ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: The length of the bridge, which a train 150 metres long and travelling at 45 km/h can cross in 30 seconds, is-

Solution:
Given,
Speed = 45 km/hr
= 45 × (5/18) m/sec
=25/2 m/sec
Time = 30 sec

Let, the length of bridge = x metres

Now
(150 + x)/30 = 25/2
⇒ 300 + 2x = 750
⇒ 2x = 750 - 300
⇒ 2x = 450
⇒ x = 450/2
∴ x = 225

Question: Walking 3/5 of his normal speed, Sami is 20 minutes late in reaching his coaching. The usual time taken by him to cover the distance between his home and coaching ?

Solution:
Let,
Distance y meter and speed x meter/min.
usual time taken y/x min

According to the question,
(y/3x/5) - (y/x) = 20
⇒ (y/x) {(5/3) - 1} = 20
⇒ (y/x) (2/3) = 20
∴ (y/x) = 30
 
∴ The usual time taken by Sami to reach his coaching = 30 minutes

Qustion: A man rows downstream at 35 km/h and rows upstream at 25 km/h. At what speed can he row in still water?

Solution:
Given,
Man rows downstream = 35 km/h
Man rows upstream = 25 km/h
We know that,
Speed in still water = (Downstream speed + Upstream speed​) ÷ 2
= (35 + 25) ÷ 2
= 60 ÷ 2
= 30 km/h

Question: On a river, C is the mid-point between two points A and B on the same bank of the river. A boat can go from A to C and back in 14 hours and from A to B in 24 hour. How long it would take to go from B to A?

Solution:
Time required to travel from A to B = 24 hour
Time required to travel from A to C = 1/2 (24 hours)
= 12 hour
Given total time from A to C and C to A = 14h
∴ 12 hour + C to A = 14h
∴ C to A = 2 hour
Time taken from B to A is twice of C to A
then, time taken from B to A = (2 × 2) hour
= 4 hours

Question: A car covers a distance of 15 km in 15 minutes. If its speed is decreased by 10 km/h, then the time taken by it to cover the distance of 20 km will be-

Solution:
Given,
15 minutes covers 15 km
∴ 1 minutes = 15/15 km
= 1 km
∴ 60 minutes or 1 hours = (1 × 60) km
= 60 km

If its speed is decreased by 10 km/h
Then new speed = (60 - 10) km
= 50 km/h

∴ 1 km cover in (60 ÷ 50) minutes
= 6/5 minutes
∴ 20 km cover in = (6/5 × 20) minutes
= 24 minutes

Question: A 100 meters long train is running at a speed of 90 km per hour. It will cross a railway platform 200 m long in-

Solution:
Here,
Speed of the running train = 90 km/hr
= {90 × (5/18)} m/sec
= 25 m/sec

And length of the train is = 100 metres
Length of platform = 200 m

So, the time will taken by the train = (Length of train + Length of platform)/Speed
= (100 + 200)/25
= 300/25  
= 12 sec

Question: After traveling 35km, a train meets with an accident and travels at (3/4)th of the usual Speed and reaches 45 min late. Had the accident happened 15km further on it would have reached 30 min late. Find the usual Speed?

Solution:
Here there are 2 cases
Case 1: accident happens at 35 km
Case 2: accident happens at 50 km
Difference between two cases is only for the 15 kms between 35 and 50.
Time difference of 15 minutes is only due to these 15 kms.

In case 1, 15 kms between 35 and 50 is covered at (3/4)th Speed.
In case 2, 15 kms between 35 and 50 is covered at usual Speed.

So the usual Time 't' taken to cover 15 kms, can be found out as below.
(4/3)t - t = 15 mins [s = vt]
⇒ t = 45 mins, d = 15kms

so usual
Speed = Distance/Time
= 15/45min
= 15/(3/4) km/hr.
= 20 km/hr.

Question: Two bicycles start at the same time from points A and B, moving toward each other. If the distance between A and B is 125 km and their speeds are 14 km/h and 11 km/h respectively then after how much time will they meet each other?

Solution:
Given,
The distance between A and B = 125 km
Speed of 1^st bicycle = 14 km/h
Speed of 2^nd bicycle = 11 km/h

The bicycles are moving toward each other,
So their relative speed = (Speed of 1^st bicycle + Speed of 2^nd bicycle)
= (14 + 11) km/h
= 25 km/h

Time = (Distance ÷ relative speed)
= (125 ÷ 25) 
= 5 h

Question: Two trains of equal length are running on parallel lines in different direction at 40 km/h and 32 km/h. The faster train passes the slower train in 36 seconds. The length of each train is-

Solution:
Let
The length of each train = x metres.
Then, distance covered = 2x metres.
Relative speed = (40 + 32)km/hr
= 72 km/h
= 72 × (5/18) m/sec
= 20 m/sec

ATQ,
2x = 20 × 36
⇒ 2x = 720
∴ x = 360

Questin: Working 10 hours a day, Polas can Complete a work in 4 days. Working 3 hours a day, Mahin can complete the same work in 20 days. Working 8 hours a day, they can jointly complete the work in

Solution: 
Given,
Working 10 hours a day, Polash can complete the work in 4 days
Polash's total working hour = (10 × 4) hours 
= 40 hours

∴ Polas's 1 hour's work = 1/40 part

Working 3 hours a day, Mahin can complete the work in 20 days
Mahin's total working hour = (3 × 20) hours 
= 60 hours

∴ Mahin's 1 hour's work = 1/60 part

( Polas + Mahin )'s 1 hour's work = (1/40 + 1/60) part
= ( 3 + 2)/120 part
= 5/120
= 1/24 part

So (Polas + Mahin) complete whole part = 24 hours

Hence, they work 8 hours a day
i.e. they require 3 days to complete the work.

Question: A train covers half of his journey at 60 km/h and the remaining half at 40 km/h. It's average speed is-

Solution:
let,
The total distance is 2x
First x distance is covered in 60 km/h
∴ time = x/60 h

Second x distance is covered in 40 km/h
∴ time = x/40 h 

∴ Average Speed = Total distance ÷ Total time 
= 2x ÷ {(x/60) + (x/40)}
= 2x ÷ (5x/120)
= 2x ÷ (x/24)
= 48

Question: A person can swim in still water with a speed of 12 km/h. If the speed of the stream is 3 km/h, what will be the time taken by the person to go 54 km upstream?

Solution:
Given,
Speed of the person in still water = 12 km/h
Speed of the stream = 3 km/h
Distance to be covered upstream = 54 km
We know,
The effective speed = Speed in still water - Speed of stream
= (12 - 3) km/h
= 9 km/h

Time = (Distance ÷ Effective speed) hours
= (54 ÷ 9) hours
= 6 hours