ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: Two trains of equals length, running in opposite direction, pass a pole in 48 and 24 seconds. The trains will cross each other in-

Solution:
Let,
the length of both train be = a meters
Speed of the first train = (a/48) m/s
and speed of the second train = (a/24) m/s

When running in opposite directions, relative speed = (a/48) + (a/24)
= (a + 2a)/48
= 3a/48
= a/16

Now,
to cross each other, distance to be covered = (a + a) = 2a meters

∴ the two train will cross each other = (2a)/(a/16)
= 32 sec

Question: Rafiq and Abir start simultaneously from a place A towards B 50 km apart. Rafiq's speed is 3km/h less than that of Abir. Abir, after reaching B, turns back and meets Rafiq at a places 10 km away from B. Rafiq's speed is-

Question:
Let, the speed of Rafiq be = a kmph
Now,
Abir's speed = (a + 3) kmph

∴ Distance covered by Abir = (50 + 10) = 60 km
∴ Distance covered by Rafiq  = (50 - 10) = 40 km.

ATQ,
60/(a + 3) = 40/a
⇒ 60a = 40a + 120
⇒ 60a - 40a = 120
⇒ 20a = 120
⇒ a = 120/20
∴ a = 6 kmph

Question: A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is-

Solution:
Let,
the speed of the stream = b mph

Then,
Speed downstream = (10 + b) mph
Speed upstream = (10 - b) mph

ATQ,
{36/(10 - b) - 36/(10 + b)} = 90/60
⇒ (72b × 60) = 90(100 - b²)
⇒ b² + 48b - 100 = 0
⇒ (b + 50)(b - 2) = 0
⇒ b = 2mph

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]

Question: A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of total time, to cover the remaining distance in the remaining time, his speed in kmph must be-

Solution:
Remaining distance = (6 - 3) km
= 3 km

∴ remaining time = (1/3) × 45
= 15 min
= 15/60 hr
= 1/4 hr

∴ Required speed = 3/(1/4) kmph
= 12 kmph

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.

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.

Question: If Rahim walks at 14 km/hr instead of 10 km/hr for a certain time, he would have walked 30 km more. if Rahim walks at a speed of 10 km/hr, the distance travelled by him within that time is-

Solution:
Let,
the actual distance travelled be = a km.

Then,
a/10 = (a + 30)/14
⇒ 14a = 10a + 300
⇒ 14a - 10a = 300
⇒ 4a = 300
⇒ a = 300/4
∴ a = 75 km

Question: 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?

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

Then,
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

Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Solution:
Speed = {54 × (5/18)} m/sec
=15 m/sec
∴ Length of the train =(15 × 20)m
=300m

Let,
the length of the platform be = a metres
Then,
(a + 300)/36 = 15
⇒ a + 300 = 540
⇒ a = 240m

Question: A bus travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr and the last one-third distance with a speed of 60 km/hr. The average speed of the bus for the whole journey is:

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

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

∴ Average speed = (a × 18)/a km/hr
= 18 km/hr

Question: A man can row at 4 kmph in still water. If the velocity of the current is 2 kmph and it takes him 12 hours to row to a place and comes back, how far is the place?

Solution:
Downstream speed = (4 + 2) = 6 kmph
Upstream speed = (4 - 2) = 2 kmph

Let, the required distance be = a km

ATQ,
(a/6) + (a/2) = 12
⇒ (a + 3a)/6 = 12
⇒ 4a = 72
⇒ a = 18

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

Solution:
Distance covered = (108 + 112)
= 220 meter.
and Time = 6 seconds.

∴ Relative speed = (220/6) = (110/3) m/s.
= (110 × 3600)/(3 × 1000) km/hr
= 132 km/hr

Now,
50 + Speed of second train = 132 km/hr

∴ Speed of second train = (132 - 50) km/hr
= 82 km/hr.

Question: A train 165 m long is running at a uniform speed of 54 km/hr. How much time will it take to cross a pole?

Solution:
Speed of train = 54 km/hr
= 54 × 5/18 m/sec
= 15 m/sec

Length of the train = 165 meters

Therefore, time taken by the train to cross a pole = length of train/speed of train
= 165/15 sec
= 11 sec

Thus, train takes 11 seconds to cross the pole.

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 = a kmph
Then, his rate downstream = 2a kmph

Now,
(speed in still water) : (Speed of stream)
= {(2a + a)/2 : (2a - a)/2}
= (3a/2) : (a/2)
= 3 : 1