Ratio & Proportion, Alligation or Mixture

PrepBank · পাতা ৪ / ১১ · ৩০১–৪০০ / ১,০৮৬

৩০১.

The price of 2 pencils is less than 20% of the price of a pen. What is the ratio of the price of a pen to that of a pencil?

ক
7 : 3
খ
5 : 2
গ
5 : 3
ঘ
None of these

ব্যাখ্যা

Question: The price of 2 pencils is less than 20% of the price of a pen. What is the ratio of the price of a pen to that of a pencil?

Solution:
Let, the price of pen = 100

20% less, price of 2 pencils = 100 - 20 = Tk. 80
20% less, price of 1 pencil = 80/2 = Tk. 40

∴ pen : pencil = 100 : 40
= 5 : 2

৩০২.

If A : B : C = 1/2 : 1/3 : 1/5, then what is the ratio of A/B : B/C : C/A ?

ক
ক) 11 : 41 : 91
খ
খ) 19 : 18 : 13
গ
গ) 37 : 45 : 15
ঘ
ঘ) 45 : 50 : 12

ব্যাখ্যা

A : B : C = 1/2 : 1/3 : 1/5

A : B : C = 1/2 : 1/3 : 1/5
⇒ A : B : C = 30/2 : 30/3 : 30/5
⇒ A : B : C = 15 : 10 : 6

Let A = 15, B = 10 and C = 6, then

∴ A/B : B/C : C/A = 15/10 : 10/6 : 6/15 = (3/2) : (5/3) : (2/5) = 90/2 : 150/3 : 60/5 = 45 : 50 : 12

৩০৩.

What is the ratio of 8 inches to 6 feet?

ক
ক) 9 : 1
খ
খ) 1 : 9
গ
গ) 2 : 9
ঘ
ঘ) 9 : 2

ব্যাখ্যা

Question: What is the ratio of 8 inches to 6 feet?

Solution:
1 feet = 12 inches
So, 6 feet = 6 × 12 = 72 inches

Now,
8 inches : 6 feet = 8 : 72 = 1 : 9

৩০৪.

A solution has a ratio of water to acid as 4 : 1. If 5 liters of water is added, the ratio becomes 5 : 1. What was the original quantity of the solution?

ক
30 liters
খ
25 liters
গ
24 liters
ঘ
20 liters

ব্যাখ্যা

Question: A solution has a ratio of water to acid as 4 : 1. If 5 liters of water is added, the ratio becomes 5 : 1. What was the original quantity of the solution?

Solution:
Let the original quantity of water and acid be 4x liters and x liters, respectively
The total original quantity of the solution is:
4x + x = 5x

When 5 liters of water is added, the new quantity of water becomes 4x + 5 liters, while the quantity of acid remains x liters. The new ratio of water to acid is given as 5 :1, so:
(4x + 5)/x = 5/1
⇒ 4x + 5 = 5x
⇒ 5 = 5x - 4x
⇒ x = 5

The original quantity of the solution is:
5x = 5 × 5 = 25 liters

৩০৫.

15% of A's income is equal to 25% of B's income. What is the ratio of the income of B to A?

ক
ক) 5 : 3
খ
খ) 3 : 2
গ
গ) 3 : 5
ঘ
ঘ) 2 : 3

ব্যাখ্যা

Question: 15% of A's income is equal to 25% of B's income. What is the ratio of the income of B to A?

Solution:
15% of A = 25% of B
⇒ 15A/100 = 25B/100
⇒ 15A = 25B
⇒ B/A = 15/25
⇒ B/A = 3/5
∴ B : A = 3 : 5

৩০৬.

A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

ক
6 : 10 : 5
খ
3 : 5 : 2
গ
5 : 3 : 2
ঘ
7 : 8 : 5
ঙ
None of the above

ব্যাখ্যা

Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

Solution:
Let the initial investments of A and B be 3a and 5a.

A : B : C = (3a × 12) : (5a × 12) : (5a × 6)
= 36 : 60 : 30
= 6 : 10 : 5

৩০৭.

In a mixture of 80 liters of juice and water, the ratio of juice to water is 5 : 3. How much water should be added to make the ratio of juice to water 1 : 1?

ক
25 liters
খ
20 liters
গ
15 liters
ঘ
30 liters

ব্যাখ্যা

Question: In a mixture of 80 liters of juice and water, the ratio of juice to water is 5 : 3. How much water should be added to make the ratio of juice to water 1 : 1?

Solution:
The ratio 5 : 3 means there are 5 parts juice and 3 parts water, making a total of 5 + 3 = 8 parts.

Juice = (5/8) × 80 = 50 liters
Water = (3/8) × 80 = 30 liters

Let, x liters of water be added
Then new amount of water = 30 + x liters

ATQ,
⇒ 50/(30 + x) = 1/1
⇒ 30 + x = 50
⇒ x = 50 - 30
∴ x = 20

∴ 20 liters of water should be added to make the ratio 1 : 1.

৩০৮.

A and B invest in a business in a ratio of 3 : 2. If 5% of the total profit goes to charity. A's share is Tk. 855, the total profit is:

ক
Tk. 1425
খ
Tk. 1500
গ
Tk. 1537.50
ঘ
Tk. 1576

ব্যাখ্যা

Question: A and B invest in business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share in Tk. 855, the total profit is:

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

If A's share is Tk. 57, total profit = 100.
If A's share is Tk. 855, total profit = (100/57) × 855
= 1500.

৩০৯.

35% of Nabila's income is equal to 25% of Sakira's income. The ratio of their income is

ক
5 : 7
খ
4 : 7
গ
7 : 3
ঘ
4 : 3

ব্যাখ্যা

35% of Nabila's income = 25% of Sakira's income
Nabila's income/Sakira's income = 25/35 = 5/7

৩১০.

The ratio of the number of boys and girls in a school is 7 : 4. If the percentage increase in the number of boys and girls be 25% and 15% respectively, what will be the new ratio?

ক
160 : 92
খ
92 : 160
গ
175 : 92
ঘ
92 : 175

ব্যাখ্যা

Question: The ratio of the number of boys and girls in a school is 7 : 4. If the percentage increase in the number of boys and girls be 25% and 15% respectively, what will be the new ratio?

Solution:
Let,
The number of boys and girls in a school be 7X and 4X respectively
their increased number number is (125% of 7X) and (115% of 4X)
⇒ (125/100) of 7X and (115/100) of 4X
⇒ 35X/4 and 23X/5

∴ required ratio = 35X/4 : 23X/5
= 175X : 92X [multiply by 20]
= 175 : 92

৩১১.

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?

ক
ক) 16 : 17
খ
খ) 55 : 84
গ
গ) 60 : 77
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

৩১২.

A motorcycle costs Tk. 2,500 when it is brand new. At the end of each year it is worth 4/5 of what it was at the beginning of the year. What is the motorcycle worth when it is 3 years old?

ক
ক) Tk. 1,000
খ
খ) Tk. 1,280
গ
গ) Tk. 1,340
ঘ
ঘ) Tk. 1,430

ব্যাখ্যা

Question: A motorcycle costs Tk. 2,500 when it is brand new. At the end of each year it is worth 4/5 of what it was at the beginning of the year. What is the motorcycle worth when it is 3 years old?

Solution:
প্রথমে, মোটরসাইকেলটির দাম ২৫০০ টাকা

১ বছর শেষে দাম = ২৫০০ × ৪/৫
= ২০০০ টাকা

২ বছর শেষে দাম = ২০০০ × ৪/৫
= ১৬০০ টাকা

৩ বছর শেষে দাম = ১৬০০ × ৪/৫
= ১২৮০ টাকা

৩১৩.

Rimon saves Tk. 3395 from his salary. He needs to pay this money as a milk bill, electricity bill and mobile phone bill in the ratio 42 : 32 : 23. Find the money to be paid for each bill.

ক
ক) Tk. 1245, Tk. 1150 and Tk 1000
খ
খ) Tk. 1470, Tk. 1120 and Tk. 805
গ
গ) Tk. 1550, Tk. 1235 and Tk. 610
ঘ
ঘ) Tk. 1764, Tk. 1022 and Tk. 529

ব্যাখ্যা

Common factor helps in finding actual values easily
So, take 'A' as a common factor.
∴ 3 numbers will now be 42A, 32A and 23A
∴ 42A + 32A + 23 A = 3395
∴ 97A = 3395
∴ A = 35
3 parts of 3395 are
42A = 42 x 35 = 1470;
⇒ 32A = 32 x 35 = 1120
⇒ 23A = 23 x 35 = 805
These are the amounts to be paid.

৩১৪.

The sum of the squares of three numbers is 1197 and the ratio of the first and the second as also of the second and the third is 3 : 2 . The third number is-

ক
10
খ
12
গ
15
ঘ
9

ব্যাখ্যা

Question: The sum of the squares of three numbers is 1197 and the ratio of the first and the second as also of the second and the third is 3 : 2 . The third number is-

Solution:
Given,
First : Second = 3 : 2 = 9 : 6
Second : Third = 3 : 2 = 6 : 4

∴ First : Second : Third = 9 : 6 : 4

Let,
the number be 9x, 6x and 4x

ATQ,
(9x)² + (6x)² + (4x)² = 1197
⇒ 81x² + 36x² + 16x² = 1197
⇒ 133x² = 1197
⇒ x² = 9
∴ x = 3

So the third number = 4 × 3 = 12

৩১৫.

Parimal has two grandchildren, Jasmine, aged 2, and Holly, aged 4. Parimal divides Tk. 30 between them in the ratio of their ages. How much does Jasmine get?

ক
Tk. 10
খ
Tk. 12
গ
Tk. 15
ঘ
Tk. 18
ঙ
Tk. 20

ব্যাখ্যা

Question: Parimal has two grandchildren, Jasmine, aged 2, and Holly, aged 4. Parimal divides Tk. 30 between them in the ratio of their ages. How much does Jasmine get?

Solution:
Tk. 30 is the whole amount.
Parimal divides Tk. 30 in the ratio 2 : 4.

The total number of shares is 2 + 4 = 6.
Each share is worth Tk. 30 ÷ 6 = Tk. 5.
∴ Jasmine gets 2 shares, 2 × 5 = Tk. 10

৩১৬.

A and B are two alloys of gold and copper prepared by mixing metals in the ratios 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, then the ratio of gold and copper in alloy C will be -

ক
7 : 8
খ
7 : 9
গ
7 : 5
ঘ
6 : 5

ব্যাখ্যা

Question: A and B are two alloys of gold and copper prepared by mixing metals in the ratios 7:2 and 7:11 respectively. If equal quantities of the alloys are melted to form a third alloy C, then the ratio of gold and copper in alloy C will be -

Solution: A and B are two alloys of gold and copper prepared by mixing metals in the ratios 7:2 and 7:11 respectively. If equal quantities of the alloys are melted to form a third alloy C

Gold in C

Copper in C

∴ Gold: Copper = 7/6:5/6 = 7:5

৩১৭.

Copper is 9 times as heavy as water, and tin is 3 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water?

ক
1 : 3
খ
1 : 2
গ
1 : 1
ঘ
2 : 1
ঙ
None

ব্যাখ্যা

Question: Copper is 9 times as heavy as water, and tin is 3 times as heavy as water. In what ratio should these be mixed to get an alloy 6 times as heavy as water?

Solution:
Let copper be 9x times as heavy and tin 3y times as heavy as water.

9x + 3y = 6(x + y)
⇒ 9x + 3y = 6x + 6y
⇒ 9x − 6x = 6y − 3y
⇒ 3x = 3y
⇒ x/y = 1/1

∴ Copper and tin should be mixed in the ratio 1 : 1.

৩১৮.

In a vessel, milk and water are in a ratio of 3 : 5. In the second vessel, the milk and water are in the ratio of 3 : 2. In what ratio should these two mixtures be mixed to form a new mixture in which the milk and water are in the ratio 2 : 3?

ক
1 : 8
খ
6 : 1
গ
7 : 1
ঘ
8 : 1

ব্যাখ্যা

Question: In a vessel, milk and water are in a ratio of 3 : 5. In the second vessel, the milk and water are in the ratio of 3 : 2. In what ratio should these two mixtures be mixed to form a new mixture in which the milk and water are in the ratio 2 : 3?

Solution:
The ratio of milk and water in the first vessel = 3 : 5
The ratio of milk and water in the second vessel = 3 : 2
The ratio of milk and water in the final mixture = 2 : 3

Let
The mixture from the two-vessel be mixed in the ratio x : y.

Quantity of milk taken from the first vessel = 3x/8
Quantity of water taken from the first vessel = 5x/8

Quantity of milk taken from the second vessel = 3y/5
Quantity of water taken from the second vessel = 2y/5

Then,
{(3x/8) + (3y/5}/{(5x/8) + (2y/5)} = 2/3
⇒ {(15x + 24y)/40}/{(25x + 16y)/40} = 2/3
⇒ 3(15x + 24y) = 2(25x + 16y)
⇒ 45x + 72y = 50x + 32y
⇒ 50x - 45x = 72y - 32y
⇒ 5x = 40y
⇒ x/y = 8/1

∴ The first and second mixure are mixed in the ratio 8 : 1

৩১৯.

Two vessels of equal capacity contain juice and water in the ratio of 7 : 2 and 11 : 7 respectively. The mixture of both vessels is mixed and transferred into a bigger vessel. What is the ratio of juice and water in the new mixture?

ক
18 : 9
খ
21 : 6
গ
22 : 7
ঘ
25 : 11

ব্যাখ্যা

Question: Two vessels of equal capacity contain juice and water in the ratio of 7 : 2 and 11 : 7 respectively. The mixture of both vessels is mixed and transferred into a bigger vessel. What is the ratio of juice and water in the new mixture?

Solution:
The ratio of juice and water in the first vessel = 7 : 2 ................(1)
Total capacity of first vessel = 7 + 2 = 9 units

The ratio of juice and water in the second vessel = 11 : 7 ...............(2)
Total capacity of second vessel = 11 + 7 = 18 units

We will have to equal the total capacity of both vessels, so multiply by 2 in equation (1).
The ratio of juice and water in the first vessel = 14 : 4 ................(3)

∴ Ratio of juice and water in bigger vessel = (14 + 11) : (4 + 7) = 25 : 11

৩২০.

The ratio of milk and water in a solution is 7 : 4. After adding 8 liters of water, the ratio of milk and water becomes 3 : 2. Find the final amount of water in the solution.

ক
56 liters
খ
42 liters
গ
48 liters
ঘ
72 liters

ব্যাখ্যা

Question: The ratio of milk and water in a solution is 7 : 4. After adding 8 liters of water, the ratio of milk and water becomes 3 : 2. Find the final amount of water in the solution.

Solution:
Let the initial amount of milk = 7x liters
Let the initial amount of water = 4x liters

According to the question,
7x/(4x + 8) = 3/2
⇒ 2 × 7x = 3 × (4x + 8)
⇒ 14x = 12x + 24
⇒ 14x - 12x = 24
⇒ 2x = 24
⇒ x = 12

∴ Final amount of water = 4x + 8
= 4 × 12 + 8
= 48 + 8
= 56 liters

৩২১.

By mixing two qualities of pulse in the ratio 2 : 3 and selling the mixture at the rate of Tk. 22 per kilogram, a shopkeeper makes a profit of 10%. If the cost of the smaller quantity be Tk. 14 per kg, the cost in Tk per kg of the larger quantity is :

ক
21
খ
22
গ
23
ঘ
24
ঙ
None of the above

ব্যাখ্যা

Question: By mixing two qualities of pulse in the ratio 2 : 3 and selling the mixture at the rate of Tk. 22 per kilogram, a shopkeeper makes a profit of 10%. If the cost of the smaller quantity be Tk. 14 per kg, the cost in Tk per kg of the larger quantity is :

Solution:
Let’s assume,
The price of a larger quantity of lentils = x Tk.

Given,
Small quantity : Large quantity = 2 : 3
The sum of the ratios = 2 + 3 = 5

The purchase price of 5 kg = 14 × 2 + x × 3
= 28 + 3x

The selling price of 5 kg = 22 × 5 = 110

Thus, Profit = 110 - (28 + 3x)
= 110 - 28 - 3x
= 82 - 3x

ATQ,
{(82 - 3x)/(28 + 3x)}× 100 % = 10%
⇒ (82 - 3x)/(28 + 3x) = 1/10
⇒ 820 - 30x = 28 + 3x
⇒ 3x + 30x = 820 - 28
⇒ 33x = 792
⇒ x = 792/33
∴ x = 24

৩২২.

‘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?

ক
ক) 40
খ
খ) 42
গ
গ) 48
ঘ
ঘ) 52
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

৩২৩.

A jar contains white, red and green marbles in the ratios 2 : 3 : 5. Sixteen more green marbles are added to the jars and the ratio becomes 2 : 3 : 9. How many red marbles are there in the jar?

ক
ক) 8
খ
খ) 10
গ
গ) 12
ঘ
ঘ) 20

ব্যাখ্যা

সাদা , লাল এবং সবুজ মার্বেলের অনুপাত 2 : 3 : 5
সাদা মার্বেল আছে = 2x
সবুজ মার্বেল আছে = 5x

এখানে
2x : (5x + 16) = 2 : 9
2x/(5x + 16) = 2/9
x/(5x + 16) = 1/9
9x = 5x + 16
9x - 5x = 16
4x = 16
x = 4
লাল মার্বেল আছে = 3 × 4 = 12

৩২৪.

a : b : c = 2 : 3 : 4 and 2a - 3b + 4c = 33, then the value of c is = ?

ক
12
খ
10
গ
8
ঘ
6
ঙ
None of the above

ব্যাখ্যা

Question: a : b : c = 2 : 3 : 4 and 2a - 3b + 4c = 33, then the value of c is = ?

Solution:
Let,
a = 2x
b = 3x
c = 4x

So,
2a - 3b + 4c = 4x - 9x + 16x = 33
⇒ 11x = 33
⇒ x = 3

∴ c = 4x = 4 × 3 = 12

৩২৫.

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?

ক
10 liters
খ
20 liters
গ
30 liters
ঘ
40 liters

ব্যাখ্যা

Question: 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?

Solution:
Number of liters of water in 150 liters of the mixture = 20% of 150 = 1/5 of 150 = 30 liters

Let us Assume that another '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)
⇒ (30 + P) = (1/4)(150 + P)
⇒ 120 + 4P = 150 + P
⇒ 3P = 30
∴ P = 10 liters

৩২৬.

Sumon bought 2 varieties of rice, costing taka 8 per kg and taka 12 per kg each, and mixed them in some ratio, then he sold the mixture at taka 12 Per kg. Making a profit of 20%. what was the ratio of the mixture?

ক
ক) 2 : 1
খ
খ) 1 : 2
গ
গ) 1 : 1
ঘ
ঘ) 3 : 1
ঙ
ঙ) None

ব্যাখ্যা

Let, the rice of two verities be in amount x and y
ATQ,
(8x + 12y)120/100 = 12(x + y)
⇒ 8x + 12y = (12×100)/120(x + y) = 10x + 10y
⇒ 2x = 2y
∴ x : y = 1 : 1

৩২৭.

3/4th of square were taken to form shape A and the rest was made to form shape B. Shape A was divided into four equal squares (Shape C), what will be the ratio of the one shape C to one shape B.

ক
ক) 1 : 4
খ
খ) 3 : 16
গ
গ) 1 : 2
ঘ
ঘ) 3 : 4

ব্যাখ্যা

Let, A = 3x/4
and, B = x/4
So, C = (3x/4) / 4 = 3x/16
∴ C:B = 3x/16 : x/4 = 3:4

৩২৮.

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. 1140, the total profit is:

ক
ক) Tk. 1000
খ
খ) Tk. 1200
গ
গ) Tk. 1440
ঘ
ঘ) Tk. 2000

ব্যাখ্যা

Let total profit be Tk. 100
After paying 5% to charity, A's share = 95 × 3/5 = 57
Total profit = 100/57 × 1140 = 2000

৩২৯.

If the ratio of syrup and water in a mixture is 7 : 3, then the percentage of water in mixture is-

ক
15%
খ
20%
গ
30%
ঘ
25%

ব্যাখ্যা

Question: If the ratio of syrup and water in a mixture is 7 : 3, then the percentage of water in mixture is-

Solution:
The ratio of syrup and water in a mixture is 7 : 3
Total = 10
∴ percentage of water = (3 × 100)/10 %
= 30%

৩৩০.

Kabir bought 4 times as many shares in Company X as Carl and Carl bought 3 times as many shares in the same company as Tom. Which of the following is the ratio of the number of shares bought by Kabir to the number of shares bought by Tom?

ক
12 : 5
খ
12 : 1
গ
11 : 5
ঘ
12 : 7

ব্যাখ্যা

Question: Kabir bought 4 times as many shares in Company X as Carl and Carl bought 3 times as many shares in the same company as Tom. Which of the following is the ratio of the number of shares bought by Kabir to the number of shares bought by Tom?

Solution:
Let,
Tom bought = a shares
Carl bought = 3a shares
Kabir bought = 4 × 3a = 12a shares

We're asked for the ratio of Kabir's shares to Tom's shares
Kabir : Tom = 12a : a = 12 : 1

৩৩১.

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

ক
ক) 3
খ
খ) 9
গ
গ) 12
ঘ
ঘ) 13

ব্যাখ্যা

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

৩৩২.

The first number is 25% greater than a third number, and the second number is 40% greater than the same third number. What is the ratio of the first number to the second number?

ক
25 : 30
খ
36 : 25
গ
5 : 8
ঘ
25 : 28
ঙ
None

ব্যাখ্যা

Question: The first number is 25% greater than a third number, and the second number is 40% greater than the same third number. What is the ratio of the first number to the second number?

Solution:
Let the third number be x

Then,
First number = 125% of x
= 125x/100
= 5x/4

Second number = 140% of x
= 140x/100
= 7x/5

∴ Ratio of first two numbers
= 5x/4 : 7x/5
= 25x : 28x
= 25 : 28

৩৩৩.

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-

ক
ক) Tk 13666.67
খ
খ) Tk 13333.33
গ
গ) Tk 14373.67
ঘ
ঘ) Tk 16666.67
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

৩৩৪.

The milk and water in a mixture are in the ratio 5 : 4. When 15 litres of water are added to it, the ratio of milk and water in the new mixture becomes 5 : 7. The total quantity of water in the new mixture is:

ক
24 litres
খ
35 litres
গ
42 litres
ঘ
50 litres

ব্যাখ্যা

Question: The milk and water in a mixture are in the ratio 5 : 4. When 15 litres of water are added to it, the ratio of milk and water in the new mixture becomes 5 : 7. The total quantity of water in the new mixture is:

Solution:
Let the initial quantity of milk = 5x litres
and initial quantity of water = 4x litres

According to the question,15 litres of water is added.

New amount of water = (4x + 15)
The amount of milk remains the same = 5x

As per the new ratio,
5x/(4x + 15) = 5/7
⇒ 7(5x) = 5(4x + 15)
⇒ 35x = 20x + 75
⇒ 35x − 20x = 75
⇒ 15x = 75
⇒ x = 5

The total quantity of water in the new mixture,
= (4x + 15)
= (4 × 5) + 15
= 20 + 15
= 35 litres

∴ Total quantity of water in new mixture 35 litres.

৩৩৫.

The ratio of boys and girls in a class is 4:5. If 10% of the boys and 20%of the girls failed In an examination, what percentage of students passed in the exam?

ক
ক) 80%
খ
খ) 82%
গ
গ) 85%
ঘ
ঘ) None

ব্যাখ্যা

The percentage of boys = {4/(4+5)}×100 = (4/9)×100 = 400/9%
and The percentage = {5/(4 + 5)}×100 = (5/9)×100 = 500/9% .
So, The percentage of students passed in the exam = (400/9 - 10)% + (500/9 - 20)% = 310/9 + 320/9 = 630/9 = 70%.

৩৩৬.

A shopkeeper mixes 3 litres of water with 15 litres of milk costing Tk 60 per litre and sells the whole at cost price. What is the profit percentage?

ক
10%
খ
15%
গ
20%
ঘ
25%

ব্যাখ্যা

Question: A shopkeeper mixes 3 litres of water with 15 litres of milk costing Tk 60 per litre and sells the whole at cost price. What is the profit percentage?

Solution:
→ Total cost = 15 × 60 = Tk 900
→ Total volume = 18 litres, Selling price per litre = 900/18 = Tk 50
→ Profit per litre = 60 – 50 = Tk 10
→ Profit % = (10/50)×100 = 20%

৩৩৭.

A jar contains white, red and green marbles in the ratios 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?

ক
ক) 5
খ
খ) 6
গ
গ) 9
ঘ
ঘ) 10

ব্যাখ্যা

Ratio of W : R : G = 2 : 3 : 5
If 6 Green marbel is added, Ratio becomes W : R : G = 2 : 3 : 7
Difference of ratio for 6 marbles = 7 – 5 = 2
So, 1 ratio = 3 marbles
∴ White marbles = 2×3 = 6

৩৩৮.

If 13:11 is the ratio of the present age of Jolly and Lopa respectively and 15:9 is the ratio between Jolly’s age 4 years hence and Lopa's age 4 years ago. Then what will be the ratio of Jolly’s age 4 years ago and Lopa's age 4 years hence?

ক
15:9
খ
9:15
গ
11:13
ঘ
13:11

ব্যাখ্যা

Let the present age of Jolly and lopa be 13X and 11X respectively.
Given, Jlly's age 4 years hence and lopa's age 4 years ago in the ratio 15:9.
That is,
(13X + 4)/(11X - 4) = 15/9
⇒ 9(13X + 4) = 15(11X - 4)
⇒ 117X + 36 = 165X - 60
⇒ 48X = 96
⇒ X = 2.
Now, required ratio is (13X-4)/(11X + 4)
= 13(2) - 4/11(2) + 4
= 22/26
= 11/13.
Hence the answer is 11:13.

৩৩৯.

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

ক
14500 taka
খ
14700 taka
গ
14800 taka
ঘ
15000 taka

ব্যাখ্যা

Question: A, B, C subscribe Tk. 50,000 for a business. A subscribes 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 subscribes x taka
B subscribes x + 5000 taka
A subscribes x + 5000 + 4000
= x + 9000 taka

x + x + 5000 + x + 9000 = 50000
⇒ 3x + 14000 = 50000
⇒ 3x = 36000
⇒ x = 12000 taka

A receives = {(x + 9000)/50000} × 35000
= (21000/50000) × 35000
= 14700 taka

৩৪০.

The number of students in 3 classes is in the ratio 2 : 3 : 4. If 10 students are increased in each class this ratio changes to 8 : 11 : 14. The total number of students in the three classes in the beginning was-

ক
ক) 135
খ
খ) 150
গ
গ) 140
ঘ
ঘ) 125

ব্যাখ্যা

Question: The number of students in 3 classes is in the ratio 2 : 3 : 4. If 10 students are increased in each class this ratio changes to 8 : 11 : 14. The total number of students in the three classes in the beginning was-

Solution:
Let the number of students in the classes be 2x, 3x and 4x respectively;
Total students = 2x + 3x + 4x = 9x
According to the question,
(2x+10) : (3x+10) = 8 : 11
or, 11(2x+10) = 8(3x+10)
or, 22x + 110 = 24x + 80
or, 2x = 30
or, x = 15

Hence,
Original number of students,
9x = 9×15 = 135

৩৪১.

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?

ক
4 kg
খ
5 kg
গ
6 kg
ঘ
7 kg
ঙ
8 kg

ব্যাখ্যা

Question: 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?

Solution:
Let's say the initial amount of sugar is x kg
Given the 8:3 ratio, the initial amount of water is (8x/3) kg

After adding 2 kg of sugar, new amount of sugar = x + 2 kg
Amount of water remains same = (8x/3) kg

ATQ,
⇒ (8x/3)/(x + 2) = 2/1
⇒ 8x/3 = 2(x + 2)
⇒ 8x/3 = 2x + 4
⇒ 8x = 6x + 12
⇒ 2x = 12
∴ x = 6
Therefore, the original amount of sugar was 6 kg.

৩৪২.

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

ক
ক) 100°
খ
খ) 105°
গ
গ) 120°
ঘ
ঘ) 135°

ব্যাখ্যা

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°

৩৪৩.

Tk. 7800 are distributed among A, B, and C. The share of "A" is the 3/4 of the share of B, and the share of B is the 2/3 of the share of C. Find the difference between the share of B and C.

ক
1200
খ
1300
গ
1500
ঘ
800

ব্যাখ্যা

Question: Tk. 7800 are distributed among A, B, and C. The share of "A" is the 3/4 of the share of B, and the share of B is the 2/3 of the share of C. Find the difference between the share of B and C.

Solution:
The share of A: B is 3: 4
The share of B: C is 2: 3

Note: Whenever such form is given, multiply a to b, then b to b, and then b to c.

i.e., A: B: C = 3×2: 4×2: 4×3
Or, A: B: C = 6: 8: 12
Or, A: B: C = 3: 4: 6
Sum of ratios = 13
Now, the share of B = [4/13] × 7800 = 2400
Share of C = [6/13]× 7800 = 3600

The difference between the share of B and C = 3600- 2400 = 1200

৩৪৪.

30 kgs of rice costing Tk. 12/kg is mixed with some kgs of rice costing Tk. 18 to get the mixture costing Tk. 13.5. Find the quantity of rice costing Tk. 18.

ক
10 kg
খ
12 kg
গ
18 kg
ঘ
20 kg

ব্যাখ্যা

Question: 30 kgs of rice costing Tk. 12/kg is mixed with some kgs of rice costing Tk. 18 to get the mixture costing Tk. 13.5. Find the quantity of rice costing Tk. 18.

Solution:
Let, the amount of rice costing Tk.18 is x kg

ATQ,
30 × 12 + 18x = 13.5 × (x + 30)
⇒ 360 + 18x = 13.5x + 405
⇒ 18x - 13.5x = 405 - 360 = 45
⇒ 4.5x = 45
∴ x = 45/4.5 = 10 kg

৩৪৫.

If a : b = 1 : 3, b : c = 5 : 7, then what is the value of a : b : c?

ক
ক) 3 : 5 : 7
খ
খ) 5 : 9 : 15
গ
গ) 5 : 15 : 21
ঘ
ঘ) 4 : 13 : 24

ব্যাখ্যা

দেয়া আছে ,
a : b = 1 : 3 = 5 : 15
b : c = 5 : 7 = 15 : 21

a : b : c = 5 : 15 : 21

৩৪৬.

If m : n = 3 : 2, then find the ratio (4m + 5n) : (4m - 5n).

ক
ক) 1 : 10
খ
খ) 11 : 1
গ
গ) 10 : 1
ঘ
ঘ) 11 : 3

ব্যাখ্যা

Question: If m : n = 3 : 2, then find the ratio (4m + 5n) : (4m - 5n).

Solution:
here,
m : n = 3 : 2
2m = 3n
∴ 4m = 6n

hence,
(4m + 5n) : (4m - 5n) = (6n + 5n) : (6n - 5n)
= 11n : n
= 11 : 1

৩৪৭.

P, Q and R are three towns on a river which flows uniformly. Q is equidistant from P and R. I row from P to Q and back in 10 hours and I can row from P to R in 4 hours. Compare the speed of my boat in still water with that of the river.

ক
ক) 4 : 3
খ
খ) 5 : 3
গ
গ) 6 : 5
ঘ
ঘ) 7 : 3

ব্যাখ্যা

Let PQ = Qr = x km
Let speed downstream = a km/hr.
and speed upstream = b km/hr.

Then,
x/a + x/b = 10
x = 10ab/(a + b) .........(i)

And,
2x/a = 4
x = 4a/2
x = 2a .............(ii)

From (i) and (ii) we have:
2a = 10ab/(a + b)
5b = a + b
a = 4b

Required ratio = Speed in the water/Speed of river
= {1/2(a + b)}/{(1/2) (a - b)}
= (a + b)/(a - b)
= (4b + b)/(4b - b)
= 5b/3b
= 5/3

৩৪৮.

In a 48 ltr mixture, the ratio of milk and water is 5:3. How much water should be added in the mixture so as the ratio will become 3:5 ?

ক
24 lit
খ
16 lit
গ
32 lit
ঘ
8 lit
ঙ
None of the above

ব্যাখ্যা

Given mixture = 48 lit
Milk in it = 48 x 5/8 = 30 lit
=> Water in it = 48 - 30 = 18 lit
Let 'L' lit of water is added to make the ratio as 3:5
=> 30/(18+L) = 3/5
=> 150 = 54 + 3L
=> L = 32 lit.

৩৪৯.

A man spends a part of his monthly income and saves the rest. The ratio of his expenditure to the savings is 61 : 6. If his monthly income is Tk. 8710, the amount of his monthly savings is-

ক
Tk. 660
খ
Tk. 780
গ
Tk. 810
ঘ
Tk. 840

ব্যাখ্যা

Question: A man spends a part of his monthly income and saves the rest. The ratio of his expenditure to the savings is 61 : 6. If his monthly income is Tk. 8710, the amount of his monthly savings is-

Solution:
Expenditure : Savings = 61 : 6

∴ Sum of the terms of ratio = (61 + 6) = 67

Given,
Total monthly salary = Tk. 8710

∴ Monthly savings = Tk.{(6/67) × 8710}
= Tk. 780

৩৫০.

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?

ক
ক) 120 liters
খ
খ) 180 liters
গ
গ) 110 liters
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.

৩৫১.

If 6m - n = 4m + 13n, find the value of 2m + n : 2m - 3n.

ক
14 : 11
খ
15 : 14
গ
15 : 11
ঘ
None of these

ব্যাখ্যা

Question: If 6m - n = 4m + 13n, find the value of 2m + n : 2m - 3n.

Solution:
6m - n = 4m + 13n
⇒ 2m = 14n
∴ m = 7n.

∴ Required ratio = (2m + n : 2m - 3n)
= 14n + n : 14n - 3n
= 15n : 11n
= 15 : 11

৩৫২.

A 180 liter mixture of syrup and water contains 20% of syrup. What quantity of syrup must be added with that mixture to get 25% syrup?

ক
ক) 10 liter
খ
খ) 24 liter
গ
গ) 12 liter
ঘ
ঘ) None of the above

ব্যাখ্যা

Total mixture = 180 liter
Syrup contains = 20%

Quantity of syrup in solution = 180 × 20% =180 × (1/5) = 36liter
Quantity of water in mixture = (180 ─ 36) liter = 144 liter
Now in mixture contain 25% of syrup
∴ Water = (100% ─ 25%) = 75%

According to the question,
⇒ 75x = 144
⇒ x = 144/75

∴ Total mixture = 100x liter = 100 × (144/75) = 192 liter
∴ Syrup should be added in mixture = (192 ─ 180) = 12 liter

৩৫৩.

A distance is covered by a cyclist at a certain speed. If a jogger covers half of the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is -

ক
ক) 1:4
খ
খ) 4:1
গ
গ) 1:2
ঘ
ঘ) 2:1

ব্যাখ্যা

Cyclist:Jogger
Ratio of distance→ 2:1
Ratio of time→ 1:2
Ratio of their speed (Jogger:Cyclist)
= (1/2):(2/1)
= 1:4

৩৫৪.

If a : b : c = 2 : 3 : 4 and 2a - 2b + 4c = 42, then the value of c is

ক
ক) 6
খ
খ) 12
গ
গ) 14
ঘ
ঘ) 16

ব্যাখ্যা

Question: If a : b : c = 2 : 3 : 4 and 2a - 2b + 4c = 42, then the value of c is

Solution:
let,
a = 2x
b = 3x
c = 4x

so,
2a - 2b + 4c = 4x - 6x + 16x = 42
14x = 42
x = 3

∴ c = 4x = 4 × 3 = 12

৩৫৫.

In 60 liters of mixture milk and water ratio is 7 : 3. If we add more water to that mixture, the ratio of milk and water will be 2 : 9. How much water will be added to that mixture?

ক
ক) 168 liters
খ
খ) 169 liters
গ
গ) 171 liters
ঘ
ঘ) 156 liters

ব্যাখ্যা

Question: In 60 liters of mixture milk and water ratio is 7 : 3. If we add more water to that mixture, the ratio of milk and water will be 2 : 9. How much water will be added to that mixture?

Solution:
৬০ লিটার মিশ্রণে দুধের পরিমাণ = ৬০ এর ৭/১০ = ৪২ লিটার
৬০ লিটার মিশ্রণে পানির পরিমাণ = ৬০ এর ৩/১০ = ১৮ লিটার

ধরি,
ক লিটার পানি মিশালে মিশ্রণের অনুপাত ২ : ৯ হবে।

শর্তমতে,
৪২/(১৮ + ক) = ২/৯
বা, ৩৬ + ২ক = ৩৭৮
বা, ২ক = ৩৭৮ - ৩৬
বা, ২ক = ৩৪২
∴ ক = ১৭১ লিটার
মিশ্রণে ১৭১ লিটার পানি মিশালে অনুপাত ২ : ৯ হবে।

৩৫৬.

A bag contains red, blue, and green balls in the ratio 2 : 3 : 5. If there are 15 blue balls, how many total balls are there in the bag?

ক
15
খ
40
গ
60
ঘ
50

ব্যাখ্যা

Question: A bag contains red, blue, and green balls in the ratio 2 : 3 : 5. If there are 15 blue balls, how many total balls are there in the bag?

Solution: Given ratio = Red : Blue : Green = 2 : 3 : 5
Let the numbers be:
Red = 2x, Blue = 3x, Green = 5x

Given,
Blue balls, 3x = 15
∴ x = 5

Now calculate total balls:
= 2x + 3x + 5x
= (2 + 3 + 5)x
= 10x
= 10 × 5
= 50

৩৫৭.

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:

ক
ক) 18%
খ
খ) 32%
গ
গ) 40%
ঘ
ঘ) 45%
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.]

৩৫৮.

Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?

ক
1 : 1
খ
2 : 1
গ
3 : 2
ঘ
2 : 3

ব্যাখ্যা

Question: Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 15 times as heavy as water?

Solution: Let Gold is 19x times as heavy as water and copper is 9y times as heavy as water.

Now,
→ 19x+ 9y = 15(x+y)
→ 19x+ 9y = 15 x+ 15y
→ 4x= 6y
→ x:y =6:4
→ x:y = 3:2

৩৫৯.

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 -

ক
ক) 1 : 4
খ
খ) 2 : 3
গ
গ) 2 : 5
ঘ
ঘ) 3 : 7

ব্যাখ্যা

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

৩৬০.

Two numbers are in ratio of 3 : 7. If 6 is added in each, the new numbers are in ratio of 5 : 9. Find the ratio of numbers, if 6 subtracted from each number?

ক
ক) 1 : 5
খ
খ) 2 : 3
গ
গ) 3 : 5
ঘ
ঘ) 1 : 3

ব্যাখ্যা

ধরি
সংখ্যা দুটি 3x এবং 7x
⇒ (3x + 6)/(7x + 6) = 5/9
⇒ 27x + 54 = 35x + 30
⇒ 8x = 24
⇒ x = 3
সংখ্যা দুটি 9 এবং 21

নতুন অনুপাত = (9 - 6)/(21- 6)
= 3/15
= 1/5
= 1 : 5

৩৬১.

A starts 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?

ক
ক) 7500
খ
খ) 8000
গ
গ) 8500
ঘ
ঘ) 9000

ব্যাখ্যা

Let B's capital be tk. x.
Then, (3500 x 12)/7x = 2/3
or, 14x = 126000
so, x = 9000 tk

৩৬২.

If A : B : C = 2 : 3 : 5 and A = x% of (B + C), then x equal to:

ক
ক) 35
খ
খ) 32
গ
গ) 30
ঘ
ঘ) 25

ব্যাখ্যা

Let A = 2k, B = 3k, C = 5k
A = x% of (B + C)
⇒ 2k = x% of (3k + 5k)
⇒2k = x% of 8k
⇒ 2k = 8kx/100
⇒ 1 = 4x/100
⇒ 4x = 100
x = 25

৩৬৩.

Sabit, Sabbir, and Salman started a business. Sabit 1/2 part, Sabbir 1/3 part, and the rest of the capital were invested by Salman. The ratio of their profits will be?

ক
ক) 1 : 2 : 4
খ
খ) 3 : 2 : 1
গ
গ) 2 : 3 : 4
ঘ
ঘ) 3 : 4 : 5

ব্যাখ্যা

Question: Sabit, Sabbir, and Salman started a business. Sabit 1/2 part, Sabbir 1/3 part, and the rest of the capital were invested by Salman. The ratio of their profits will be?

Solution:
Let the total capital be 6x
Then, Sabit's share = 6x × (1/2) = 3x
Sabbir's share = 6x × (1/3) = 2x
Salman's share = 6x - (3x + 2x) = x

So, required ratio = 3x : 2x : x = 3 : 2 : 1

৩৬৪.

In a mixture of 30 liters, the ratio of acid and water is 7 : 3. How much more water is to be added to get a new mixture containing acid and water in the ratio of 3 : 7?

ক
30 liters
খ
35 liters
গ
40 liters
ঘ
50 liters

ব্যাখ্যা

Question: In a mixture of 30 liters, the ratio of acid and water is 7 : 3. How much more water is to be added to get a new mixture containing acid and water in the ratio of 3 : 7?

Solution:
৩০ লিটার দ্রবণে এসিড ও পানির অনুপাত ৭ : ৩
এসিডের পরিমাণ = (৭/১০) × ৩০
= ২১ লিটার

পানির পরিমাণ = ৩০ - ২১ লিটার
= ৯ লিটার

ধরি, ক লিটার পানি মেশাতে হবে।

প্রশ্নমতে,
২১/(ক + ৯) = ৩ / ৭
⇒ ১৪৭ = ৩ক + ২৭
⇒ ৩ক = ১৪৭ - ২৭
⇒ ৩ক = ১২০
∴ ক = ৪০

অর্থাৎ, ৪০ লিটার পানি মেশাতে হবে।

৩৬৫.

In what proportion water must be added to spirit to gain 20% by selling it at the cost price?

ক
3 : 8
খ
2 : 7
গ
1 : 5
ঘ
none of these

ব্যাখ্যা

Question: In what proportion water must be added to spirit to gain 20% by selling it at the cost price?

Solution:
The percentage gain is essentially the ratio of pure spirit to water in the diluted solution. This gain is made because the addition of water increases the volume without increasing the cost, allowing the adulterated spirit to be sold at the original price (the cost price for the pure spirit).
Since the selling price equals the cost price (CP) in this case, the 20% gain represents the proportion of water in the solution.

Therefore, the proportion of spirit to water is 100% : 20% or 5 : 1.

Hence, water should be added to spirit in a 1 ∶ 5 proportion to gain 20% by selling it at the cost price.

৩৬৬.

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?

ক
ক) 16 : 5
খ
খ) 14 : 5
গ
গ) 16 : 7
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.

৩৬৭.

If x : y = y : z = 1.5 and z = 2 , What is the value of x?

ক
ক) 3
খ
খ) 4
গ
গ) 4.5
ঘ
ঘ) 3.5
ঙ
ঙ) 5

ব্যাখ্যা

Given, y : z = 1.5
∴ y = 1.5 × 2 = 3
And, x : y = 1.5
∴ x = 1.5 × 3 = 4.5

৩৬৮.

For a circle where the diameter is 4π, calculate the radius-to-circumference ratio.

ক
1 : 2π
খ
2 : 3π
গ
2π : 3
ঘ
2 : 5π

ব্যাখ্যা

Question: For a circle where the diameter is 4π, calculate the radius-to-circumference ratio.

Solution:
Here
The diameter of the circle is d = 4π
So the radius of the circle r = 2π

∴ Circumference of circle = 2. π. 2π
= 4π²

So the ratio between radius and Circumference of circle = 2π : 4π²

= 2π/4π²

= 1 : 2π

৩৬৯.

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?

ক
ক) 11/3
খ
খ) 2/13
গ
গ) 3/11
ঘ
ঘ) 13/4
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.

৩৭০.

The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

ক
ক) 8 : 7
খ
খ) 1 : 1
গ
গ) 7 : 8
ঘ
ঘ) 21 : 22

ব্যাখ্যা

প্রশ্ন: The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

সমাধান:
ধরি,
বালকের সংখ্যা ৭ক জন
বালিকার সংখ্যা ৮ক জন

বালকের সংখ্যা ২০% বাড়লে,
বালকের সংখ্যা হয় ৭ক + {৭ক × (২০/১০০)} জন
= ৭ক + ১.৪ক জন
= ৮.৪ক

বালিকার সংখ্যা ১০% বাড়লে,
বালিকার সংখ্যা হয় ৮ক + {৮ক × (১০/১০০)} জন
= ৮ক + ০.৮ক
= ৮.৮ক

বালক : বালিকা = ৮.৪ক : ৮.৮ক = ৮.৪ : ৮.৮ = ৮৪ : ৮৮ = ২১ : ২২

৩৭১.

What is the ratio of 5 inches to 9 feet?

ক
7 : 108
খ
6 : 108
গ
5 : 108
ঘ
5 : 18
ঙ
None

ব্যাখ্যা

Question: What is the ratio of 5 inches to 9 feet?

Solution:
We know, 1 foot = 12 inches
So, 9 feet = 9 × 12 = 108 inches

Now,
5 inches : 9 feet = 5 : 108

∴ The ratio = 5 : 108

৩৭২.

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 -

ক
ক) 56 : 99 : 69
খ
খ) 69 : 56 : 99
গ
গ) 99 : 56 : 69
ঘ
ঘ) 99 : 69 : 56

ব্যাখ্যা

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

৩৭৩.

A jar contains milk and water in the ratio 5:1. If the quantity of milk is more than that of water by 8 liters, then what is the quantity of water?

ক
1.5 liters
খ
2 liters
গ
2.5 liters
ঘ
3.5 liters
ঙ
4 liters

ব্যাখ্যা

let, A jar contains milk and water be 5x and X

the quantity of milk is more than that of water (5x -x ) = 4x

so, the quantity of water = (x * 8)/4x = 2

৩৭৪.

The angle between the minute hand and the hour hand of a clock when the time is 4:20, is:

ক
ক) 0º
খ
খ) 10º
গ
গ) 5º
ঘ
ঘ) 20º

ব্যাখ্যা

Angle traced by hour hand in 13/ 3 hrs
=( 360/12 × 13/3)^∘ =130^∘Angle traced by min. hand in 20 min
=( 360/60 ×20)^∘=120^∘∴Required angle
=(130−120)^∘ =10^∘

৩৭৫.

The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250. The sum of the numbers is-

ক
90
খ
65
গ
60
ঘ
30

ব্যাখ্যা

Question: The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250. The sum of the numbers is-

Solution:
Let, the number be 3x, 4x, 5x

According to the question,
(3x)² + (4x)² + (5x)² = 1250
⇒ 9x² + 16x² + 25x² = 1250
⇒ 50x² = 1250
⇒ x² = 1250/50
⇒ x² = 25
∴ x = 5

∴ The sum of the numbers = 3x + 4x + 5x
= 12x
= 12 × 5
= 60

৩৭৬.

In what ratio must a grocer mix two varieties of tea worth Tk. 60 a kg and Tk. 65 a kg so that by selling the mixture at Tk. 68.20 a kg he may gain 10%?

ক
3 : 2
খ
3 : 4
গ
3 : 5
ঘ
4 : 5

ব্যাখ্যা

Question: In what ratio must a grocer mix two varieties of tea worth Tk. 60 a kg and Tk. 65 a kg so that by selling the mixture at Tk. 68.20 a kg he may gain 10%?

Solution:
Quantity of Tk. 60 tea is x kg.
Quantity of Tk. 65 tea is y kg

S.P. of 1 kg of the mixture = Tk. 68.20,
Gain = 10%.
C.P of 1 kg of the mixture = Tk. (100/110 × 68.20) = Tk. 62

ATQ,
60x + 65y = (x + y)62
⇒ 60x + 65y = 62x + 62y
⇒ 62x - 60x = 65y - 62y
⇒ 2x = 3y
∴ x/y = 3/2

৩৭৭.

If the square of the sum of two numbers is equal to 4 times of their product, Then the ratio of these numbers is:

ক
ক) 2 : 1
খ
খ) 1 : 3
গ
গ) 1 : 1
ঘ
ঘ) 1 : 2

ব্যাখ্যা

(x + y)² = 4xy
=> (x + y)² - 4xy = 0
=> (x - y)² = 0
=> x = y
=> x/y = 1
∴ x : y = 1 : 1

৩৭৮.

The monthly incomes of two workers are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves TK. 100 per month, find their monthly incomes.

ক
400 and 600
খ
650 and 950
গ
600 and 800
ঘ
300 and 600

ব্যাখ্যা

Question: The monthly incomes of two workers are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves TK. 100 per month, find their monthly incomes.

Solution:
Let,
Incomes be 3x and 4x
Expenditures be 5y and 7y

Savings Equations,
3x - 5y = 100 .......(1)
4x - 7y = 100 ........(2)
Now,
(1) × 4 ⇒ 12x - 20y = 400
(2) × 3 ⇒ 12x - 21y = 300

Now subtract ⇒ (12x - 20y) - (12x - 21y) = 400 - 300
⇒ 12x - 20y - 12x + 21y = 100
⇒ y = 100

From (1),
3x - 5(100) = 100
⇒ 3x = 600
∴ x = 200

∴ The monthly incomes are,
First worker = 3x = (3 × 200) = 600
Second worker = 4x = (4 × 200) = 800

৩৭৯.

In a mixture of 45 liters, the ratio of milk and water is 4 : 1. How much water must be added to make the mixture ratio 3 : 2?

ক
15 liters
খ
20 liters
গ
25 liters
ঘ
10 liters

ব্যাখ্যা

Question: In a mixture of 45 liters, the ratio of milk and water is 4 : 1. How much water must be added to make the mixture ratio 3 : 2?

Solution:
Quantity of milk in 45 litres of mixture 45 × (4/5) litres = 36 litres
∴ Quantity of water in the mixture = 45 - 36 litres = 9 litres

Let x litres of water be added to the mixture.
Then,
36/(9 + x) = 3/2
⇒ 72 = 27 + 3x
⇒ 3x = 45
∴ x = 15

৩৮০.

Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

ক
2 : 3
খ
3 : 4
গ
4 : 3
ঘ
4 : 5
ঙ
None

ব্যাখ্যা

Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

Solution:
5% of A + 4% of B = (2/3) (6% of A + 8% of B)
⇒ A/20 + B/25 = A/25 + 4B/75
⇒ (A/20) - (A/25) = (4B/75) - (B/25)
⇒ A/100 = B/75
⇒ A/B = 100/75 = 4/3
∴ A : B = 4 : 3

৩৮১.

An iron rod that weight 28 kg is cut into two pieces so that one of these pieces weight 18 kg and is 36 m long. If the weight of each pieces is proportional to its length, how long is the other pieces?

ক
34m
খ
10m
গ
20m
ঘ
72m

ব্যাখ্যা

Question: An iron rod that weight 28 kg is cut into two pieces so that one of these pieces weight 18 kg and is 36 m long. If the weight of each pieces is proportional to its length, how long is the other pieces?

Solution:
Weight of second piece = 28 − 18 = 10 kg

Let x is the length of the second piece.

According to the Question,
⇒ 18/36 = 10/x
⇒ x = (36 × 10)/18
⇒ x = 20

∴ The length of the other piece is 20 meters.

৩৮২.

Find the number in the place of sign `?'.

ক
9
খ
21
গ
27
ঘ
81

ব্যাখ্যা

Question: Find the number in the place of sign `?'.

Solution:
Let, the number be x
So,
9/x = x/81
⇒ x² = 81 × 9
⇒ x² = 729
⇒ x² = 27²
∴ x = 27

৩৮৩.

The ratio of X : Y is 2 : 5, and the ratio of Y : Z is 3 : 4. If X = 12, what is the value of Z?

ক
40
খ
30
গ
25
ঘ
32

ব্যাখ্যা

Question: The ratio of X : Y is 2 : 5, and the ratio of Y : Z is 3 : 4. If X = 12, what is the value of Z?

Solution:
Given:
X : Y = 2 : 5 -------(1)
Y : Z = 3 : 4 -------(2)
X = 12

From equation (1):
X/Y = 2/5
⇒ 2Y = 5X
⇒ Y = (5 × 12)/2 = 30
∴ Y = 30

From equation (2):
Y/Z = 3/4
⇒ 3Z = 4Y
⇒ Z = (4 × 30)/3 = 40

Therefore, the value of Z is 40.

৩৮৪.

A sum of Tk. 4950 is distributed among A, B and C such that the ratio of amount received by A and B is 5 : 4 and that of B and C is 6 : 3 respectively. Find the share of B ?

ক
1800
খ
1500
গ
1200
ঘ
900

ব্যাখ্যা

Question: A sum of Tk. 4950 is distributed among A, B and C such that the ratio of amount received by A and B is 5 : 4 and that of B and C is 6 : 3 respectively. Find the share of B ?

Solution:
A : B = 5 : 4
B : C = 6 : 3

A : B = 15 : 12 ( multiply by 3 )
B : C = 12 : 6 ( multiply by 2 )

∴ A : B : C = 15 : 12 : 6

ATQ,
15X + 12X + 6X = 4950
33X = 4950
X = 150

∴ Share of B is = 12 × 150 = 1800

৩৮৫.

The number of students in 3 classes is in the ratio 3 : 4 : 5. If 10 students are increased in each class this ratio changes to 4 : 5 : 6. The total number of students in the three classes in the beginning was

ক
ক) 135
খ
খ) 120
গ
গ) 110
ঘ
ঘ) 100

ব্যাখ্যা

Question: The number of students in 3 classes is in the ratio 3 : 4 : 5. If 10 students are increased in each class this ratio changes to 4 : 5 : 6. The total number of students in the three classes in the beginning was

Solution:
Let the number of students in the classes be 3x, 4x and 5x respectively;
Total students = 3x + 4x + 5x = 12x
According to the question,
(3x + 10) : (4x + 10) = 4 : 5
or, 5(3x + 10) = 4(4x+10)
or, 15x + 50 = 16x + 40
or, x = 10

Hence,
Original number of students,
12x = 12 × 10
= 120

৩৮৬.

A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is-

ক
400 kg
খ
560 kg
গ
600 kg
ঘ
640 kg

ব্যাখ্যা

Question: A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is -

Solution:

⇒ Quantity of cheaper : Quantity of Dearer = (CP of of Dearer - Mean Price) : (Mean Price - CP of Cheaper)
⇒ Quantity of cheaper : Quantity of Dearer = (18 - 14) : ( 14 - 8) = 4 : 6 = 2 : 3

∴ Quantity of suger sold at 18% profit = (3/5) × 1000
= 600 Kg

৩৮৭.

The income of Asim, Shakil and Riaz is in the ratio of 12 : 9 : 7 and their spendings are in the ratio 15 : 9 : 8. If Asim saves 25% of his income. What is the ratio of the savings of Asim, Shakil and Riaz?

ক
ক) 15 : 18 : 11
খ
খ) 5 : 8 : 7
গ
গ) 23 : 18 : 11
ঘ
ঘ) 25 : 16 : 13

ব্যাখ্যা

Income = Expenditure + Saving
Asim : 12x = 15y + 3x (3x = 25% of 12x)
Shakil : 9x = 9y + (9x – 9y)
Riaz : 7x = 8y + (7x – 8y)
Therefore, 12x – 3x = 15y
x/y = 5/3
y = 3x/5
Therefore, savings = (income – expenditure)
Asim = 12x – 9x = 3x
Shakil = 9x - 9y = 9x - (27x/5)
= 18x/5
Riaz = 7x - 8y = 7x - (24x/5)
= 11x/5
i.e., the ratio of savings of Asim : Shakil : Riaz
= 3x : 18x/5 : 11x/5
= 15 : 18 : 11.

৩৮৮.

Three vessels contain a milk mixture 30 litre each. When put in a big vessel, they result in a mixture of milk and water in the ratio 2:1. If the ratio is to be reversed to make it 1: 2, how much more water should be added to the mix?

ক
ক) 20L
খ
খ) 40L
গ
গ) 90L
ঘ
ঘ) 100L

ব্যাখ্যা

3 vessels of 30 litres each = 3 X 30 = 90 ml milk mixture
Amount of milk in mixture = 2/(2 + 1) × 90 = 60L
Amount of water = 90 - 60 = 30L

To make milk to water ratio 1 : 2, we simply need to make water double of milk.
By direct observation,
we can say that we should have 60L x 2 = 120L water to make the required ratio

We already have 30L,
we need (120 - 30) = 90L more water.

৩৮৯.

In a kilometre race, A, B and C are three participants. A can give B start of 50 m and C a start of 69 m. The start which B can allow C, is -

ক
17 m
খ
18 m
গ
19 m
ঘ
20 m

ব্যাখ্যা

A : B : C
= 1000 : (1000 - 50) : (1000 - 69)
= 1000 : 950 : 931

In a 950 m race, B can give C a start of
(950 - 931) m
= 19 m

In a 1000 m race, B can give C a start of
(19/950) × 1000 = 20 m

৩৯০.

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?

ক
ক) 4%
খ
খ) 6(/4)%
গ
গ) 20%
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%

৩৯১.

A, B and C enter into partnership with investment in the ratio of 5:7:8. If at the end of the year A's share of profit is Tk. 42360, how much is the total profit?

ক
ক) Tk 169,440
খ
খ) Tk 183,000
গ
গ) Tk 196,700
ঘ
ঘ) Tk. 168,440

ব্যাখ্যা

Let, A's profit = 42,360 = 5x
So, x = 42,360/5 = 8472
total profit = 5x + 7x + 8x = 20x = 20×8472
∴ The total profit is tk. 1,69,440

৩৯২.

In a ratio which is equal to 5 : 6, if the antecedent is 45, what is the consequent?

ক
ক) 48
খ
খ) 52
গ
গ) 54
ঘ
ঘ) 60

ব্যাখ্যা

Question: In a ratio which is equal to 5 : 6, if the antecedent is 45, what is the consequent?

Solution:
Let the consequent is x.

then,
5 : 6 = 45 : x
5x = 270
x = 54

৩৯৩.

Babu bought two varieties of pulse, costing Tk. 50 and Tk. 60 per Kg. each, and mixed them in some ratio. He then sold the mixture at Tk. 70 per kg., making a profit of 20 percent. What was the ratio of the mixture?

ক
ক) 1 : 10
খ
খ) 1 : 5
গ
গ) 2 : 7
ঘ
ঘ) None

ব্যাখ্যা

Question: Babu bought two varieties of pulse, costing Tk. 50 and Tk. 60 per Kg. each, and mixed them in some ratio. He then sold the mixture at Tk. 70 per kg., making a profit of 20 percent. What was the ratio of the mixture?

Solution:
50 টাকা দরে ডাল ক্রয় করা হয় = x কেজি
60 টাকা দরে ডাল ক্রয় করা হয় = y কেজি
মোট ক্রয়মূল্য = 50x + 60y

প্রশ্নমতে
(50x + 60y) এর 120% = 70(x + y)
⇒ (6/5) × 10(5x+ 6y) = 70x + 70y
⇒ 12(5x+ 6y) = 70x + 70y
⇒ 60x + 72y = 70x +70y
⇒ 72y - 70y = 70x - 60x
⇒ 2y = 10x
⇒ y = 5x
⇒ x/y = 1/5
x : y = 1 : 5

৩৯৪.

X, Y & Z has started a business with a profit sharing ratio 7 : 8 : 9. If at the end of the year, Y gets a total of Taka 4,800 what will be X's profit?

ক
ক) Tk. 4,200
খ
খ) Tk. 4,000
গ
গ) Tk. 3,800
ঘ
ঘ) Tk. 3,600

ব্যাখ্যা

Question: X, Y & Z has started a business with a profit sharing ratio 7 : 8 : 9. If at the end of the year, Y gets a total of Taka 4,800 what will be X's profit?

Solution:
X, Y এবং Z এর লাভের অনুপাত = 7 : 8 : 9
X এর লাভের পরিমাণ = 7a
Y এর লাভের পরিমাণ = 8a
Z এর লাভের পরিমাণ = 9a

প্রশ্নমতে,
8a = 4800
a = 4800/8
a = 600

X এর লাভের পরিমাণ = 7 × 600 = 4200

৩৯৫.

Salaries of Rakib and Rasel are in the ratio 2 : 3. If the salary of each is increased by Tk. 4000, the new ratio becomes 40 : 57. What is Rasel's salary after increased?

ক
ক) Tk.34000
খ
খ) Tk.38000
গ
গ) Tk.36000
ঘ
ঘ) Tk.42000

ব্যাখ্যা

প্রশ্ন: Salaries of Rakib and Rasel are in the ratio 2 : 3. If the salary of each is increased by Tk. 4000, the new ratio becomes 40 : 57. What is Rasel's salary after increased?

সমাধান:
ধরি,
রাকিবের বেতন ২ক টাকা
রাসেলের বেতন ৩ক টাকা

শর্তমতে,
(২ক + ৪০০০)/(৩ক + ৪০০০) = ৪০/৫৭
বা, ১১৪ক + ২২৮০০০ = ১২০ক + ১৬০০০০
বা, ৬ক = ৬৮০০০
বা, ৩ক = ৩৪০০০

৪০০০ টাকা বাড়ানোর পর রাসেলের বেতন ৩৪০০০ + ৪০০০ টাকা
= ৩৮০০০ টাকা

৩৯৬.

A person who has a rice storage has two types of rice costing Tk. 50 per kg and Tk. 70 per kg. In what ratio should he mix them to make a mixture worth Tk. 58 per kg?

ক
1 : 2
খ
3 : 2
গ
5 : 2
ঘ
7 : 2

ব্যাখ্যা

Question: A person who has a rice storage has two types of rice costing Tk. 50 per kg and Tk. 70 per kg. In what ratio should he mix them to make a mixture worth Tk. 58 per kg?

Solution:
Cheaper variety price, a = Taka 50 per kg
Expensive variety price, b = Taka 70 per kg
Mixture price, c = Taka 58 per kg

Ratio = (b - c)/(c - a)
= (70 - 58)/(58 - 50)
= 12/8
= 3 : 2

৩৯৭.

There are 30 students in a class. The number of students who like Math and the ones who like Science is expressed in the ratio 2 : 3. Find the number of students who like Math.

ক
ক) 20
খ
খ) 18
গ
গ) 15
ঘ
ঘ) 12

ব্যাখ্যা

প্রশ্ন: There are 30 students in a class. The number of students who like Math and the ones who like Science is expressed in the ratio 2 : 3. Find the number of students who like Math.

সমাধান:
Total number of students = 30.
Let
the number of students who like Math = 2x
the number of students who like Science = 3x

We can say that,
2x + 3x = 30
⇒ 5x = 30
⇒ x = 6

∴ the numbers of students who like Math = 2x = 2 × 6 = 12

৩৯৮.

In a mixture of milk and water, the ratio is 7 : 5. If 6 liters of water is added, the new ratio becomes 7 : 6. What was the original amount of milk in the mixture?

ক
30 liters
খ
42 liters
গ
36 liters
ঘ
44 liters

ব্যাখ্যা

Question: In a mixture of milk and water, the ratio is 7 : 5. If 6 liters of water is added, the new ratio becomes 7 : 6. What was the original amount of milk in the mixture?

Solution:
ধরি, শুরুতে দুধ ছিল = 7x লিটার,
পানি ছিল = 5x লিটার।

এখন 6 লিটার পানি যোগ করলে,
নতুন পানি = 5x + 6 লিটার

ATQ,
7x/(5x + 6) = 7/6
⇒ 6 × 7x = 7 × (5x + 6)
⇒ 42x = 35x + 42
⇒ 7x = 42
⇒ x = 6

∴ দুধের পরিমাণ = 7x = 7 × 6 = 42 লিটার

৩৯৯.

How many kilograms of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per Kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per Kg?

ক
36 Kg
খ
42 Kg
গ
54 Kg
ঘ
63 Kg

ব্যাখ্যা

Question: How many kilograms of sugar costing Tk. 9 per kg must be mixed with 27 kg of sugar costing Tk. 7 per Kg so that there may be a gain of 10% by selling the mixture at Tk. 9.24 per Kg?

Solution:
ধরি,
৯ টাকা টাকা দরের চিনি আছে ক কেজি
৭ টাকা দরের চিনি আছে ২৭ কেজি

মোট ক্রয়মূল্য = ৯ক + ২৭ × ৭ টাকা = ৯ক + ১৮৯ টাকা
মোট বিক্রয়মূল্য = (ক + ২৭) × ৯.২৪ টাকা = ৯.২৪ক + ২৪৯.৪৮ টাকা

∴ লাভ = ৯.২৪ক + ২৪৯.৪৮ - ৯ক - ১৮৯ = ০.২৪ক + ৬০.৪৮ টাকা

প্রশ্নমতে,
(৯ক + ১৮৯) এর ১০% = ০.২৪ক + ৬০.৪৮
বা, (৯ক + ১৮৯) × (১/১০) = ০.২৪ক + ৬০.৪৮
বা, ৯ক + ১৮৯ = ২.৪ক + ৬০৪.৮
বা, ৯ক - ২.৪ ক = ৬০৪.৮ - ১৮৯
বা, ৬.৬ক = ৪১৫.৮
বা, ক = ৪১৫.৮/৬.৬
∴ ক = ৬৩

৪০০.

In a 60 liters mixture of milk and water, the ratio of milk to water is 7 : 3. To get a new mixture containing milk and water in the ratio 3 : 2, the amount of water to be added is-

ক
22 liters
খ
20 liters
গ
18 liters
ঘ
15 liters
ঙ
10 liters

ব্যাখ্যা

Question: In a 60 liters mixture of milk and water, the ratio of milk to water is 7 : 3. To get a new mixture containing milk and water in the ratio 3 : 2, the amount of water to be added is-

Solution:
Quantity of milk in 60 liters mixture is = 60 × (7/10) = 42 liters
so, water is = 60 - 42 = 18 liters

Let, p liters of water to be added to become the ratio 3 : 2

so,
42 : (18 + p) = 3 : 2
or, 42/(18 + p) = 3/2
or, 3p + 54 = 84
or, 3p = 84 - 54
or, 3p = 30
or, p = 30/3
∴ p = 10

hence, 10 liters water to be added to become the ratio 3 : 2