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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

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Percentage, Allegation or Mixture [ব্যাংকের সকল পরীক্ষা যেকোনো প্যাকেজের জন্য ফ্রি]
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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২০ প্রশ্ন

১.
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
  1. ক
    ক) 57%
  2. খ
    খ) 60%
  3. গ
    গ) 65%
  4. ঘ
    ঘ) 90%
ব্যাখ্যা

Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage =(11628/20400)x 100%
= 57%.

২.
The contents of a certain box consist of 14 apples and 23 oranges. How many oranges must be removed from the box so that 70% of the pieces of fruit in the box will be apples ?
  1. ক
    ক) 6
  2. খ
    খ) 12
  3. গ
    গ) 17
  4. ঘ
    ঘ) 36
ব্যাখ্যা

Total number of fruits = (14 + 23) = 37
Let x oranges be removed.
Then,
70% of (37 - x) = 14
⇒ 7 (37 - x) = 140
⇒ 37 - x = 20
⇒ x = 17

৩.
In an examination it is required to get 40% of the aggregate marks to pass. A student get 261 marks and is declared failed by 4% marks. What are the maximum aggregate marks a student can get ?
  1. ক
    ক) 700
  2. খ
    খ) 730
  3. গ
    গ) 745
  4. ঘ
    ঘ) None of these
ব্যাখ্যা

Let the maximum marks be x.
Then,
(40−4)% of x =261
⇒ 36% of x =261
⇒ 36x/100 =261
⇒ x = (261×100/36)
⇒ x = 725

৪.
From a container having pure milk, 20% is replaced by water and the process is repeated thrice. At the end of the third operation, the milk is :
  1. ক
    ক) 40% pure
  2. খ
    খ) 50% pure
  3. গ
    গ) 51.2% pure
  4. ঘ
    ঘ) 58.8% pure
ব্যাখ্যা

Let total quantity of original milk = 1000 gm
Milk after first operation = 80% of 1000 = 800 gm
Milk after second operation = 80% of 800 = 640 gm
Milk after third operation = 80% of 640 = 512 gm
∴ Strength of final mixture = 51.2%

৫.
Two numbers are respectively 20% and 50% of the third number. What percent is the first number of the second ?
  1. ক
    ক) 10%
  2. খ
    খ) 20%
  3. গ
    গ) 30%
  4. ঘ
    ঘ) 40%
ব্যাখ্যা

Let the 3rd number is 100
According to the question,
1st :2nd: 3rd= 20:50:100
Required % = (20/50) × 100 = 40%

৬.
In an election between two candidates, the winner got 65% of the total votes cast and won the election by a majority of 2748 votes. What is the total number of votes cast if no vote is declared invalid?
  1. ক
    ক) 8580
  2. খ
    খ) 8720
  3. গ
    গ) 9000
  4. ঘ
    ঘ) 9160
ব্যাখ্যা

Winner gets 65% 0f valid votes and loser gets 35% of votes.
Difference between this two = 2748
(65-35)% = 2748
30% = 2748
Total number of voters, 100%
= (2748×100)/30
= 9160

৭.
The price of a car depreciates in the first year by 25%, in the second year by 20% , in third year by 15% and so on. The final price of the car after 3 years, if the present cost of the car is Tk.10,00,000-
  1. ক
    ক) 7,80,000
  2. খ
    খ) 1,70,000
  3. গ
    গ) 6,90,000
  4. ঘ
    ঘ) 5,10,000
ব্যাখ্যা

1000000 × 0.75 × 0.80 × 0.85=  5,10,000

৮.
(X% of Y) + (Y% of X) is equal to:
  1. ক
    ক) X% of Y
  2. খ
    খ) 20% of XY
  3. গ
    গ) 2% of XY
  4. ঘ
    ঘ) 2% of 100 XY
ব্যাখ্যা

According to question,        
XY/100 + YX/100
= 2XY/100
= 2% o fXY

৯.
40 is subtracted from 60% of a number, the result is 50. Find the number?
  1. ক
    ক) 150
  2. খ
    খ) 140
  3. গ
    গ) 130
  4. ঘ
    ঘ) 110
ব্যাখ্যা

Let the number be x
The problem could be 40 is subtracted from 60% of a number, the result is 50.
60% of x = 60/100×x= 60x/100
60x/100 - 40 = 50
(60x - 4000) /100 = 50
Cross multiplication
60x - 4000 = 50 ×100
60x -4000 = 5000
60x = 5000 + 4000
60x = 9000
x = 9000/60
x = 150
Hence, the number is 150

১০.
After decreasing 24% in the price of an article costs Tk.912. Find the actual cost of an article?
  1. ক
    ক) 1400
  2. খ
    খ) 1300
  3. গ
    গ) 1200
  4. ঘ
    ঘ) 1100
ব্যাখ্যা

CP× (76/100) = 912
CP = 12 × 100
=> CP = 1200

১১.
How much water must be added to a bucket which contains 40 liters of milk at the cost price of Tk 3.50 per liter so that the cost of milk reduces to Tk 2 per liter?
  1. ক
    ক) 25 liters
  2. খ
    খ) 28 litres
  3. গ
    গ) 30 liters
  4. ঘ
    ঘ) 35 liters
ব্যাখ্যা

Total cost price = Tk (40 x 7/2) = Tk 140
Cost per litre = Tk n2,
Total quantity = 140/2 = 70 Litres.
Water to be added =(70-40) =30 Litres.

১২.
A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
  1. ক
    ক) 72
  2. খ
    খ) 72.9
  3. গ
    গ) 73.8
  4. ঘ
    ঘ) 74.7
ব্যাখ্যা

Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]n × T
For the given problem, T = 90, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(90 - 9)/90]2 (90) =  72.9 litres.

১৩.
In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
  1. ক
    ক) 40
  2. খ
    খ) 44
  3. গ
    গ) 48
  4. ঘ
    ঘ) 52
ব্যাখ্যা

 Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352
=> T = 44

১৪.
How many liters of oil at Tk.40 per liter should be mixed with 240 liters of a second variety of oil at Tk.60 per liter so as to get a mixture whose cost is Tk.52 per liter?
  1. ক
    ক) 120 liters
  2. খ
    খ) 180 liters
  3. গ
    গ) 110 liters
  4. ঘ
    ঘ) 160 liters
ব্যাখ্যা

Apply Allegation Method and first calculate the ratio in which they have to be mixed.
= 8 : 12 = 2 : 3
Thus, the two varieties of oil should be mixed in the ratio 2 : 3. So, if 240 liters of the second variety are taken, then 160 liters of the first variety should be taken.

১৫.
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
  1. ক
    ক) 7 liters
  2. খ
    খ) 15 liters
  3. গ
    গ) 10 liters
  4. ঘ
    ঘ) 9 liters
ব্যাখ্যা

Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 × 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 × (150 + P)
120 + 4P = 150 + P
=> P = 10 liters.

১৬.
In an examination 80% candidates passed in English and 85% candidates passed in Mathematics. If 73% candidates passed in both these subjects, then what percent of candidates failed in both the subjects?
  1. ক
    ক) 8
  2. খ
    খ) 15
  3. গ
    গ) 27
  4. ঘ
    ঘ) 35
ব্যাখ্যা

Students passed in English = 80%
Students passed in Math's = 85%
Students passed in both subjects = 73%
Then, number of students passed in at least one subject
= (80+85)-73
= 92%.
Thus, students failed in both subjects = 100-92 = 8%

১৭.
The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by
  1. ক
    ক) 25%
  2. খ
    খ) 20%
  3. গ
    গ) 80%
  4. ঘ
    ঘ) 75%
ব্যাখ্যা

Let the initial expenses on Sugar was Tk. 100.
Now, Price of Sugar rises 25%. So, to buy same amount of Sugar, they need to expense,
= (100 + 25% of 100) = Tk. 125.
But, They want to keep expenses on Sugar, so they have to cut Tk. 25 in the expenses to keep it to Tk. 100.
Now, % decrease in Consumption,
(25/125)×100=20%

১৮.
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
  1. ক
    ক) 16 : 5
  2. খ
    খ) 14 : 5
  3. গ
    গ) 16 : 7
  4. ঘ
    ঘ) 19 : 5
ব্যাখ্যা

Quantity of alcohol in vessel P = 62.5/100 × 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 × 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed
 = 4.75 : 1.25 = 19 : 5.

১৯.
In an examination 36% are pass marks. If an examine gets 17 marks and fails by 10 marks, what are the maximum marks?
  1. ক
    ক) 90
  2. খ
    খ) 75
  3. গ
    গ) 60
  4. ঘ
    ঘ) 55
ব্যাখ্যা

Pass mark = (17 + 10) = 27
Let maximum marks be x
Then 36% of x = 27
Or, 36x/100 = 27
Or, 36x = 2700
Hence, x = 75

২০.
40 litres of a mixture of milk and water contains 10% of water, the water to be added, to make the water content 20% in the new mixture. Find how many litres water will be added ?
  1. ক
    ক) 6 litres
  2. খ
    খ) 6.5 litres
  3. গ
    গ) 5.5 litres
  4. ঘ
    ঘ) 5 litres
ব্যাখ্যা

Water content in 40 litres of mixture.
= 40×(10/100) =4 litres
Milk in the mixture.
= 40−4=36 litres
Let x litres of water is mixed
⇒(4+x)/(40+x)=20/100
⇒x=5 litres