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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়30 minutes
মোট প্রশ্ন২৫
সিলেবাস
Math - 07: Time, Speed, Distance, Pipes & Cisterns
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২৫ প্রশ্ন

১.
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are open in how many hours will the tank? 
  1. ক
    ক) 12 minutes
  2. খ
    খ) 30 minutes
  3. গ
    গ) 15 minutes
  4. ঘ
    ঘ) 60 minutes
ব্যাখ্যা
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
২.
A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two third of the total time, to cover the remaining distance in the remaining time, his speed (in km/hr.) must be
  1. ক
    ক) 8 km/hr.
  2. খ
    খ) 10 km/hr.
  3. গ
    গ) 12 km/hr.
  4. ঘ
    ঘ) 14 km/hr.
ব্যাখ্যা
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.
৩.
A person crosses a 900 m long street in 5 minutes. What is his speed in km per hour?
  1. ক
    ক) 12.8 km/hr.
  2. খ
    খ) 9.8 km/hr.
  3. গ
    গ) 10.8 km/hr.
  4. ঘ
    ঘ) 6.8 km/hr.
ব্যাখ্যা
Speed = 900/(5× 60) m/sec
            = 3 m/sec
            = (3 × 18)/5 km/hr.
            = 10.8 km/hr.
৪.
Two pipes A and B together can fill a tank in 6 hours. If pipe A can fill 5 hours faster than pipe B, in how many hours pipe B alone can fill the tank? 
  1. ক
    ক) 6 hours
  2. খ
    খ) 8 hours
  3. গ
    গ) 10 hours
  4. ঘ
    ঘ) 15 hours
ব্যাখ্যা
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.
৫.
A man can reach a certain place in 30 hours .If the reduces his speed by 1/15th, he goes 10 km less in that time. Find his speed.
  1. ক
    ক) 10 km/hr.
  2. খ
    খ) 8 km/hr.
  3. গ
    গ) 6 km/hr.
  4. ঘ
    ঘ) 5 km/hr
ব্যাখ্যা
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
৬.
A man complete a journey in 10 hours. He travels first half of the journey at the rate of 16 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
  1. ক
    ক) 148 km
  2. খ
    খ) 192km
  3. গ
    গ) 184 km
  4. ঘ
    ঘ) 232 km
ব্যাখ্যা
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
৭.
An outlet pipe can empty a cistern in 6 hours. In what time will it empty 2/3 part of the cistern?
  1. ক
    ক) 2 hours
  2. খ
    খ) 3 hours
  3. গ
    গ) 4 hours
  4. ঘ
    ঘ) 8 hours
ব্যাখ্যা
The outlet pipe empties the one complete cistern in 6 hours
Time taken to empty (2/3) × 6 = 4 hours
৮.
The ratio between the speeds of two trains is 8 : 9. If the second train runs 432 km in 4 hours, then the speed of the first train is:
  1. ক
    ক) 84 km/hr.
  2. খ
    খ) 72 km/hr.
  3. গ
    গ) 96 km/hr.
  4. ঘ
    ঘ) 92 km/hr.
ব্যাখ্যা
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.
৯.
A tap can fill a tank in 12 hrs. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
  1. ক
    ক) 1 hour
  2. খ
    খ) 4.5 hours
  3. গ
    গ) 7.5 hours 
  4. ঘ
    ঘ) 8 hours 
ব্যাখ্যা
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. 
১০.
With an average speed of 50 km/hr a train reaches its destination in time. If it goes with an average speed of 40 km/hr, it is late by 24 minutes. The total journey is -
  1. ক
    ক) 40 km
  2. খ
    খ) 60 km
  3. গ
    গ) 80 km
  4. ঘ
    ঘ) 90 km
ব্যাখ্যা
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.
১১.
Two pipes A and B can fill a tank in 18hrs and 6hrs respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? 
  1. ক
    ক) 7/2 hours
  2. খ
    খ) 11/2 hours
  3. গ
    গ) 5/2 hours
  4. ঘ
    ঘ) 9/2 hours
ব্যাখ্যা
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
১২.
In covering a certain distance, The speeds of A and B are in the ratio of 5 : 6. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is-  
  1. ক
    ক) 2 hours
  2. খ
    খ) 3 hours
  3. গ
    গ) 4 hours
  4. ঘ
    ঘ) 5 hours
ব্যাখ্যা
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
১৩.
A person travels equal distances with speeds of 4 km/hr , 5 km/hr and 6 km/hr and takes a total time of 37 minutes. The total distance (in km) is- 
  1. ক
    ক) 1 km
  2. খ
    খ) 2 km
  3. গ
    গ) 3 km
  4. ঘ
    ঘ) 4 km
ব্যাখ্যা
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

 
১৪.
A train travels a distance of 600 km at a constant speed. If the speed of the train is increased by 5 km/hr, the journey would take 4 h less. Find the speed of the train?
  1. ক
    ক) 30 km/hr.
  2. খ
    খ) 25 km/hr.
  3. গ
    গ) 32 km/hr.
  4. ঘ
    ঘ) 36 km/hr.
ব্যাখ্যা
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.
১৫.
A man takes 50 minutes to cover a certain distance at a speed of 6 km/hr. If he walks with a speed of 15 km/hr, he covers the same distance in :
  1. ক
    ক) 15 min
  2. খ
    খ) 18 min
  3. গ
    গ) 20 min
  4. ঘ
    ঘ) 25 min
ব্যাখ্যা
Distance=Speed × Time
Distance=(6×50)/60 km
Distance=5 km

∴ Required time=Distance/ Speed
=5/15 hrs.
=1/3 hrs
= 20 min
১৬.
A covers a certain distance in 3 hours with a constant speed of 60 km/h. What should be the speed of B to cover the same distance in 2 hours 30 minutes?
  1. ক
    ক) 78 km/h
  2. খ
    খ) 71 km/h
  3. গ
    গ) 72 km/h
  4. ঘ
    ঘ) 79 km/h
ব্যাখ্যা
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
১৭.
A tank is filled in 8 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?
  1. ক
    ক) 36 hours 
  2. খ
    খ) 56 hours 
  3. গ
    গ) 46 hours 
  4. ঘ
    ঘ) 52 hours 
ব্যাখ্যা
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 
১৮.
A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 78 minutes, will be covered by A in :  
  1. ক
    ক) 12 minutes
  2. খ
    খ) 13 minutes
  3. গ
    গ) 14 minutes
  4. ঘ
    ঘ) 15 minutes
ব্যাখ্যা
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.

১৯.
Two pipes A and B can fill a cistern in 12 minutes and 15 minutes respectively while a third pipes C can empty the full cistern in 6 minutes. A and B are kept open for 5 minutes in the beginning and then C is also opened. In what time is the cistern emptied? 
  1. ক
    ক) 40minutes
  2. খ
    খ) 42minutes
  3. গ
    গ) 45minutes
  4. ঘ
    ঘ) 48minutes
ব্যাখ্যা
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
২০.
A cyclist rides 24 km at 16 kmph and further 36 km at 20 kmph. Find his average speed for the journey. 
  1. ক
    ক) 18.18 km/hr.
  2. খ
    খ) 27.18 km/hr.
  3. গ
    গ) 15.18 km/hr.
  4. ঘ
    ঘ) 22.18 km/hr.
ব্যাখ্যা
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.
২১.
If Nazir travels at a speed of 70 kmph and covers a distance in 9 hours. Then how much time will he takes to travel the same distance at a speed of 90 kmph?  
  1. ক
    ক) 9 hours 
  2. খ
    খ) 8 hours 
  3. গ
    গ) 7 hours 
  4. ঘ
    ঘ) 6 hours 
ব্যাখ্যা
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 
২২.
A pump can fill a tank with water in 4 hours. Because of a leak, it took 9/2 hours to fill the tank. The leak can drain all the water of the tank in:
  1. ক
    ক) 18 hours
  2. খ
    খ) 24 hours
  3. গ
    গ) 36 hours
  4. ঘ
    ঘ) 38 hours
ব্যাখ্যা
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
২৩.
A fuel tank is 1/5th full and requires 32 gallons more to make it 3/7 full. What is the capacity of the tank?
  1. ক
    ক) 145 gallons
  2. খ
    খ) 138 gallons
  3. গ
    গ) 135 gallons
  4. ঘ
    ঘ) 140 gallons
ব্যাখ্যা
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
২৪.
Mamun is faster than Jahid. Mamun and Jahid each walk 24 km. The sum of their speeds is 7 km/hr and the sum of time taken by them is 14 hours. Then Mamun's speed is equal to:
  1. ক
    ক) 6 km/hr.
  2. খ
    খ) 5 km/hr.
  3. গ
    গ) 4 km/hr.
  4. ঘ
    ঘ) 2 km/hr.
ব্যাখ্যা
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.
২৫.
A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr. and partly on bicycle at 9 km/hr. The distance travelled on foot is:
  1. ক
    ক) 12 km.
  2. খ
    খ) 14 km.
  3. গ
    গ) 16 km.
  4. ঘ
    ঘ) 18 km.
ব্যাখ্যা
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