ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: A train passes two bridges of length 1000 m and 600 m in 120 seconds and 80 seconds respectively. The length of the train.

Solution:
Distance covered in 120 second = 1000 + length of train(l) 
Distance covered in 80 seconds = 600 + l 
So, distance covered in 40 seconds = (1000 + l) - (600 + l) 
= 400 m 

Speed = 400/40 = 10 m/s 

∴ Distance covered in 80 second = 80 × 10 = 800 m 
So, 600 + l = 800 
∴ Length of the train (l) = 200 m 

Question: If the speed of the boat in still water is 5 km/hr and the speed of the current is 10 km/hr, then find the time taken by the boat to travel 135 km with the current. 

Solution:
Relative speed = 5 + 10 
=15 km/hr 

Time = Distance/speed 
= 135/15 
= 9 hour

Question: A car travels a distance of 500 km in 10 hours. What is its speed in m/s?

Solution: 
Speed = Distance/Time 
= 500/10 km/hr.
= 50 km/hr.
= (50 × 1000)/3600 m/s
= 13.89 m/s

Question: A train 500 m long is running at a speed of 72 km/hr. If it passes through a tunnel in 50 seconds, then the length of the tunnel is-

Solution: 
First convert speed in m/s 
So, speed= 72 × (5/18) 
= 20 m/s 

Train covers the distance in 50 seconds = length of train + length of the tunnel(l) 
⇒ 500 + l = 20 × 50 
⇒ 500 + l = 1000 
∴ l = 500 m 

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 20 hours 20 min. How long it would take to go from B to A?

Solution: 
Time required to travel from A to B = 20 hour 20 min 
Time required to travel from A to C = 1/2 (20 h 20 m) 
= 10 h 10 m 

Given total time from A to C and C to A = 14 h 
∴ 10 h 10 m + C to A = 14 h 
∴ C to A = 3 h 50 m 

Time taken from B to A is twice of C to A 
then, time taken from B to A =2 × (3 h 50 m) =7 h 40 m 

Question: Tofail drives first 120 km in 2 hrs and next 180 km in next 4 hrs. What is his average speed for the entire trip in km per hour?

Solution: 
Total Distance travelled = 120 + 180 = 300 km.
Total Time taken = 2 + 4 = 6 hrs.

∴ Average Speed = Total Distance Travelled/Total Time Taken
= 300/6 km/hr.
= 50 km/hr.

Question: A train reaches from A to B in 5 hours travelling at a speed of 60 km/hr. If its speed is increased by 15 km/hr, then the time of journey is reduced by-

Solution: 
Total distance = speed × time 
= 60 × 5 = 300 km

If speed increased then new speed = 60 + 15 = 75 km/hr 

New time = Total distance/speed 
= 300/75
= 4 hour 

Time reduced by 5 - 4 = 1 hour 

Question: The ratio of speed of a motor-boat to that of the current of water is 17 : 5. The boat goes along with the current in 4 hours. It will come back in-

Solution: 
Since the ratio 17 : 5 is given. 
Let the speed of boat in still water = 17 km/hr
and speed of stream = 5 km/hr

Downstream speed = 17 + 5 = 22 km/hr 
Upstream speed = 17 - 5 = 12 km/hr 

Distance = Downstream speed × downstream time 
= 22 × 4 = 88 km 

Upstream time = Distance/upstream speed 
= 88/12 
∴ Come back time = 7 hour 20 minute 

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

Question: Dhaka and Mymensingh apart from each other 760 km. A train starts from Dhaka at 9 am and travels towards Mymensingh at speed 60 km/hr. Another train starts from Mymensingh at 10 am and travels towards Dhaka at speed 80 km/hr. At what time both will meet?

Solution: 
Total distance between D and M = 760 km. 
A travels 1 hour before B so it travels = 60 × 1 = 60 km 
Now the remaining distance D and M= 760 - 60 = 700 km 
Relative speed = 60 + 80 = 140 km/hr 

Time = 700/140 
= 5 hour. 

So, the time when they meet = 10 am + 5 hour = 3 pm 

Question: Speed of motorboat in still water is 35 kmph. If the motorboat travels 100 km along the stream in 2 hour 30 min, then the time taken by it to cover the same distance against the stream is-

Solution: 
The speed of the motorboat in still water is 35 km/hr. 
let the speed of the stream = x km/hr 
Downstream speed = Distance/time 
= 100/2.5 
= 40 km/hr 

Speed of stream = 35 + x = 40 
∴ x = 5 km/hr 

Upstream speed = 35 - 5 = 30 km/hr 
Time taken in upstream = 100/30 = 3 hour 20 min

Question: On my way from the office to the Live MCQ class, I drive at 30 kmph and on the return journey I drive at 45 kmph. What is my average speed of travel?

Solution:
Let the distance between the office and Live MCQ class be x km.

∴ Time taken on my onward journey = x/30 hours
and time taken on my return journey = x/45 hours

∴ The total time taken for my onward and return journey = x/30 + x/45 = 5x/90 hours.
The total distance traveled both ways = 2x km

∴ Average speed = 2x/(5x/90) = 36 kmph.

Question: Two trains 180 m and 120 m long respectively pass each other in 54 seconds when they run in the same direction and in 18 seconds when run in opposite directions. Find the speed of first train.

Solution: 
Let the speed of 1st train is S1 and speed of 2nd train is S2 
Time = total distance/ relative speed 

1) In same direction 
54 = (180 + 120)/(S1 - S2) × (5/18)
⇒ (S1 - S2)54 = (300 × 18)/5 
⇒ (S1 - S2) = 20 

2) In opposite direction 
18 = (180 + 120) / (S1 + S2) × (5/18)
⇒ (S1 + S2)18 = (300 × 18)/5 
⇒ (S1 + S2) = 60 

from 1 and 2 
S1 = 40 km/hr

Question: A boatman can row a boat upstream at 14 km/hr and downstream at 20 km/hr. Find the speed of the boat in still water.

Solution:
We are given that speed downstream, D = 20 km/hr
and speed upstream, U = 14 km/hr 
Therefore, Speed of boat in still water = 0.5 × (D + U) km / hr = 0.5 × (14 + 20) = 17 km/hr 

 
Another method:
Speed of the stream = 0.5 × (D - U) = 0.5 × 6 = 3 km/hr 
Speed of the boat in still water = Speed of the stream + Speed Upstream = 3 + 14 = 17 km/hr

Question: A jogger is running at a speed of 15 km/hr. In what time he will cross a track of length 400 meters?

Solution:
Speed = 15 km/hr = 15 × (5/18) m/s = 75/18 m/s
Distance = 400 meters

∴ Required time = 400/(75/18) sec
= (400 × 18)/75 sec
= 96 sec

Question: Two trains start from station A and B and travels towards each other at speed of 48km/hr and 72km/hr respectively. At the time of their meeting, the second train has traveled 144 km more than the first. The distance between A and B is-
 
Solution: 
The second train has traveled 144 km more than the first train because the speed of second train is 24 km/hr more than first. 
Time taken by second train to cover 144 km with surplus 24km/hr = 144/24 = 6 hours. 
then, time taken by both train before meeting is 6 hours. 
So, their relative speed = 48 + 72 = 120 
Total distance travel by both = 120 × 6 = 720 km 
Distance between A and B = 720 km 

Question: A boatman 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…(i)

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…(ii)

 
Solving both equations
B = 10 km/h and S = 5 km/h

∴ Speed of the stream is 5 km/h

Question: What is the distance covered by a car traveling at a speed of 40 kmph in 15 minutes?

Solution: 
converting speed into km/min, we get
40 kmph = 40/60 km/min = 2/3 km/min.

Therefore, distance traveled = 15 × (2/3) = 10 km.

Question: A train moving at speed of 90 km/hr crosses a pole in 7 seconds. Find the length of the train.

Solution:
Length of the train is equal to the distance covered by train to cross the pole.
So, we will find the distance travelled by the train in 7 seconds by applying the following formula:
Distance= Speed × Time

Speed is given in Km/hr so we will convert it into m/s as answers are given in meters.
Speed = 90 × (5/18)  = 25 m/s

Time = 7 seconds
Distance = 25 × 7 = 175 meters

Question: A man has to go from a port to an island and return. He can row a boat with a speed of 7 km/hr in still water. The speed of the stream is 2 km/hr. If he takes 56 minutes to complete the round trip, find the distance between the port and the island.

Solution:
Speed upstream = 7 - 2 = 5 km/hr 
Speed downstream = 7 + 2 = 9 km/hr 

Let the distance between the port and the island be D km.
Also, we know that Time = Distance / Speed 
⇒ (D/5) + (D/9) = 56/60 
⇒ (14D)/45 = 56/60 
⇒ D = 3 km 

Therefore, the distance between the port and the island = 3 km 

Question: A horse covers a distance of 1500 meters in 1 minute 20 seconds. At what speed the horse is running?

Solution:
Distance = 1500 meters
Time = 1 minute 20 seconds = 60 + 20 = 80 seconds

So, Required Speed = 1500/80 = 75/4 m/s

We need answer in km/hr:
So, Speed in km/hr = (75/4) × (18/5) = 67.5 km/hr

Question: A train of length 180 meters crosses a man running at 10 km/hr in the same direction in 10 seconds. What is the speed of the train?

Solution:
When the train and man are moving in same direction then relative speed will be the difference between their individual speeds. In this problem the other way to find the relative speed is to divide the distance covered (length of train) by the time taken by the train to cross the man.

Relative Speed = 180/10 m/s

We will convert it into Km/hr
(180/10) × (18/5) = 64.8 km/hr

Now, let the speed of the train is X km/hr.
So, the relative speed, 64.8 km/hr = X km/hr - 10 km/hr
⇒ X - 10 = 64.8
⇒ X = 64.8 + 10
∴ X = 74.8 km/hr

Question: In a boat race, a person rows a boat 6 km upstream and returns to the starting point in 4 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.

Solution:
Let the speed of the boat in still water be B km/hr
⇒ Speed upstream = (B - 2) km/hr 
⇒ Speed downstream = (B + 2) km / hr 

We know that Time = Distance / Speed 
⇒ 6/(B - 2) + 6/(B + 2) = 4 
⇒ 6B + 12 + 6B - 12 = 4(B - 2)(B + 2) 
⇒ 12B = 4(B - 2)(B + 2) 
⇒ 3B = B² - 4 
⇒ B² - 3B - 4 = 0 
⇒ (B + 1) (B - 4) = 0 
⇒ B = 4 km/hr (Speed cannot be negative) 

Question: Two boys start running at the same time in the same direction at a speed of 10 km/hr and 12 km/hr respectively. In what time they will be 8 km apart?

Solution:
Both the boys are in motion so we will consider relative speed to find the time.
Relative speed = 12 - 10 = 2 km/hr

Distance = 8 km

Time = 8/2 = 4 hours

Question: A train is moving at 120 km/hr. The length of the train is 250 meters. How long it will take to cross a platform of length 100 meters?

Solution:
Speed of train in m/s = 120 × (5/18) m/s = 100/3 m/s
Distance covered to cross the platform is equal to the sum of length of the train and length of the platform.
So, distance= 250 + 100 = 350 meters

Time = distance/speed
= 350 × (3/100)
= 10.5 sec