ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: A train running at the speed of 90 km/h crosses a pole in 10 seconds. What is the length of the train?

Solution:
Speed = 90 km/h
= [90 × (5/18)] m/sec
= 25 m/sec

∴ Length of the train = (25 × 10) m
= 250 m

So, the length of the train is 250 meters.

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

Question: A boat takes 12 hours to cover a certain distance upstream and 8 hours to cover the same distance downstream. What is the ratio between the speed of the boat and the speed of the water current, respectively?

Solution:
Let,
Upstream speed = x kmph
Downstream speed = y kmph

Since distance is same,
x × 12 = y × 8
⇒ 12x = 8y
⇒ y = 3x/2

Now,
Speed of boat = (y + x)/2
Speed of current = (y - x)/2

∴ Required ratio
= (y + x) : (y - x)
= [(3x/2) + x] : [(3x/2) - x]
= (5x/2) : (x/2)
= 5x : x
= 5 : 1

∴ The ratio of the speed of the boat to the speed of the water current is 5 : 1.

Question: A boat running downstream covers a distance of 30 km in 3 hours, while it takes 5 hours to cover the same distance upstream. What is the speed of the boat in still water?

Solution:
Rate while running downstream = (30/3) km/h
= 10 km/h

Rate while running upstream = (30/5) km/h
= 6 km/h

∴ Speed of the boat in still water
= (10 + 6)/2 km/h
= 8 km/h

So, the speed of the boat in still water is 8 km/h.

Question: Two trains are moving in opposite directions at speeds of 60 km/h and 90 km/h. Their lengths are 800 m and 700 m respectively. Find the time taken to cross each other.

Solution:
Relative speed = (60 + 90) km/h
= 150 × (5/18) m/sec
= 125/3 m/sec

Distance covered = (800 + 700) m
= 1500 m

Required time
= 1500 ÷ (125/3) sec
= (1500 × 3)/125 sec
= 36 sec

∴ The required time is 36 seconds.

Question: A man takes 6 hours to walk to a place and ride back to the starting point. If he were to walk both ways, it would take him 9 hours. How much time would he take to ride both ways?

Solution:
Time taken in walking both ways = 9 hours ................(i)
Time taken in walking one way and riding back = 6 hours ........(ii)

By the equation (ii) × 2 - (i), we have:
Time taken by the man in riding both ways
= (6 × 2) - 9
= 12 - 9
= 3 hours

∴ The time taken by him to ride both ways is 3 hours.

Question: A train passes a telegraph post and a 300 m long bridge in 10 seconds and 25 seconds, respectively. Find the speed of the train in km/h.

Solution:
Let,
Length of the train = x metres
Speed of the train = y m/sec

Time to pass the telegraph post:
x/y = 10
⇒ x = 10y

Time to pass the bridge:
(x + 300)/25 = y
⇒ x + 300 = 25y
⇒ 10y + 300 = 25y
⇒ 25y - 10y = 300
⇒ 15y = 300
⇒ y = 20 m/sec

∴ Speed of the train = 20 × (18/5) km/h
= 72 km/h

So, the speed of the train is 72 km/h.

Question: P runs three times faster than Q, and Q runs twice as fast as R. If R covers a certain distance in 120 minutes, how long will it take P to cover the same distance?

Solution:
Let,
Speed of R = x
Then speed of Q = 2x
Speed of P = 2x × 3 = 6x

Ratio of speeds P : Q : R = 6x : 2x : x = 6 : 2 : 1

Since time is inversely proportional to speed,
Ratio of time taken P : Q : R = 1/6 : 1/2 : 1 = 1 : 3 : 6
Given that,
R covers a certain distance in 120 minutes.
So,
6 units = 120 minutes
1 unit = (120 ÷ 6) minutes = 20 minutes

∴ P will cover the same distance in 20 minutes.

Question: A 180 meter long train running at the speed of 72 km/h crosses another train running in the opposite direction at the speed of 108 km/h in 10 seconds. What is the length of the other train?

Solution:
Relative speed = (72 + 108) km/h
= 180 × (5/18) m/sec
= 50 m/sec

Let,
Length of the other train = x metres

Then,
(x + 180)/10 = 50
⇒ x + 180 = 500
⇒ x = 500 - 180
∴ x = 320

∴ The length of the other train is 320 meters.

Question: A man can row at 10 kmph in still water. If the speed of the current is 2 kmph and it takes him 1.5 hours to row to a place and come back, how far is the place?

Solution:
Speed downstream = 10 + 2 = 12 kmph
Speed upstream = 10 - 2 = 8 kmph

Let the required distance = x km

ATQ,
(x/12) + (x/8) = 1.5
Or, (2x + 3x)/24 = 1.5
Or, 5x/24 = 1.5
Or, 5x = 36
∴ x = 36/5
∴ x = 7.2 km

∴ The place is 7.2 km away.

Question: A boat moves at a speed of 30 km/h in still water. The speed of the current is 5 km/h. How far will the boat travel downstream in 12 minutes?

Solution:
Speed of the boat in still water = 30 km/h
Speed of the current = 5 km/h

∴ Speed downstream = 30 + 5 = 35 km/h

Time = 12 minutes = 12/60 hours = 1/5 hours

∴ Distance travelled downstream = 35 × (1/5) km
= 7 km

∴ The distance travelled downstream is 7 km.

Question: Two trains start at the same time from Chittagong and Sylhet and proceed towards each other at 80 km/h and 100 km/h, respectively. When they meet, it is found that one train has travelled 80 km more than the other. Find the distance between Chittagong and Sylhet.

Solution:
Let the trains meet after t hours.

ATQ,
(100 × t) = (80 × t) + 80
⇒ 100t - 80t = 80
⇒ 20t = 80
∴ t = 4 hours

∴ Distance between Chittagong and Sylhet = (100 × 4) + (80 × 4)
= 400 + 320
= 720 km

∴ The distance between Chittagong and Sylhet is 720 km.

Question: Sonar Bangla express, normally reaches its destination at 72 km/h in 6 hours. Find the speed at which it must travel to reduce the travel time by 2 hours?

Solution:
Distance to be covered = Speed × Time
= 72 × 6
= 432 km

Reduced time = 6 - 2 = 4 hours

∴ Required speed = 432/4
= 108 km/h

∴ The train must travel at 108 km/h to reduce the time by 2 hours.

Question: A machine wheel has a circumference of 50 cm and completes 24 rotations in 4 seconds. What is the speed of the wheel in kilometers per hour (km/h)?

Solution:
Total distance covered = (50 × 24) cm
= 1200 cm
= (1200 ÷ 100) m
= 12 m

We know,
Speed = (Total distance ÷ Time)
= (12 ÷ 4) m/sec
= 3 m/sec

Converting into km/h,
= 3 × (18/5) km/h
= 10.8 km/h

∴ The speed of the wheel is 10.8 km/h.

Question: A train covers a certain distance at a speed of 240 kmph in 6 hours. To cover the same distance in 4 hours, it must travel at a speed of-

Solution:
Given,
Distance = (240 × 6)
= 1440 km

We know,
Speed = (Distance ÷ Time)

∴ Required speed = (1440 ÷ 4) km/h
= 360 km/h

∴ The required speed is 360 km/h.