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ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

পরীক্ষাব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্সতারিখতারিখ অনির্ধারিতসময়45 minutes
মোট প্রশ্ন১৮
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 · ১৮ প্রশ্ন

১.
If (x + y) : (x - y) = 4 : 1, then (x2 + y2) : (x2 - y2) is equal to -
  1. ক
    ক) 8 : 17
  2. খ
    খ) 17 : 8
  3. গ
    গ) 16 : 1
  4. ঘ
    ঘ) 25 : 9
ব্যাখ্যা

According to the question,
(x + y)/(x - y) = 4
⇒ x + y = 4x - 4y
⇒ 4x - x = 4y + y
⇒ 3x = 5y
⇒ x/y = 5/3
⇒ x2/y2 = 25/9
Now,
⇒ x2 + y2/x2 - y2
= {(x2 /y2) + 1}/{(x2/y2) - 1}
= {(25/9) +1}/{(25/9 - 1}
(34/9) × (9/16)
= 17/8

২.
If A : B = 4 : 5, B: C = 7 : 9 and C : D = 3 : 4, and if A’s share is Tk. 1680, the share of D is -
  1. ক
    ক) Tk. 2100
  2. খ
    খ) Tk. 2700
  3. গ
    গ) Tk. 2900
  4. ঘ
    ঘ) Tk. 3600
ব্যাখ্যা

A : B = 4 : 5;

B : C = 7 : 9
= (7 × 5/7) : (9 × 5/7)
= 5 : 45/7

C : D = 3 : 4
= (3 × 15/7) : (4 × 15/7)
= 45/7 : 60/7.

A : B : C : D
= 4 : 5 : 45/7 : 60/7
= 28 : 35 : 45 : 60.

Let the shares of A, B, C, D be 28x, 35x, 45x, 60x respectively.

Then,
28x = 1680
⇒ x = 1680/28
= 60

∴ D's Share = 60x = Tk. (60 × 60)
= Tk. 3600.

৩.
Between two consecutive years my incomes are in the ratio of 2 : 3 and expenses in the ratio 5 : 9. If my income in the second year is Tk. 45000 and my expenses in the first year is Tk. 25000 my total savings for the two years is -
  1. ক
    ক) Nil
  2. খ
    খ) Tk. 5000
  3. গ
    গ) Tk. 10000
  4. ঘ
    ঘ) Tk. 15000
ব্যাখ্যা

Let,
income in the first year be Tk. x and expenses in the second year be Tk. y
Then, x/45000 = 2/3 and 25000/y = 5/9
⇒ x = (2 × 45000)/3
= 30000
and y (25000 × 9)/5
= 45000.
∴ Total savings for 2 years
= Tk. [(30000 - 25000) + (45000 - 45000)]
= Tk. 5000.

৪.
The cost of a table and a chair are in the ratio of 5 : 7. If the cost of chair and table is increased by 20% and 10% respectively, then what will be the new ratio?
  1. ক
    ক) 16 : 17
  2. খ
    খ) 55 : 84
  3. গ
    গ) 60 : 77
  4. ঘ
    ঘ) Data inadequate
ব্যাখ্যা

Let,
the cost of the table and chair be Tk. 5x and Tk. 7x respectively.
New cost of chair = 120% of Tk. 7x = Tk (6/5 × 7x)
= Tk. 42x/5.
New cost of table = 110% of Tk. 5x = Tk.(11/10 × 5x)
= Tk. 55x/10.
∴ New ratio = 55x/10 : 42x/5
= 55 : 84

এছাড়াও,
5 : 7
নতুন অনুপাতঃ
5 এর 110% : 7 এর 120%
= 5.5 : 8.4

৫.
A student took five papers in an examination, where full marks were the same on each paper. Her marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all these papers together, the candidate obtained 60% of the total marks. Then the number of papers in which she got more than 50% marks is -
  1. ক
    ক) 2
  2. খ
    খ) 3
  3. গ
    গ) 4
  4. ঘ
    ঘ) 5
ব্যাখ্যা

Let,
the full marks for each paper be x.
Let the marks obtained in the five papers be 6y, 7y, 8y, 9y and 10y respectively.
Then, (6y + 7y + 8y + 9y + 10y)/5x = 60/100
⇒ 40y/5x = 3/5
⇒ 40y = 3x
⇒ x = (40/3)y
50% of x = (50/100) × (40/3)y
= 20y/3
= 6(2/3)y.
Clearly, the student got more than 50% marks in each of the last 4 papers.

৬.
15 men, 18 women and 12 boys working together earned Tk. 2070. If the daily wages of a man, a woman and a boy are in the ratio of 4 : 3 : 2, the daily wage (in Tk) of 1 man, 2 women and 3 boys are -
  1. ক
    ক) 135
  2. খ
    খ) 180
  3. গ
    গ) 205
  4. ঘ
    ঘ) 240
ব্যাখ্যা

Let,
the daily wage of a man, a woman and a boy be Tk. 4x, Tk. 3x and Tk. 2x respectively.
Then, 15 × 4x + 18 × 3x + 12 × 2x = 2070
⇒ 60x + 54x + 24x = 2070
⇒ 138x = 2070
⇒ x = 15
∴ daily wages of 1 man, 2 women and 3 boys
= Tk. (4x + 2 × 3x + 3 × 2x)
= Tk. (4x + 6x + 6x)
= Tk. 16x
= Tk. (16 × 15)
= Tk. 240.

৭.
Find the third proportional to 25 and 30
  1. ক
    ক) 36
  2. খ
    খ) 32
  3. গ
    গ) 34
  4. ঘ
    ঘ) 38
ব্যাখ্যা

Let third proportional be x
⇒ 25 : 30 : : 30 : x
⇒ 25 × x = 30 x 30
⇒ x = (30 x 30)/25
= 36.

৮.
If a2 + b2 + c2 - ab - bc - ca = 0 then a : b : c is -
  1. ক
    ক) 1 : 1 : 2
  2. খ
    খ) 1 : 1 : 1
  3. গ
    গ) 1 : 2 : 1
  4. ঘ
    ঘ) 2 : 1 : 1
ব্যাখ্যা

a2 + b2 + c2 - ab - bc - ca = 0 .....(i)
Multiple equation (i) by 2 we get
⇒ 2a2 + 2b2 + 2c2 - 2ab - 2bc - 2ca = 0
⇒ (a2 + b2 - 2ab) + (b2 + c2 - 2bc) + (c2 + a2 - 2ca) = 0 [ (a + b)2 = a2 + b2 + 2ab]
⇒ (a - b)2 + ((b - c)2 + (c - a)2 = 0 [if x2 + y2 + z2 = 0 then x = 0, y = 0, z = 0]
∴ a - b = 0
⇒ a = b
b - c = 0
⇒ b = c
c - a = 0
⇒ c = a
∴ a : b : c = 1 : 1 : 1

৯.
Two alloys contain zinc and copper in the ratio of 2 : 1 and 4 : 1.In what ratio the two alloys should be added together to get a new alloy having zinc and copper in the ratio of 3 : 1?
  1. ক
    ক) 3 : 5
  2. খ
    খ) 5 : 9
  3. গ
    গ) 7 : 5
  4. ঘ
    ঘ) None of these
ব্যাখ্যা

Zinc in first allow = 2/3 units;
Zinc in second alloy = 4/5 units.
copper in first alloy = 1/3 units;
copper in second alloy = 1/5 units.
Let the first and second alloys be mixed in the ratio 1 : y.
Then, {(2/3) + (4y/5)}/{(1/3 + (y/5)) = 3/1
⇒ 10 + 12y = 3 (5 + 3y)
⇒ 10 + 12y = 15 + 9y
⇒ 3y = 5
⇒ y = 5/3.
∴ Required ratio = 1 : 5/3
= 3:5

১০.
A, B and C enter into a partnership with the capital in the ratio 7/2 : 4/3 : 6/5. After 4 months A increases his share of capital by 50%. If at the end of the year the total profit earned is Tk. 2430, find the share of each in the profit.
  1. ক
    ক) 1680, 580, 450
  2. খ
    খ) 1575, 450, 405,
  3. গ
    গ) 1460, 415, 380
  4. ঘ
    ঘ) 1245, 380, 240
ব্যাখ্যা

Ratio of capitals = 7/2 : 4/3 : 6/5 = (7/2 × 30) : (4/3 × 30) : (6/5 × 30)
= 105 : 40 : 36.
Let the initial capitals of A, B and C be Tk. 105x, 40x, 36x respectively.
Then, ratio of profit = [105x × 4 + (150% of 105x) × 8] : (40x × 12 ) : (36x × 12)
1680 : 480 : 432
= 35 : 10 : 9.
∴ A's share = Tk. (2430 × 35/54) = Tk. 1575; B's share = Tk (2430 × 10/54) = Tk. 450
C's share = Tk. (2430 × 9/54) = Tk. 405.

১১.
Sima started a software business by investing Tk. 50,000. After six months, Rajon joined her with a capital of Tk. 80000. After 3 years, they earned a profit of Tk. Tk. 24500. What was Sima’s share in the profit?
  1. ক
    ক) Tk. 9423
  2. খ
    খ) Tk. 10250
  3. গ
    গ) Tk. 10500
  4. ঘ
    ঘ) Tk. 14000
ব্যাখ্যা

Sima : Rajon = (50000 × 36) : (80000 × 30)
1800000 : 2400000
= 3 : 4
∴ Sima's share = Tk. (24500 × 3/7)
= Tk. 10500.

১২.
Two friends P and Q started a business investing in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Q’s. At the end of the year, 20% profit was earned which was equal to Tk. 98000. What was the amount invested by R?
  1. ক
    ক) Tk. 105000
  2. খ
    খ) Tk. 175000
  3. গ
    গ) Tk. 210000
  4. ঘ
    ঘ) Tk. 24000
ব্যাখ্যা

Let the total investment be Tk. z
Then, 20% of z = 98000
⇒ z = 98000 × 100)/20
= 490000.
Let the capitals of P, Q and R be Tk. 5x, Tk. 6x and Tk. 6x respectively.
Then, (5x × 12) + (6x 12) + (6x × 6) = 490000 × 12
⇔ 168x = 490000 × 12 ⇔ x = (490000 × 12)/168 = 35000.
∴ R's investment = 6x = Tk. (6 × 35000)
= Tk. 210000.

১৩.
Rahul, Amin, and Akash started a business. Rahul invested 1/2 part, Amin 1/3 part and rest of the capital was invested by Akash. The ratio of their profit will be?
  1. ক
    ক) 2 : 3 : 1
  2. খ
    খ) 3 : 2 : 1
  3. গ
    গ) 2 : 3 : 6
  4. ঘ
    ঘ) 3 : 2 : 5
ব্যাখ্যা

Let the total capital be Tk. x.
Then, Rahul's share = Tk. x/2
Amin's share = Tk. x/3
Akash's share = [x - {(x/2) + (x/3)}]
= Tk. x/6
∴ Required ratio = x/2 : x/3 : x/6 = 1/2 : 1/3 : 1/6
= 3 : 2 : 1

১৪.
In a sugar-water solution, the ratio of water to sugar is 8 : 3. If you add 2 kgs of sugar, the ratio becomes 2 : 1. What is the amount of sugar in the original solution in kg?
  1. ক
    ক) 3
  2. খ
    খ) 4.5
  3. গ
    গ) 6
  4. ঘ
    ঘ) 8
ব্যাখ্যা

Let
amount of water be 8x.
So, the amount of sugar is 3x.
According to question,
8x/(3x + 2) = 2/1
Solving this equation, we get, x = 2
Therefore, the amount of sugar in the original solution = 3 × 2 = 6 kg.

১৫.
The ratio of water and salt in a 16 kg of salt - water solution is 3 : 1. How much water in kg must be added to make the ratio of water to salt 4 : 1?
  1. ক
    ক) 2
  2. খ
    খ) 3
  3. গ
    গ) 4
  4. ঘ
    ঘ) 6
ব্যাখ্যা

salt = 16 × 1/4 = 4 Kg
water = 16 - 4
= 12 kg.
এখন water/salt = 4
∴ water = 4 × 4 = 16 Kg
∴ (16 - 12) = 4 Kg water add করতে হবে।

১৬.
Ibrahim has 20 ounces of a 20% flavoured solution. How much salt should he add to make it a 25% solution?
  1. ক
    ক) 10.3
  2. খ
    খ) 50
  3. গ
    গ) 1.33
  4. ঘ
    ঘ) 5
ব্যাখ্যা

Let y be the amount of flavour.
(0.2 × 20) + 1 × y = 0.25 (20 + y)
Or, 4 + y = 5 + 0.25y
Or, 0.75y = 1
So, y = 1.33

১৭.
A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is?
  1. ক
    ক) 4%
  2. খ
    খ) 6(/4)%
  3. গ
    গ) 20%
  4. ঘ
    ঘ) 25%
ব্যাখ্যা

Let C.P of 1 litre milk be Tk. 1.
Then, S.P of 1 litre of mixture = Tk. 1, Gain = 25%
C.P. of 1 litre mixture = Tk. (100/125) × 1
= Tk. 4/5
By the rule of alligation, we have:

∴ Ratio of the milk to water = 4/5 : 1/5
= 4 : 1.
Hence, percentage of water in the mixture
= {(1/5) × 100}%
= 20%

১৮.
A container contains 40 litres of milk. From this container, 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
  1. ক
    ক) 26.34 litres
  2. খ
    খ) 27.36 litres
  3. গ
    গ) 28 litres
  4. ঘ
    ঘ) 29.16 litres
ব্যাখ্যা

Amount of milk left after 3 operations
= [40 {1 - (4/40)}3] litres
= (40 × 9/10 × 9/10 × 9/10) litres
= 29.16 litres.