ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: A train passes a man at 110 kmph running towards the train at the speed of 10 kmph. If it took 3 seconds to cross the man, what would be the length of the train?

Solution: 
As both of them are facing towards each other.
total speed will be = 110 + 10 kmph
= 120 kmph

length of the train = 120 × (3/3600) km
= 0.1 km
= 100 m

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.

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 the length of the train is x m and speed is s.
ATQ,
s = (x + 800)/100 and,
s = (x + 400)/60

∴ (x + 800)/100 = (x + 400)/60
or, 60x + 48000 = 100x + 40000
or, 40x = 8000
or, x = 200 m

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 the stream is:

Solution:
Let man's rate upstream be x kmph.
Then, his rate downstream = 2x kmph.

∴ (Speed in still water) : (Speed of stream) = {(2x + x)/2} : {(2x - x)/2}
= (3x/2) : (x/2)
= 3 : 1

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

Solution: 
Let the distance travelled by x km.

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

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

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

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

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

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:
Given,
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.

So, Total time taken = (105/15 ) + (105/21) hours
= (7 + 5) hours
= 12 hour

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/h 

ATQ,
5x = 60
⇒ x= 60/5 
∴ x = 12

Speed of bike = 8x = (8 × 12) = 96 km/h

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.

Question: A man can row upstream at 10 kmph and downstream at 20 kmph. Find the man's rate in still water and the rate of the stream.

Solution:
If a is rate downstream and b is rate upstream 
Rate in still water = (a + b)/2 
Rate of current = (a - b)/2 

Rate in still water = (20 + 10)/2 = 15 kmph 
Rate of current = (20 - 10)/2 = 5 kmph 

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

Question: A boat can travel 48 km upstream in 6 hours. If the speed of the stream is 2 km/hr, how much time will the boat take to cover a distance of 120 km downstream?

Solution:
Distance covered by a boat in 6 hours = 48 km
Rate upstream of boat = 48/6 
= 8 km/hr

Now,
Speed of stream = 2 km/hr
∴ Speed of boat in still water = (8 + 2)
= 10 km/hr

∴ Rate downstream of boat = (10 + 2) km/hr
= 12 km/hr

∴ Time taken in covering 120 km distance = 120/12 
= 10 hours

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

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

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

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

Question: Rahman is a boatman. He can row a boat at the speed of 5 km/hr upstream and 15 km/hr downstream. Find the speed of the stream.

Solution:
Let’s denote:
B as Speed of the boat in still water (km/h)
S as Speed of the stream (km/h)

Speed of the boat upstream is the speed of the boat in still water minus the speed of the stream:
B - S = 5 km/hr -------- (1)

Speed of the boat downstream is the speed of the boat in still water plus the speed of the stream:
B + S = 15 km/hr -------- (2)

(1) + (2)
B - S = 5
B + S = 15
2B = 20
∴ B = 10 km/hr

Putting the value of B in (2)
∴ S = (15 - 10) km/hr = 5 km/hr

∴ The speed of the stream is 5 km/hr