ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: The ratio of income and expenditure of a person is 5 : 3 per annum. If he saves Tk 24000 per annum, his monthly income is - 

Solution:
Let income be Tk 5x
and expenditure is Tk 3x

ATQ,
5x - 3x = 24000
⇒ 2x = 24000
⇒ x = 12000

His annual income = 5 × 12000 = 60000 Tk
His monthly income = 60000/12 = 5000 Tk

Question: If A : B = 2 : 3 and B : C = 4 : 5 then A  : C is - 

Solution: 
A : B = 2 : 3
= (2 × 4 ) : (3 × 4)
= 8 : 12

B : C = 4 : 5
= (4 × 3) : (5 × 3)
= 12 : 15

∴ A : B : C = 8 : 12 : 15
∴ A : C = 8 : 15

Question: What is the mean proportional of √5 and √125?

Solution: 
Mean proportional = √(√5 × √125)
= √(√625)
= √25
= 5

Question: What is the difference between the third proportional of 12 and 18, and mean proportional of 9 and 25?

Solution:
Third proportional = (18 × 18)/12 = 27
Mean proportional = √(9 × 25) = √225 = 15

So, the difference = 27 - 15 = 12

Question: 80% of a number is equal to the 4/5th of the other number. What is the ratio between the first number and the second number respectively?

Solution:
Let the first number be x and the second number be y
According to the question,
80% of x = 4/5 of y
⇒ 80x/100 = 4y/5
⇒ 4x/5 = 4y/5
⇒ x = y
⇒ x : y =1 : 1

Question: The income of A, B, and C are in the ratio 7 : 9 : 12 and their spending are in the ratio 8 : 9 : 15. If A saves 1/4 th of his income then the savings of A, B, and C are in the ratio of -

Solution:
Let the income of A, B and C are 7x, 9x, and 12x respectively
and expenditure of A, B and C are 8y, 9y and 15y respectively

ATQ,
7x - 8y = 7x × 1/4
⇒ 28x - 32y = 7x
⇒21x = 32y
⇒ x : y = 32 : 21

∴ The ratio of savings of A, B, and C
⇒ (7x - 8y) : (9x - 9y) : (12x - 15y)
⇒ (7 × 32 - 8 × 21) : (9 × 32 - 9 × 21) : (12 × 32 - 15 × 21)
⇒ (224 - 168) : (288 - 189) : (384 - 315)
⇒ 56 : 99 : 69

Question: In what ratio a mixture of 30%  alcohol strength be mixed with that of 50%  alcohol strength so as to get a mixture of 45% alcohol strength?

Solution:
Let the ratio be 1:x
Then according to the question
⇒ 30 × 1 + 50x = (1+x) 45
⇒ 30 + 50x = 45 + 45x
⇒ 50x - 45x = 45 - 30
⇒ 5x = 15
⇒ x = 3

∴ the ratio is 1 : 3

Question: In what ratio must tea at Tk 62 per kg be mixed with at Tk 72 per kg so that the mixture must be worth Tk 64.5 per kg?

Solution:
Let the quantity of the tea that is Tk 62 per kg be x kg and that of tea that is Tk 72 per kg be y kg.

Hence, the required ratio is x : y

Price of x kg tea = Tk 62x
Price of y kg tea = Tk 72y

If we mix both varieties of tea, the quantity of the mixture will be x + y.

Now, this mixture is Tk 64.50 per kg.
Hence, the total price of the mixture = Tk 64.50(x + y)

So, 62x + 72y = 64.50 (x+y)
⇒ 62x + 72y = 64.5x + 64.5y
⇒ 64.5x - 62x = 72y - 64.5y
⇒ 2.5x = 7.5y
⇒ x/y ​= 7.5​/2.5
⇒ x/y ​= 3
So, x : y = 3 : 1

Hence, the required ratio is 3:1.

Question: A, B, and C invested Tk 50,000 for a business. A invested Tk 4000 more than B and B Tk 5000 more than C. Out of a total profit of Tk 35,000, A receives - 

Solution:
Let C = x.
Then, B = x + 5000
and A = x + 5000 + 4000 = x + 9000

So, x + x + 5000 + x + 9000 = 50000
⇒ 3x = 36000
⇒ x = 12000

A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12

So A's Share = 35000 × (21/50) = Tk 14700

Question: A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Tk 1425, the total profit is-

Solution:
Let the total profit be 100
After paying to charity, A's share =Tk (95 × 3/5) = Tk 57

If A's share is Tk 57, Total profit = Tk 100
If A's share Tk 1425 ,Total profit = (100/57) × 1425 = 2500

Question: A starts a business with Tk 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?

Solution:
Let B's capital be Tk x
∴ A's share in 12 months = 3500 × 12
And, B's share in 7 months = 7x

Then,
(3500 × 12)/7x = 2/3
⇒ 14x = 126000
⇒ x = 9000

Question: If two times A is equal to three times of B and also equal to four times of C, then A : B : C is -

Solution:
2A = 3B
Or, B = 2A/3
and 2A = 4C
Or, C = A/2

Hence, A : B : C = A : 2A/3 : A/2
=1 : 2/3 : 1/2
= 6 : 4 : 3

Question: What must be added to each term of the ratio 2 : 5, So as to make it equal to 5 : 6?

Solution:
Let x be added to each term.

According to the question,
(2 + x) / (5 + x) = 5/6
⇒ 12 + 6x = 25 + 5x
⇒ x = 13

Question: The difference between two positive numbers is 15 and the ratio between them is 7 : 4. Find the sum of the two numbers.

Solution:
Let the two positive numbers be 7x and 4x respectively

According to the question,
7x - 4x = 15
⇒ 3x = 15
⇒ x = 5

Then numbers are 7 × 5 = 35 and 4 × 5 = 20
So, sum of numbers = 35 + 20 = 55

Question: A cat leaps 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?

Solution:
Given;
3dog = 4 cat
Or, dog/cat = 4/3

Let cat's 1 leap = 3 meter and dogs 1 leap = 4 meter

Then, ratio of speed of cat and dog = (3 × 5) / (4 × 4) = 15 : 16

Question: To gain 10% on selling sample of milk at the cost price of pure milk, the quantity of water to be mixed with 50 kg of pure milk is -

Solution:
Let the quantity of water mixed be x kg.
Let CP of 1 kg of pure milk = Tk 1

Hence,
% gain = x × (100/50)
⇒ 10 = 100x/50
⇒ 100x = 500
⇒ x = 5

Question: How many liters of water should be added to a 30 liters mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?

Solution:
Water in the mixture = 30 × (3/10) = 9 liters

ATQ,
9 + x = 40% of (30 + x)
⇒ 9 + x = (2/5)(30 +x)
⇒ 45 + 5x = 60 + 2x
⇒ 3x = 15
⇒ x = 5

Question: The ratio of syrup and water in a mixture is 3 : 1, the percentage of water in this mixture is -

Solution:
Percentage of water = (1/4) × 100%  = 25%

Question: A milkman mixed some water with milk to gain 25% by selling the mixture at the cost price. The ratio of water and milk is respectively -

Solution:
Let, the milkman has milk of Tk 100
∴ After mixing water the mixture sold for Tk = 100 + 25 = Tk 125

In Tk 125, Milk is of Tk 100 and Water is of Tk 25
So, The ratio of water and milk in mixture = 25 : 100 = 1 : 4

Question: A started a business with Tk 24000 and was joined afterward by B with Tk 36000. After how many months did B join if the profits at end of the year are divided equally?

Solution:
Suppose, B invested after x months

ATQ,
24000 × 12 = 36000 × (12 - x)
⇒ 24 × 12 = 36 × (12 - x)
⇒ 12 - x = (24 × 12)/36
⇒ 12 - x = 8
⇒ x = 4

Question: Niamul, Sabbir, and Mosharaf started a shop by investing Tk 10500, Tk 7000, and Tk 3500 respectively. At the end of the one year, the profit earned was distributed. If Sabbir's gained a profit of Tk 2400, what would be Niamul gain?

Solution:
Let the total profit  be Tk x

Now,
Niamul : Sabbir : Mosharaf = 10500 : 7000 : 3500 = 3 : 2 : 1

Sabbir's profit = x × (2/6) = x/3

ATQ,
x/3 = 2400
⇒ x = 7200

Niamul's profit = 7200 × (3/6) = 3600 Tk

Question: Moni and Mimi are partners in a business. Moni invests 36000 for 8 months and Mimi invests Tk 48000 for 10 months. Out of a profit of 32768, Moni's share is - 

Solution:
Ratio of their shares = (36000 × 8) : (48000 × 10)
= 288 : 480
= 3 : 5

Moni's share = 32768 × (3/8) = 12288

Question: The ratio of the four angles of a quadrilateral is 3 : 4 : 5 : 6. What is the largest angle?

Solution:
Sum of the angles of a quadrilateral = 360°
Largest angle = 360° × (6/18) = 120°

Question: If A : B : C = 2 : 3 : 4, then the ratio (A/B) : (B/C) : (C/A) = ?

Solution:
Let, 
A = 2k
B = 3k
C = 4k

Then,
A/B = 2k/3k = 2/3
B/C = 3k/4k = 3/4
C/A = 4k/2k = 2

(A/B) : (B/C) : (C/A) = (2/3) : (3/4) : 2
= (2/3) × 12 : (3/4) × 12 : 2 × 12
= 8 : 9 : 24

Question: Let x : y = a/b : - b/a,  If (x - y) = (a/b + b/a) then x is equal to -

Solution:
Given,
⇒ x/y =(a/b)/(-b/a)
⇒ x/y = - a²/b²
⇒ y =(−b²/a²)x

Now,
x - y = a/b + b/a
⇒ x + (b²/a²)x = (a² + b²)/ab
⇒ x(a² + b²)/a² = (a²+b²)/ab
⇒ x = a²/ab
⇒ x = a/b

Question: Rahim's expenditures and savings are in the ratio of 3 : 2. His income increases by 10%. His expenditure also increases by 12%. How much percent does his savings increase?

Solution:
Let Rahim's expenditures be 3x and his savings be 2x
So, his income = 3x + 2x = 5x

Increased income = 110% of 5x = 5.5x
Increased expenditures = 112% of 3x = 3.36x

New savings = 5.5x - 3.36x = 2.14x

Increased savings = 2.14x - 2x = 0.14x

So, increases in percentage = (0.14x/2x) × 100 = 7%