ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: A boys goes to school with a speed of 4 km/hr and returns to the village with a speed of 3 km/hr. If he takes 7 hours in all, the distance between the village and the school is:

Solution: 
Let the required distance be x km.

Now,
⇒x/4 + x/3 = 7
⇒ (3x + 4x)/12 = 7
⇒ 7x = 84
⇒ x = 12 

∴ the distance between the village and the school is 12 km.

Question: A and B two taps fill in a tank in 5 hours and 10 hours respectively. If both tapes are opened together, the tank will be full in: 

Solution: 
A's 1 hour's work = 1/5
B's 1 hour's work = 1/10

(A+B)'s 1 hour's work = (1/5) + (1/10)
= (2 + 1)/10
= 3/10 

Now, 
3/10 parts both the taps can fill the tank in 1 hour
∴ 1 part both the taps can fill the tank in 10 × (1/3) hours
= 10/3 hours

 ∴ The tank will be full in 10/3 hours.

Question: Three pipes A, B and C can fill a tank in 8 hours. After working together for 2 hours, B is closed and then A and C can fill in the remaining part in 8 hours. The number of hours taken by B alone to fill the cistern, is:

Solution: 
(A + B + C )'s 1 hour's work = 1/8 parts.

Part filled in 2 hours = 2/8 = 1/4 part.
Remaining part = 1- (1/4) = 3/4 

Now,
(A + C)'s 8 hour's work = 3/4
∴ (A + C)'s 1 hour's work = 3/(4 × 8) = 3/32 

∴  B's 1 hour's work = (1/8) - (3/32) parts [ এখানে (A + B + C ) - (A + C) বিয়োগ করে ] 
= (4 - 3)/32
= 1/32 parts

1/32 parts work B can alone fill the tank in 1 hour
∴ 1  part work B can alone fill the tank in 1× (32/1) hours
= 32 hours

∴ B can alone fill the tank in 32 hours

Question: If a man covers 15.2 km in 4 hours, the distance covered by him in 5 hours is:

Solution:
Speed = (15.2/4) km/hr
           = 3.8 km/hr.

Distance covered in 5 hours = ( 3.8 × 5) km
                                              = 19 km.

Question:
A man walking at a speed of 3 km/hr. crosses a square field diagonally in 5 minutes. What is the area of the field (in m²) ?

Solution: 
Man walks in 5 mins = 3 × (5/60) = 1/4 km = 250m

So, the length of the diagonal of the square field = 250m
Let the measure of each side of the square field be X.

According to the question,
X√2 = 250
⇒ X = 250√2
⇒ X² = 31250

∴ The area of the square field is 31250 m².

Question: A speed of 65 m/sec is the same as:

Solution: 
65 m/sec = 65 × (18/5 )
= 234 km/hr. [meter × 18/5]

Question: Robinson crosses a street 500 m long in 6 minutes. His speed in km, per hour is:

Solution: 
  ৬ মিনিটে যায় ৫০০ মিটার
∴ ১ মিনিটে যায় ৫০০/৬ মিটার
∴ ৬০ মিনিট বা ১ ঘণ্টায় যায় (৫০০ × ৬০)/৬ মিটার 
= ৫০০০ মিটার বা ৫ কিলোমিটার। 

Question: A distance is covered in 3 hrs 30 minutes at 5 km/hr. How much time will be taken to cover it at 21 km/hr?

Solution: 
Distance = [5 × 3 (1/2)]
= 5 × (7/2)
= 17.5 km.

Time taken to cover it at 21 km/hr = [(17.5/21) × 60] min
= 50 min.

Question: Shafiq performs 6/15 of the total journey by rail 8/20 by train and the remaining 12 km on foot, his total journey is: 

Solution: 
Let, the total journey be x km.

ATQ,
∴ (6x/15) + (8x/20) + 12 = x
or,  (24x + 24x + 720)/60 = x
or, 24x + 24x + 720 = 60x
or, 60x - 48x = 720
or, 12x = 720
or, x = 60

∴ Total journey = 60 km.

Question: A truck travels 150 km from A to B at 75 km/hr and returns from B to A along the same route at 50 km/hr. The average speed, in kilometers per hour, for the round trip is: 

Solution: 
Here round trip means total distance 150 + 150 = 300 km
And total hours = (150/75) + (150/50) = 2+3 = 5 hours

∴ Average Speed: 300/5 = 60 km/hr. [ মোট দূরত্বকে মোট সময় দ্বারা ভাগ করলে গড় গতিবেগ পাওয়া যায়]

Question: Three pipes A, B, and C would fill a tank in 10 hours, 15 hours, and 20 hours respectively. If all these pipes are opened simultaneously, how much time will be taken to fill the tank? 

Solution:
A, 1 ঘন্টায় পূর্ণ করে (1/10) অংশ
B, 1 ঘন্টায় পূর্ণ করে (1/15) অংশ
C, 1 ঘন্টায় পূর্ণ করে (1/20) অংশ

তিনটি পাইপ একত্রে পূর্ণ করে = (1/10) +  (1/15) + (1/20) = 13/60 অংশ

আবার,
13/60 অংশ পূর্ণ করে 1 ঘণ্টায় 
∴ 1 অংশ পূর্ণ করে 60/13 ঘণ্টায়

Question: Pipes A, B  can fill a tank in 15 minutes and 20 minutes respectively. But pipe C can empty the full tank in 12 minutes. If all these pipes are opened simultaneously, how much time will be taken to fill the tank?

Solution: 
 A, 1 মিনিটে পূর্ণ করে (1/15) অংশ
 B, 1 মিনিটে পূর্ণ করে (1/20)  অংশ 
অপরদিকে,
C, 1 মিনিটে খালি করে (1/12) অংশ 

সবগুলো পাইপ খুলে দিলে ট্যাংকটি পূর্ণ হবে- 
= (1/15) + (1/20) −  (1/12) 
= (4 + 3 − 5)/60
= 2/60
= 1/30 

1/30 অংশ পূর্ণ করে 1 মিনিটে
∴ 1  অংশ পূর্ণ করে 30/1 মিনিটে
= 30 মিনিটে

Question: Two pipes A and B can fill a pool in 5 hours and 6 hours respectively. If both pipes work together, how long will it take to fill the pool?

Solution: 
A, 1 ঘণ্টায় পূর্ণ করে (1/5) অংশ
B, 1 ঘণ্টায় পূর্ণ করে (1/6) অংশ 

উভয় পাইপ একত্রে 1 ঘণ্টায় পূর্ণ করে (1/5) + (1/6) অংশ 
= (6 + 5)/30
= 11/30

আবার,
11/30 অংশ পূর্ণ করে 1 ঘণ্টায় 
∴ 1 অংশ পূর্ণ করে (1×30)/11 ঘণ্টায়
= 30/11 ঘণ্টা

Question: If kamal travels 20 km/hr, he reaches the office 10 minutes late and if he travels at 25 km/hr, he reaches the office 5 minutes earlier. The office is at a distance of.

Solution: 
অফিসের দূরত্ব x হলে, 
কামাল x দূরত্ব যায় (x/20) এবং (x/25) সময়ে। 
The difference between the time = {5 - (-10)} ⇒ 15 minutes

ATQ,
Or, (x/20) - (x/25) = 15/60 
Or, (5x - 4x)/100 = 1/4
Or, x/100 = 1/4
Or, 4x = 100
Or, x = 25

Question: A person crosses a 900 m long street in 5 minutes. What is his speed in km per hour?

Explanation:
Speed = 900m/(5 x 60) sec.
= 3 m/sec.

এখন কিলোমিটারে পরিণত করতে হলে- 
= 3 × (18/5) km/hr
= 10.8 km/hr.

Question: The ratio between the speeds of two trains is 5 : 6. If the second train runs 270 km in 3 hours, then the speed of the first train is:

Solution: 
Let,
the speed of first train be 5x
the speed of second train be 6x

ATQ, 
6x = 270/3 
Or, 6x = 90
Or, x = 90/6 
Or, x = 15

∴  Speed of first train =  5x = 5 × 15 = 75 km/hr. 

Question: Sharif travelled a distance of 41 km in 9 hours. He travelled partly on foot 3 km/hr and partly on bicycle 9 km/hr. The distance travelled on bicycle is:

Solution: 
Let,
the distance travelled on bicycle be x km.
distance travelled on foot = (41 -x) km.

ATQ,
Or, (x/9) + (41 − x)/3 = 9
Or, x + 123 − 3x = 81
Or, 2x = 42
Or, x = 21

Question: A boy on travels first 120 km at 40 km/hr and the next 150 km at 50 km/hr. The average speed for the first 270 km  is:

Solution: 
Total time taken:
= (120/40) + (150/50)
= (3 + 3)
= 6 hrs.

∴ Average Speed:
= (270/6) km/hr
= 45 km/hr.

Question: If a person walks at 18 km/hr instead of 12 km/hr, he would have walked 25 km more. The actual distance travelled by him is:

Solution: 
Let the actual distance travelled be x km.

ATQ, 
Or, x/12 = (x + 25)/18
Or, 18x = 12x + 300
Or, 18x − 12x = 300
Or, 6x = 300
Or, x = 50
∴ distance = 50 km.

Question: Two pipes A and B can fill a tank in 45 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

Solution: 
Part filled by A in 1 min = 1/45
Part filled by B in 1 min = 1/30 
Part filled by (A + B) in 1 min = (1/45) + (1/30) = 1/18 

1/18 part filled by (A + B) in = 1 minute
∴ 1 part  filled by (A + B) in = 1× 18/1 = 18 minutes

 ∴  Both pipes can fill the tank in 18 minutes

Question: An outlet pipe can empty a cistern in 9 hours. In what time will it empty 2/3 part of the cistern?

Solution: 
Time taken to empty (2/3) × 9 = 6 hours

Question: The average speed of a bus is one-third of the speed of a train. The train covers 1200 km in 16 hours. How much distance will the bus cover in 48 minutes? 

Solution:
Speed of the train = (1200/16) km/hr.
                              = 75 km/hr.

Speed of the bus = (1/3)×75 km/hr.
                             = 25 km/hr.

Distance covered by the bus in 60 min = 25 km
Distance covered by the bus in 48 min =(25/60) × 48 = 20 km

Question: A Tank is normally filled in 8 hours but takes 5 hours longer to fill because of a leak in its bottom. If the tank is full, the leak will empty it in?

Solution: 
Let the leak will empty the tank in x hrs.
Total time = 8 + 5 = 13 hrs.

Then,
Or, 1/8 - 1/x = 1/13
Or, (x − 8)/8x = 1/13
Or, 13x −  104 = 8x
Or, 13x − 8x = 104
Or, 5x = 104
Or, x = 20.8

Question: A car travelling with 5/6 of its actual speed covers 35 km in 150 minutes. Find the actual speed of the car.

Solution: 
Let,
the actual speed be x km/hr.
Time taken: 
= 150 minutes
= (150/60) hrs.
= 2.5 hrs

ATQ,
Or, (5x/6) × 2.5 = 35
Or, (5x/6) × (25/10) = 35
Or, (5x/6) = (35 × 10)/25 
Or,  x = (35 × 6 ×10)/( 25 × 5)
Or, x = 16.8 km/hr. 

 ∴ the actual speed of the car16.8 km/hr.

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water of the tank in:

Solution:
Work done by the leak in 1 hour
= 1/2 - 3/7
= 1/14

∴ The leak will empty the tank in 14 hours

Question: A tank is filled in 6 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Solution: 
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.

∴1/x + 2/x + 4/x = 1/6
⇒ 7/x =1/6
⇒ x = 42 hours

Question: 3/4 part of the tank is full of water. When 30 liters of water is taken out, the tank becomes empty. The capacity of the tank is -

Solution:
If the tank has 4x liters of total capacity and its holds 3x liters of water.
If 30 liters of water is taken out, then the tank becomes empty.

It means 3x liters of water is taken out
3x = 30 liters
x = 10 liters

Capacity of tank = 4x = 4 × 10 = 40 liters