ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Part filled by (A and B) pipes in 1 min = (1​/20) + (1/30​)
                                                            = (3 + 2)/60
                                                            = 5/60
                                                            = 1/12

Time taken to fill the tank = (1 × 12)/1 minutes
                                          = 12 minutes

Distance = 6 Km.
Time = 45 minutes.
He covers half of the distance (3 km) in 2/3 of the time

i.e. (2 × 45)/3 = 30 minutes = 1/2 hour.
Now, Time = 15 minutes = 15/60 = 1/4 hours.

Distance = 3 km.
Speed = 3/(1/4) = 12 Kmph.

Speed = 900/(5× 60) m/sec
            = 3 m/sec
            = (3 × 18)/5 km/hr.
            = 10.8 km/hr.

Pipe A and B can fill the tank = 6 hours 

Let
Pipe B can fill the tank in x hours
Pipe A will take x - 5 hours

Now
(1/x) + 1/(x - 5) = 1/6
(x - 5 + x)/x(x - 5) = 1/6
⇒ 6(x - 5 + x) = x² - 5x
⇒ 12x - 30 = x² - 5x
⇒ x² - 17x + 30 = 0
⇒ x² - 15x - 2x + 30 = 0
⇒ x(x - 15) - 2(x - 15) = 0
⇒ (x -15)(x - 2) = 0
x = 15 and x = 2

If x = 2, A = - 3 and time cannot be negative
So x = 15 hours
∴ B will fill the tank in 15 hours.

Let’s the speed of man = x km/hr.

According to the question
x × 30 - x × (14/15) × 30 = 10
⇒ 30x - 28x = 10
⇒ 2x = 10
⇒x = 10/2 
∴  x = 5

Let 
The total journey x km
Now
{(1/2)x/16} + {(1/2)x/24} = 10
(x/16) + (x/24) = 20
(3x + 2x)/48 = 20 
5x/48 = 20
x = (20 × 48)/5
x = 192km

The outlet pipe empties the one complete cistern in 6 hours
Time taken to empty (2/3) × 6 = 4 hours

Let the speed of two trains be 8x and 9x km/hr.
It is given that the second train runs 432 km in 4 hours,

We have,
9x = 432/4
9x= 108
x = 108/9 
x = 12

The speed of the first train is = 8 × 12 = 96 km/hr.

A tap can fill the tank in 12 hours
 One hour work of one tap = 1/12
⇒ One hour work of 4 taps = 4/12 = 1/3

4 taps 1/3 part can fill the tank in 1 hour 
4 taps 1 part can fill the tank in 1× 3 hours 
4 taps 1/2 part can fill the tank in (1× 3)/2 hours 
                                                     = 3/2 = 1.5 hours

⇒ Total time to fill the tank = 6 hours to first half + 1.5 hour to second half
∴ The required result will be 7.5 hours. 

Let the distance to be covered be x km
⇒ (x/40) - (x/50) = 24/60
⇒ (5x - 4x)/200 = 2/5
⇒ x/200 = 2/5
⇒ x = (2/5) × 200
⇒ x = 80 km.

Part filled by A in 1 hour =1​/18

Part filled by B in 1 hour =1/6

Part filled by (A + B) in 1 hour =(1/18) + (1/6)
                                                = (1 + 3)/18
                                                = 4/18
                                                = 2/9

Hence, both the pipes together will fill the tank in 9/2 hours

Ratio of speeds =5 : 6 
⇒ Ratio of times taken =6 : 5
Let A and B take 6x and 5x hrs. to reach the destination. 
Then
6x - 5x=30​/60
x =1/2​

∴ Time taken by A =(6 × 1​)/2 hours
                               = 3 hours

Let the total distance be 3x km
Now 
(x/4) + (x/5) + (x/6) = 37/60
(15x + 12x + 10x)/60 = 37/60
37x/60 = 37/60
37x = 37
x = 1 
The total distance be 3x km
                                = 3 × 1 = 3 km

 

Let the speed of the train be x km/hr.

Now
(600/x) - 600/(x + 5) = 4
{600(x + 5) - 600x}/x(x + 5) = 4
3000/x(x + 5) = 4
4x² + 20x - 3000 = 0
4(x² + 5x - 750) = 0
x² + 5x - 750 = 0
x² + 30x - 25x - 750 = 0
x(x + 30) - 25(x + 30) = 0
(x + 30)(x - 25) = 0 
∴ x = 25 

The initial speed of the train is 25 km/hr.

Distance=Speed × Time
Distance=(6×50)/60 km
Distance=5 km

∴ Required time=Distance/ Speed
=5/15 hrs.
=1/3 hrs
= 20 min

A's time = 3 hours
A's speed = 60 km/h

B's time = 2 hours 30 minutes

Speed = Distance/time

D = 60 × 3 = 180 km

B's speed = 180/2.5
⇒ B's speed = 72 km/h
∴ B's speed is 72 km/h

Let
Pipe A can fill the tank in x hours. Then,
Pipe B can fill the tank in x/2 hours,
Pipe C can fill the tank in x/4 hours.

Part filled by pipe A in 1 hour = 1/x
Part filled by pipe B in 1 hour = 2/x
Part filled by pipe C in 1 hour = 4/x

Now 
1/x + 2/x + 4/x = 1/8
(1 + 2 + 4)/x = 1/8
7/x = 1/8 
x = 56 hours 

The ratio of the speed of A, B and C = 6 ∶ 3 ∶ 1
The ratio of the time taken = 1/6 ∶ 1/3 ∶ 1 = 1 ∶ 2 ∶ 6

Time taken by C to cover the distance = 78 minutes

If C takes 6 min, then A takes 1 min.
If C takes 78 min, then A takes 78 × (1/6) min.
                                                = 13 minutes.

Part filled in 5 min = 5 × {(1/15) + (1/12)}
                              = 5 × {(4 + 5)/60}
                              = 5× (9/60)
                              = 3/4

Part emptied in 1 minute when all the pipes are opened = (1/6) - {(1/15) + (1/12)}
                                                                                          = (10 - 4 - 5)/60
                                                                                          = 1/60
Now,
1​/60 part is emptied in 1 minute.
3/4 part is emptied in =60 ×(3/4) = 45minutes

Total distance travelled :
= (24 + 36) km
= 60 km


Total time taken :
(24/16) + (36/20) hours 
= (3/2) + (9/5) hours
= (15 + 18)/10 hours
= 33/10 hours

∴ Average speed : 60 × (10/33) km/hr.
                            = 600/33 km/hr.
                              = 18.18 km/hr.

Speed of Nazir = 70 kmph
Time = 9 hours
distance = 70 × 9 = 630 Km 

Time taken to cover 630 km at 90 km/hr 

Required time = 630/90 = 7 hours 

Part of the tank filled by the pump in 1 hour = 1/4
Part of the tank filled by the pump in 1 hour because of the leak = 2/9
∴ Part of the tank emptied by the leak in 1 hour = 1/4 - 2/9
                                                                             = (9 - 8)/36
                                                                             = 1/36
∴ Leak will empty the tank in 36 hours

দেওয়া আছে,
একটি ট্যাংকে 1/5 অংশ পূর্ণ আছে।
ট্যাংকটির  3/7 অংশ পূর্ণ করতে আরো 32 গ্যালন জ্বালানী লাগবে।
মনে করি, ট্যাংকটির ধারণ ক্ষমতা = x গ্যালন

প্রশ্নমতে,
    3x/7 - x/5 = 32 
বা, (15x - 7x)/35 = 32
বা, 8x/35 = 32বা, x = (35 × 32)/8
বা, x = 140

Let Mamun's speed = x km/hr
Then, Jahid's speed = (7 - x) km/hr
So,
(24/x) + {24/(7 - x)} = 14 
⇒24(7 - x) + 24x =14x(7 - x)
⇒ 168 - 24x + 24x = 98x - 14x²
⇒ 14x²  - 98x + 168 = 0 
⇒ 14(x² - 7x + 12) = 0
x² - 7x + 12 = 0
x² - 3x - 4x + 12 = 0
x(x - 3) - 4(x - 3) = 0
(x - 3)(x - 4) = 0
x = 3, 4 
Mamun is faster than Jahid
Mamun's speed = 4 km/hr.
Jahid's speed = 3 km/hr.

Let
the distance travelled on foot be x km.
Then, distance travelled on bicycle = (61 -x) km.
(x/4) + {(61 -x)/9} = 9
9x + 4(61 - x) = 9 × 36 
9x + 244 - 4x = 324 
5x + 244 = 324 
5x = 324 - 244 
5x = 80
x = 16