৩.

Train A passes a lamp post in 3 seconds and 900 meter long platform in 30 seconds. How much time will the same train take to cross a platform which is 800 meters long? (in seconds)

ক
24 seconds
খ
27 seconds
গ
33 seconds
ঘ
37 seconds
ঙ
None of the above

ব্যাখ্যা

Question: Train A passes a lamp post in 3 seconds and 900 meter long platform in 30 seconds. How much time will the same train take to cross a platform which is 800 meters long? (in seconds)

Solution:
Let, the length of the train is = x m.
and its speed is = v. m/s.

∴ Distance = Speed × time [S = V × T]
x = v × 3 .........(i)
(x + 900) = v × 30 ........(ii)

Dividing the eqn. (i) by (ii)
x/(x + 900) = 1/10
⇒ 10x = x + 900
⇒ 9x = 900.
⇒ x = 900/9
⇒ x = 100 m.

putting x = 100 in eqn. (1).
100 = v × 3
⇒ v = 100/3 m/s.

Let, the train crosses a 800 m. long platform in t seconds.
(x + 800) = v × t .........(iii) [ S = V × T]
⇒ (100 + 800) = (100/3) × t [putting x= 100 and v= 100/3]
⇒ 900 = (100/3) × t
⇒ t = (900 × 3)/100
⇒ t = 2700/100
⇒ t = 27 seconds.

১,৪২৪.

A man runs opposite to a train at 10 km/hr. The relative speed between them is 40 km/hr. If it takes 18 seconds for the train to pass the man when he is at rest, find the length of the train.

ক
200 meters
খ
150 meters
গ
300 meters
ঘ
250 meters
ঙ
None of these

ব্যাখ্যা

Question: A man runs opposite to a train at 10 km/hr. The relative speed between them is 40 km/hr. If it takes 18 seconds for the train to pass the man when he is at rest, find the length of the train.

Solution:
Relative speed = Train’s speed + Man’s speed
⇒ vt + 10 = 40
⇒ vt = 40 - 10
⇒ vt = 30 × (5/18) = 25/3 m/s
∴ vt = 25/3 m/s

∴ Length of the train = Speed × Time to cross
= (25/3) × 18
= 150 meters

১,৪২৫.

Speed of a boat in standing water is 10 kmph and the speed of the stream is 2.5 kmph. A man rows to a place at a distance of 112.5 km and comes back to the starting point. The total time taken by him is:

ক
ক) 20 hours
খ
খ) 21 hours
গ
গ) 22 hours
ঘ
ঘ) 24 hours

ব্যাখ্যা

Speed upstream = 7.5 kmph.
Speed downstream = 12.5 kmph.

∴ Total time taken =(112.5/7.5) +(112.5/12.5)
= (15 + 9) hours
= 24 hours

১,৪২৬.

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
60 kmph
খ
65 kmph
গ
90 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

১,৪২৭.

Sumi and Shila start simultaneously from a place A towards B 120 km apart. Sumi's speed is 4 km/h less than that of Shila. Shila, after reaching B, turns back and meets Sumi at a place 20 km away from B. Find Sumi's speed-

ক
6 kmph
খ
8 kmph
গ
10 kmph
ঘ
12 kmph

ব্যাখ্যা

Question: Sumi and Shila start simultaneously from a place A towards B 120 km apart. Sumi's speed is 4 km/h less than that of Shila. Shila, after reaching B, turns back and meets Sumi at a place 20 km away from B. Find Sumi's speed-

Question:
Let, the speed of Sumi be = a kmph
Now,
Shila's speed = (a + 4) kmph

∴ Distance covered by Sumi = (120 + 20) = 140 km
∴ Distance covered by Rafiq = (120 - 20) = 100 km.

ATQ,
140/(a + 4) = 100/a
⇒ 140a = 100a + 400
⇒ 140a - 100a = 400
⇒ 40a = 400
⇒ a = 400/40
∴ a = 10 kmph

১,৪২৮.

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

ক
60 km
খ
55 km
গ
50 km
ঘ
40 km

ব্যাখ্যা

Question: Rahim performs 6/15 of the total journey by rail 8/20 by bus 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
⇒ (24x + 24x + 720)/60 = x
⇒ 24x + 24x + 720 = 60x
⇒ 60x - 48x = 720
⇒ 12x = 720
∴ x = 60

∴ Total journey = 60 km.

১,৪২৯.

Two trains each 500 meter long, are running in opposite directions on parallel tracks. If their speeds are 45 km/hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is -

ক
ক) 50 seconds
খ
খ) 58 seconds
গ
গ) 22 seconds
ঘ
ঘ) 24 seconds

ব্যাখ্যা

Relative speed = (45 + 30) km/hr.
= 75 km/hr.
= 75 × (5/18) km/hr.
= (125/6) m/s.
We are calculating the time taken by the slower train to pass the driver of the faster one.
Hence, distance = length of the slower train = 500 meter.
Time = 500/(125/6)
= 500 × (6/125)
= 24 seconds.

১,৪৩০.

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from the opposite direction in 6 seconds. The speed of the second train is -

ক
ক) 66 km/hr
খ
খ) 54 km/hr
গ
গ) 48 km/hr
ঘ
ঘ) 82 km/hr

ব্যাখ্যা

Distance covered = (108 + 112) = 220 meter.
Time taken = 6 seconds.
Relative speed = 220/6 = 110/3 m/s.
= (110/3) × (18/5) km/hr
= 132 km/hr.

ATQ, 50 + Speed of second train = 132 km/hr.
⇒ Speed of second train = (132 - 50) = 82 km/hr.

১,৪৩১.

A train left 30 minutes later than the Schedule time and to reach its destination in time it increased its speed by 250 km/hr. If the target is 1,500 km away, find the speed of the train?

ক
ক) 800 km/hr
খ
খ) 750 km/hr
গ
গ) 715 km/hr
ঘ
ঘ) 850 km/hr

ব্যাখ্যা

Question: A train left 30 minutes later than the Schedule time and to reach its destination in time it increased its speed by 250 km/hr. If the target is 1,500 km away, find the speed of the train?

Solution:
Let, the usual speed of plane be x km/hr
and the increased speed of the plane be y km/hr.
⇒ y = (x + 250) km/hr
Distance =1500 km [Given]

According to the question,
(Scheduled time) - (time taken at increased speed) = 30 minutes = 0.5 hours.
1500/x - 1500/y = 12
⇒ 1500/x - 1500/(x + 250) = 12 [∵ Time = Distance Speed]
⇒ (1500x + 375000 - 1500x)/x(x + 250) = 1/2
⇒ x(x + 250) = 750000
⇒ x²+ 250x - 750000 = 0
⇒ x² + 1000x - 750x - 750000 = 0
⇒ x(x + 1000) - 750(x + 1000) = 0
⇒ (x - 750)(x + 1000) = 0
⇒ x = 750 or, x = - 1000
But speed cannot be negative.

∴ The usual speed is 750 km/hr.