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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়45 minutes
মোট প্রশ্ন২৩
সিলেবাস
Math - 04 - Ratio & Proportion, Partnership, Allegation or Mixture
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স · তারিখ অনির্ধারিত · ২৩ প্রশ্ন

১.
A jar contains white, red and green marbles in the ratio of 2 : 3 : 5. Six more green marbles are added to the jars, and then the ratio becomes 2 : 3 : 7. How many white marbles are there in the jar?
  1. ক
    ক) 2
  2. খ
    খ) 3
  3. গ
    গ) 4
  4. ঘ
    ঘ) 5
  5. ঙ
    ঙ) 6
ব্যাখ্যা

W : R : G = 2 : 3 : 5 [Initial]
W : R : G = 2 : 3 : 7 [Final]
Let, Initial Green = 5x Final Green = 7x
ATQ,
(7x - 5x) = 6
=> 2x = 6
=> x = 3
So, white marbles in the jar = (2 × 3) = 6

২.
The annual incomes and expenditures of a man and his wife are in the ratio of 5 : 3 and 3 : 1 respectively. If they decide to save equally and find a balance of Tk. 4000 at the end of the year, what was the income of the husband?
  1. ক
    ক) 2000
  2. খ
    খ) 3000
  3. গ
    গ) 4000
  4. ঘ
    ঘ) 5000
  5. ঙ
    ঙ) 6000
ব্যাখ্যা

Let, annual income of husband and wife respectively = 5x and 3X
Annual expenditure husband and wife respectively = 3y and y
Saving of wife = (3x - y)
Saving of husband = (5x - 3y)
ATQ,
3x - y = 2000
=> y = (3x - 2000)
And,
5x - 3y = 2000
=> 5x - 3(3x - 2000) = 2000
=> 5x - 9x + 6000 = 2000
=> x = 1000
So, Husband's Income = 5 × 1000 = 5000

৩.
Three containers A, B and C are having mixtures of milk and water in the ratio 20 : 28, 18 : 30 and 8 : 40 respectively. Find the ratio of milk to water, if the mixtures of all the three containers are mixed together?
  1. ক
    ক) 6 : 5
  2. খ
    খ) 5 : 6
  3. গ
    গ) 53 : 115
  4. ঘ
    ঘ) 23 : 49
  5. ঙ
    ঙ) None of the Above
ব্যাখ্যা

At, A ; M : W = 20 : 28 = 5 : 7 = 5/12 : 7/12
At, B; M : W = 18 : 30 = 3 : 5 = 3/8 : 5/8
At C ; M : W = 8 : 40 = 1 : 5 = 1/6 : 5/6
M : W = (5/12 + 3/8 + 1/6) : ( 7/12 + 5/8 + 5/6)
= (20 + 18 + 8)/48 : (28 + 30 + 40)/48
= 46 : 98
= 23 : 49

৪.
Alloy A contains 40% gold and 60% silver. Alloy B contains 35% gold and 40% silver and 25% copper. Alloys A and B are mixed in the ratio of 1 : 4. What is the ratio of gold and silver in the newly formed alloy?
  1. ক
    ক) 11 : 9
  2. খ
    খ) 20 : 30
  3. গ
    গ) 9 : 11
  4. ঘ
    ঘ) 25 : 35
  5. ঙ
    ঙ) 80 : 20
ব্যাখ্যা

A:: - G : S = 40 : 60
B:: - G : S : C = 35 : 40 : 25
New, G : S = {(1×40) + (4×35)} : {(40×4) + (1×60)}
= 180 : 220
= 18 : 22
= 9 : 11 [Answer. ]

৫.
A, B and C enter into partnership by making investments in the ratio of 3 : 5 : 7. After a year, C invests another Tk. 337600 while A withdraws Tk.45600. The ratio of investments then changes to 24 : 59 : 67. How much did A invest initially?
  1. ক
    ক) 10000
  2. খ
    খ) 12000
  3. গ
    গ) 141600
  4. ঘ
    ঘ) 14900
  5. ঙ
    ঙ) None Of the Above
ব্যাখ্যা

Let, A : B : C = 3x : 5x : 7x
After 1 year C investment = 7x + 337600
After 1 year A investment = 3x - 45,600
ATQ,
(3x − 45600)/5x = 24/59
=> 59 × (3x - 45,600) = 120x
=> 177x - 120x = 45600 × 59
=> 57x = 45600 × 59
=> x = 800 × 59 = 47,200
A's initial investment was = 47,200 × 3 = 141600 [Answer.]

৬.
‘X’ Liters of the mixture contains Milk and Water in the ratio of 4 : 3. If 13 liters of Water is added then the ratio becomes 1 : 1. Then what is the final quantity of water in the mixture?
  1. ক
    ক) 40
  2. খ
    খ) 42
  3. গ
    গ) 48
  4. ঘ
    ঘ) 52
  5. ঙ
    ঙ) 54
ব্যাখ্যা

Let,
Initial milk = 4x
Initial water = 3x
ATQ,
(3x + 13)/4x = 1/1
Or, 4x = 3x + 13
Or, x = 13
So, water at final = (3 × 13) + 13
= 52 L

৭.
The ratio of Solution “A” and Solution “B” in the container is 3 : 2 when 10 liters of the mixture is taken out and is replaced by the Solution “B”, the ratio become 2 : 3. The total quantity of the mixture in the container is:
  1. ক
    ক) 20
  2. খ
    খ) 25
  3. গ
    গ) 30
  4. ঘ
    ঘ) 35
  5. ঙ
    ঙ) 40
ব্যাখ্যা

Ration of A : B = 3 : 2
10 L taken out and replaced by B
So, A remain = 3x - 3×10/5 = 3x - 6 And
B remain = 2x - 2×10/5 +10
= 2x + 6
ATQ,
(3x - 6)/(2x + 6) = 2/3
Or, 9x - 18 = 4x + 12
Or, 5x = 30
or, x = 6
The total quantity of mixture = (3x + 2x) = 5x = 5 × 6 = 30 L [Answer.]

৮.
Rice worth Tk. 126 per kg and Tk. 134 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Tk. 177 per kg, the price of the third variety per kg will be:
  1. ক
    ক) Tk 224
  2. খ
    খ) Tk 200
  3. গ
    গ) Tk 250
  4. ঘ
    ঘ) Tk 150
  5. ঙ
    ঙ) Tk 75
ব্যাখ্যা

Let, the price of third variety = x
ATQ,
Or, 126×1 + 134×1 + x×2 = 177×4
Or, 260 + 2x = 708
Or, 2x = 448
Or, x = 224 [Answer.]

৯.
A 144 liters of mixture contains milk and water in the ratio of 5 : 7. How much milk needs to be added to this mixture so that the new ratio is 23 : 21 respectively?
  1. ক
    ক) 30
  2. খ
    খ) 32
  3. গ
    গ) 34
  4. ঘ
    ঘ) 36
  5. ঙ
    ঙ) 38
ব্যাখ্যা

Milk = 144 × 5/12 = 60L
Water = (144 - 60) = 84 L
ATQ,
(60 + x)/(144 + x) = 23/44
Or, 2640 + 44x = 3312 + 23x
Or, 21x = 672
Or, x = 672/21
or, x = 32L

Solution 2:
ATQ,
(60 + x)/84 = 23/21
Or, 60×21 + 21x = 23×84
Or, 21x = 672
or, x = 32 L

১০.
A sugar solution of 3 liters contains 60% sugar. One liter of water is added to this solution. Then the percentage of sugar in the new solution is:
  1. ক
    ক) 18%
  2. খ
    খ) 32%
  3. গ
    গ) 40%
  4. ঘ
    ঘ) 45%
  5. ঙ
    ঙ) 49%
ব্যাখ্যা

In 3 L solution sugar is 60%
So, Sugar Amount = 3 × 3/5 = 1.8 L
Now, 1 L water is added.
So, Total solution = (3 + 1)
= 4 L
% sugar = (1.8 × 100)/4
= 180/4
= 45% [Answer.]

১১.
The annual salary of A, B, C is in the proportion of 3 : 4 : 5. If C's annual salary is Tk 80000 more than that of A, then B's monthly salary is-
  1. ক
    ক) Tk 13666.67
  2. খ
    খ) Tk 13333.33
  3. গ
    গ) Tk 14373.67
  4. ঘ
    ঘ) Tk 16666.67
  5. ঙ
    ঙ) None of the above
ব্যাখ্যা

Let the annual salary of A, B, C respectively be 3x, 4x and 5x.
Then 5x - 3x = 80000
x = 40000
So, B's annual salary = 4x = Tk. 160000
Hence, B's monthly salary
= Tk (160000)/12
= Tk. 13333.33

১২.
Tk. 700 is received among A,B and C so that A receives half as much as B and B half as much as C. Then C’s share is:
  1. ক
    ক) 200
  2. খ
    খ) 300
  3. গ
    গ) 400
  4. ঘ
    ঘ) 500
  5. ঙ
    ঙ) 600
ব্যাখ্যা

Let C = x
Then B = x/2
and A = x/4
A : B : C = 1 : 2 : 4
C's share = Tk. (4/7 × 700) = 400

১৩.
If A : B = 2 : 3, B : C = 4 : 5, C : D = 5 : 9 then A : D = ?
  1. ক
    ক) 11 : 17
  2. খ
    খ) 8 : 27
  3. গ
    গ) 5 : 9
  4. ঘ
    ঘ) 2 : 9
  5. ঙ
    ঙ) 9 : 2
ব্যাখ্যা

A/D = (A/(B × B))/((C × C)/D)
= (2/(3 × 4))/((5 × 5)/9)
= (2 × 4 × 5)/(3 × 5 × 9)
= 8/27
= 8 : 27

১৪.
In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Tk. 30 in all, how many 5 p coins are there?
  1. ক
    ক) 50
  2. খ
    খ) 100
  3. গ
    গ) 150
  4. ঘ
    ঘ) 200
  5. ঙ
    ঙ) 250
ব্যাখ্যা

Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
Then, the sum of their values = Tk. (25x/100) + (10 × 2x/100) + (5 × 3x/100) = Tk. 60x
Or, 60x/100 = 30
Or, x = (30 x 100)/60 = 50.
Hence, the number of 5 p coins = (3 x 50) = 150.

১৫.
Gold is 19 times as heavy as water and copper 9 times as heavy as water. The ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water is :
  1. ক
    ক) 1:2
  2. খ
    খ) 2:3
  3. গ
    গ) 3:2
  4. ঘ
    ঘ) 19:135
  5. ঙ
    ঙ) None of the above
ব্যাখ্যা


Required ratio 6 : 4 = 3 : 2
১৬.
1 year ago the ratio between A’s salary and B’s Salary was 3 : 4.Ratios of their individual salaries between last year’s and present year’s are 4 : 5 & 2 : 3 respectively. At present the total of their salary is Tk 4160. The salary of A now is:
  1. ক
    ক) 1040
  2. খ
    খ) 1600
  3. গ
    গ) 2560
  4. ঘ
    ঘ) 3120
  5. ঙ
    ঙ) None of the above
ব্যাখ্যা

Present ratio of A & B
A : B
3 × (5/4) : 4 × (3/2)
= 15/4 : 12/4
= 15 : 24
= 5 : 8

A’s present salary = ( 4160 of 5/13) = 1600

১৭.
The salaries of A, B, and C are in the ratio of 1 : 2 : 3. The salary of B and C together is Tk. 6000. By what percent is the salary of C more than that of A?
  1. ক
    ক) 100%
  2. খ
    খ) 200%
  3. গ
    গ) 300%
  4. ঘ
    ঘ) 600%
  5. ঙ
    ঙ) 350%
ব্যাখ্যা

Let the salaries of A, B, C be x, 2x and 3x respectively.
Then, 2x + 3x = 6000
=> x = 1200.
A's salary = TK. 1200, B's salary = TK. 2400, and Cs salary TK. 3600.
Excess of C's salary over A's = [(2400/1200) x 100]
= 200%.

১৮.
A, B, C hired a car for Tk. 520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B were:
  1. ক
    ক) 150
  2. খ
    খ) 160
  3. গ
    গ) 170
  4. ঘ
    ঘ) 180
  5. ঙ
    ঙ) 200
ব্যাখ্যা

A : B : C = 7 : 8 : 11.
Hire charges paid by B = Tk. (520 × 8/26)
= Tk. 160.

১৯.
Three friends had dinner at a restaurant. When the bill was received, Akhi paid 2/3 as much as Mira paid and Mira paid 1/2 as much as Lamia paid. What fraction of the bill did Mira pay?
  1. ক
    ক) 11/3
  2. খ
    খ) 2/13
  3. গ
    গ) 3/11
  4. ঘ
    ঘ) 13/4
  5. ঙ
    ঙ) 4/13
ব্যাখ্যা

Let Mira paid x,
so, Akhi paid 2x/3, and
Lamia paid 2x,
So total bill paid is given by,
x + (2x/3) + 2x = 1;
we get,
x = 3/11

So, Mira paid 3/11 fraction of the total bill.

২০.
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) 10 liters
  2. খ
    খ) 20 liters
  3. গ
    গ) 30 liters
  4. ঘ
    ঘ) 40 liters
  5. ঙ
    ঙ) 50 liters
ব্যাখ্যা

Number of liters of water in 125 liters of the mixture = 20% of 150 = 1/5 of 150 = 30 liters
Let us assume that other ‘P’ liters of water are added to the mixture to make water 25% of the new mixture.
So, the total amount of water becomes (30 + P) and
the total volume of the mixture becomes (150 + P)
Thus,
(30 + P) = 25% of (150 + P)
Solving, we get P = 10 liters

২১.
The ratio of water and alcohol in two different containers is 2 : 3 and 4 : 5. In what ratio we are required to mix the mixtures of two containers in order to get the new mixture in which the ratio of alcohol and water be 7 : 5?
  1. ক
    ক) 7:3
  2. খ
    খ) 5:3
  3. গ
    গ) 8:5
  4. ঘ
    ঘ) 2:7
  5. ঙ
    ঙ) 3:5
ব্যাখ্যা

W1 : A1 W2 : A2 …… WN : AN
2 : 3 4 : 5 …… 5 : 7
W1/(W1+A1) = 2/5 ; W2/(W2+A2) = 4/9; WN/(WN+AN) = 5/12
= 72/180
= 80/180
= 75/180



=> 5 : 3
Therefore, the ratio is 5 : 3

২২.
A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is:
  1. ক
    ক) 9 : 5
  2. খ
    খ) 2 : 3
  3. গ
    গ) 4 : 7
  4. ঘ
    ঘ) 5 : 6
  5. ঙ
    ঙ) 5 : 9
ব্যাখ্যা

Dog : Hare = (3 × 3) leaps of hare : 5 leaps of hare
= 9 : 5.

২৩.
In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
  1. ক
    ক) 100
  2. খ
    খ) 150
  3. গ
    গ) 250
  4. ঘ
    ঘ) 260
  5. ঙ
    ঙ) 416
ব্যাখ্যা

Let the number of boys and girls be 8x and 5x.
Total number of students = 13x
= 13 × 32
= 416.