Ratio & Proportion, Alligation or Mixture

PrepBank · পাতা ১ / ১১ · ১–১০০ / ১,০৮৬

১.

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

ক
ক) 2:5
খ
খ) 3:5
গ
গ) 4:5
ঘ
ঘ) 6:5

ব্যাখ্যা

Let the third number be x.
First Number (120/100) × x = 6x/5
Second Number (150/100) × x = 3x/2
Ratio = 6x/5 : 3x/2
=> 4:5

২.

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

ক
30
খ
45
গ
60
ঘ
90

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

৩.

Coffee worth Tk. 180 per kg and Tk. 210 per kg are mixed with a third variety in the ratio 2 : 1 : 3. If the mixture is worth Tk. 225 per kg, the price of the third variety per kg will be:

ক
220 Tk.
খ
200 Tk.
গ
260 Tk.
ঘ
280 Tk.

ব্যাখ্যা

Question: Coffee worth Tk. 180 per kg and Tk. 210 per kg are mixed with a third variety in the ratio 2 : 1 : 3. If the mixture is worth Tk. 225 per kg, the price of the third variety per kg will be:

Solution:
Let price of third variety be x Tk. per kg
180 × 2y + 210y + x × 3y = 225(2y + y + 3y)
⇒ 360y + 210y + 3xy = 225 × 6y
⇒ 360 + 210 + 3x = 1350
⇒ 570 + 3x = 1350
⇒ 3x = 780
∴ x = 260 Tk.

৪.

The ratio, by weight, of the four ingredients A, B, C, and D of a certain mixture is 4 : 7 : 8 : 12. The mixture will be changed so that the ratio of A to C is quadrupled and the ratio of A to D is decreased. The ratio of A to B will be held constant. If B will constitute 20% of the weight of the new mixture, by approximately what percent will the ratio of A to D be decreased?

ক
45%
খ
40%
গ
50%
ঘ
None of the Above

ব্যাখ্যা

Question: The ratio, by weight, of the four ingredients A, B, C, and D of a certain mixture is 4 : 7 : 8 : 12. The mixture will be changed so that the ratio of A to C is quadrupled and the ratio of A to D is decreased. The ratio of A to B will be held constant. If B will constitute 20% of the weight of the new mixture, by approximately what percent will the ratio of A to D be decreased?

Solution:
Lets say our thing has the weight x(4 + 7 + 8 + 12) = 31x.
When we change mixture our weight changes to x(4 + 7 + 2 + 12y)
=13x + 12xy

We also know that 7x = 0.2(13x + 12xy)
Reduce that last equation by x and lets just solve it for y : y = {7 - (0.2 × 13)}/2.4
= 11/6
So the original ratio was 4/12 = 1/3
The new ratio is (1 × 6)/(3 × 11) = 2/11
The resulting percentages are: {(1/3) - (2/11)}/(1/3) = 1 - (6/11)
= 5/11
= 0.4545
≈ 45%

৫.

If 2 kg of metal, of which 1/3 is zinc and the rest is copper, be mixed with 3 kg of metal, of which 1/4 is zinc and the rest is copper, then what will be the ratio of zinc to copper in the mixture?

ক
ক) 17 : 43
খ
খ) 13 : 42
গ
গ) 19 : 43
ঘ
ঘ) 15 : 42

ব্যাখ্যা

Quantity of zinc in the mixture = 2(1/3) + 3(1/4) = 17/12
Quantity of copper in the metal = (3 + 2) - 17/12 = (60 - 17)/12 = 43/12
So, the ratio of Zinc and Copper = 17/12 : 43/12 = 17 : 43

৬.

A container contains 48 liters of milk. From this container 12 liters of milk was taken out and replaced by water. This process was repeated overall two times. How much milk is now contained by the container?

ক
ক) 25 liter
খ
খ) 24 liter
গ
গ) 26 liter
ঘ
ঘ) 27 liter

ব্যাখ্যা

Question: A container contains 48 liters of milk. From this container 12 liters of milk was taken out and replaced by water. This process was repeated overall two times. How much milk is now contained by the container?

Solution:
After first replacement the ratio of milk and water is (48 - 12) : 12 = 36 : 12 = 3 : 1

After second replacement,
remaining milk = 36 - (3/4 of 12) = 36 - 9 = 27

∴ There is 27 liter of milk in the container now.

৭.

4 kg of metal contains 1/5 copper and rest in Zinc. Another 5 kg of metal contains 1/6 copper and rest in Zinc.The ratio of Copper and Zinc into the mixture of these two metals:

ক
ক) 39 : 231
খ
খ) 49 : 221
গ
গ) 94 : 181
ঘ
ঘ) 36 : 272

ব্যাখ্যা

Copper in 4 kg = 4/5 kg and
Zinc in 4 kg = 4 x (4/5) kg

Copper in 5 kg = 5/6 kg and
Zinc in 5 kg = 5 x (5/6) kg

Therefore, Copper in mixture = (4/5) + (5/6) = 49/30 kg
and Zinc in the mixture = (16/5) + (25/6) = 221/30 kg

Therefore the required ratio = 49/30 : 221/30
= 49 : 221.

৮.

Last year, the ratio between the salaries of A and B was 3 : 4. But the ratios of their individual salaries between last year and this year were 4 : 5 and 2 : 3 respectively. If the sum of their present salaries is Tk. 4160, then how much is the salary of A now?

ক
Tk.1200
খ
Tk.1400
গ
Tk.1600
ঘ
Tk.1800

ব্যাখ্যা

Question: Last year, the ratio between the salaries of A and B was 3 : 4. But the ratios of their individual salaries between last year and this year were 4 : 5 and 2 : 3 respectively. If the sum of their present salaries is Tk. 4160, then how much is the salary of A now?

Solution:
Let,
the salaries of A and B last year be Tk. 3x and Tk. 4x respectively.
Then,
A's present salary = Tk. (5/4) × 3x
= Tk. 15x/4

B's present salary = Tk.(3/2) × 4x
= Tk. 6x.

According to the question,
(15x/4) + 6x = 4160
⇒ 39x = 4160 × 4
⇒ x = (4160 × 4)/39

So, A's present salary = Tk. (15/4) × (4160 × 4)/39
= Tk.1600

৯.

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

ক
Tk. 17,000
খ
Tk. 20,000
গ
Tk. 25,500
ঘ
Tk. 38,000

ব্যাখ্যা

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

Solution:
Let the original salaries of Ravi and Sumit be Tk. 2x and Tk. 3x respectively.
Then,
(2x + 4000)/(3x + 4000) = 40/57
⇒ 57(2x + 4000) = 40(3x + 4000)
⇒ 6x = 68,000
⇒ 3x = 34,000

∴ Sumit's present salary = (3x + 4000) = Tk.(34000 + 4000) = Tk. 38,000.

১০.

A mixture of 200 liters of milk and water contains 15% water. How much more water should be added so that water becomes 20% of the new mixture?

ক
10 liters
খ
12.5 liters
গ
16 liters
ঘ
24.5 liters

ব্যাখ্যা

Question: A mixture of 200 liters of milk and water contains 15% water. How much more water should be added so that water becomes 20% of the new mixture?

Solution:
Amount of water in the 200-liter mixture = 15% of 200
= (15/100) × 200
= 30 liters

Let,
P liters of water are added.
So, new amount of water = (30 + P)
and new total mixture = (200 + P)

ATQ,
(30 + P) = 20% of (200 + P)
⇒ 30 + P = (20/100) × (200 + P)
⇒ 30 + P = (1/5) × (200 + P)
⇒ 150 + 5P = 200 + P
⇒ 5P - P = 200 - 150
⇒ 4P = 50
∴ P = 12.5

∴ 12.5 liters more water should be added.

১১.

Given that a shop opens at 10 a.m. and closes at 6:45 p.m., with a 20-minute tea break, what is the proportion of the break to the total working hours?

ক
1/15
খ
4/10
গ
2/105
ঘ
4/105
ঙ
None

ব্যাখ্যা

Question: Given that a shop opens at 10 a.m. and closes at 6:45 p.m., with a 20-minute tea break, what is the proportion of the break to the total working hours?

Solution:
Total working time = 6:45 - 10:00
= 8 hours 45 minutes
= (8 × 60) + 45
= 525 minutes

The ratio of the break to the total working period
= 20/525
= 4/105

১২.

Tk 7,500 is divided in the ratio of 1 : 2 : 3 : 4 : 5. Find the difference between the greatest and smallest shares?

ক
ক) 1500
খ
খ) 2000
গ
গ) 2600
ঘ
ঘ) 2700

ব্যাখ্যা

Question: Tk 7,500 is divided in the ratio of 1 : 2 : 3 : 4 : 5. Find the difference between the greatest and smallest shares?

Solution:
প্রদত্ত অনুপাত 1 : 2 : 3 : 4 : 5
প্রদত্ত অনুপাতের রাশিগুলোর যোগফল = 1 + 2 + 3 + 4 + 5 = 15

সবচেয়ে বেশি শেয়ারের পরিমাণ = 7500 এর 5/15 = 2500 টাকা
সবচেয়ে কম শেয়ারের পরিমাণ = 7500 এর 1/15 = 500 টাকা
পার্থক্য = (2500 - 500) = 2000 টাকা

১৩.

If Tk. 782 is allocated into three portions according to the ratio 1/2 : 2/3 : 3/4, what is the amount of the first portion?

ক
Tk. 204
খ
Tk. 202
গ
Tk. 282
ঘ
Tk. 180
ঙ
None of the above

ব্যাখ্যা

Question: If Tk. 782 is allocated into three portions according to the ratio 1/2 : 2/3 : 3/4, what is the amount of the first portion?

Solution:
The given ratio = 1/2 : 2/3 : 3/4
= 6 : 8 : 9

∴ The first portion = 782 × (6/23)
= 204 Tk.

১৪.

The present ratio of students to teachers at a certain school is 30 to 1. If the number of students were to increase by 50 and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of students?

ক
290
খ
380
গ
450
ঘ
None of these

ব্যাখ্যা

Question: The present ratio of students to teachers at a certain school is 30 to 1. If the number of students were to increase by 50 and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of students?

Solution:
Let the number of student and teacher be represented by x and y, respectively.
x : y = 30 : 1
⇒ x/y = 30/1
⇒ x = 30y....................(1)

If the number of students increases by 50 and the number of teachers increases by 5
(50 + x) : (y + 5) = 25 : 1
⇒ (50 + x) / (y + 5) = 25/1
⇒ 50 + x = 25y + 125
⇒ 50 + 30y = 25y + 125
⇒ 30y - 25y = 125 - 50
⇒ 5y = 75
⇒ y = 75/5
⇒ y = 15

∴ Number of teachers = 15
And the number of students = 30 × 15 = 450

১৫.

If one star equals four circles and three circles equal four diamonds, then what is the ratio of star to diamond?

ক
ক) 14:3
খ
খ) 16:3
গ
গ) 17:3
ঘ
ঘ) 19:3

ব্যাখ্যা

Given one star(S) equals four circles(C) and three circles equal four diamonds(D).
Then, S = 4C and 3C = 4D
Then, C = (4/3)D
∴ S = 4×(4/3)D
⇒ S = (16/3)D
Hence, S : D = 16 : 3

১৬.

In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C -

ক
80m
খ
18m
গ
20m
ঘ
22m
ঙ
None of the above

ব্যাখ্যা

Question: In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C -

Solution:
A : B = 100 : 90
A : C = 100 : 72

∴ B : C = B : A / C : A
= 90 : 72

if B runs 90m, C runs 72m
∴ If B runs 100m, C runs = (72 × 100)/90
= 80

∴ B can give C (100 - 80) = 20m in a 100m race

১৭.

For any two numbers m, n ; (m + n ) : (m - n) : mn = 7 :1 : 60. Find the value of 1/m : 1/n =?

ক
ক) 4 : 3
খ
খ) 8 : 7
গ
গ) 3 : 4
ঘ
ঘ) 7 : 8

ব্যাখ্যা

(m+n)/(m−n) = 7x/x
⇒ m/n=4x/ 3x
Again mn=12x²
and mn =60x
so, 60x=12x²
⇒ x = 5
=> m = 20 and n= 15
Hence, 1/m : 1/n = 1/20 : 1/15 = 3 : 4

১৮.

A vessel contains 108 litres of milk and water in the ratio of 5 : 4. If 20 Liters of milk and 36 liter water is added to the mixture then difference between milk and water in mixture is Y. Find the value of 7Y?

ক
42
খ
36
গ
28
ঘ
32

ব্যাখ্যা

Question: A vessel contains 108 litres of milk and water in the ratio of 5 : 4. If 20 Liters of milk and 36 liter water is added to the mixture then difference between milk and water in mixture is Y. Find the value of 7Y?

Solution:
Given that,
Total volume of mixture = 108 liters
Ratio of milk to water = 5 : 4
Milk added = 20 liters
Water added = 36 liters

Now,
Total ratio of milk and water = 5 + 4 = 9
Milk in the mixture = (108 liters) × (5/9) = 60 liters
Water in the mixture = (108 liters) × (4/9) = 48 liters

After adding milk and water:
New amount of milk = 60 + 20 = 80 liters
New amount of water = 48 + 36 = 84 liters

∴ Difference between milk and water in the mixture = 84 - 80 = 4 liters
∴ Y = 4
⇒ 7Y = 7 × 4 = 28

∴ The value of 7Y is 28.

১৯.

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?

ক
ক) 3
খ
খ) 5
গ
গ) 9
ঘ
ঘ) 12

ব্যাখ্যা

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

২০.

একটি সভাতে মহিলা ও পুরুষের অনুপাত ৫ : ৪। যদি আরও ৩৬ জন পুরুষ সভাতে যোগ দেয় তাহলে অনুপাতটি উল্টে যাবে। সভাতে কতজন মহিলা ছিল?

ক
৬০ জন
খ
৬৪ জন
গ
৭৮ জন
ঘ
৮০ জন
ঙ
কোনোটিই নয়

ব্যাখ্যা

প্রশ্ন: একটি সভাতে মহিলা ও পুরুষের অনুপাত ৫ : ৪। যদি আরও ৩৬ জন পুরুষ সভাতে যোগ দেয় তাহলে অনুপাতটি উল্টে যাবে। সভাতে কতজন মহিলা ছিল?

সমাধান:
ধরি,
সভাতে মহিলা ও পুরুষের সংখ্যা যথাক্রমে ৫ক এবং ৪ক।

প্রশ্নমতে,
৫ক/(৪ক + ৩৬) = ৪/৫
⇒ ২৫ক = ১৬ক + ১৪৪
⇒ ২৫ক - ১৬ক = ১৪৪
⇒ ৯ক = ১৪৪
⇒ ক = ১৪৪/৯
∴ ক = ১৬

∴ মহিলার সংখ্যা ছিল = (৫ × ১৬) = ৮০ জন

২১.

The ratio of income and expenditure of a person is 5 : 2, If he saves Tk. 3000 per month, what is his monthly income?

ক
Tk. 4000
খ
Tk. 5000
গ
Tk. 1000
ঘ
Tk. 12000

ব্যাখ্যা

Question: The ratio of income and expenditure of a person is 5 : 2, If he saves Tk. 3000 per month, what is his monthly income?

Solution:
Let, income = 5x
and expenditure = 2x
Then,
Savings = 5x - 2x = 3000
⇒ 3x = 3000
∴ x = 1000

∴ monthly income = 5x = 5 × 1000 = Tk. 5000

২২.

Three numbers are in the ratio 2 : 3 : 4, If their LCM is 240 the smaller of the three numbers is = ?

ক
ক) 40
খ
খ) 60
গ
গ) 30
ঘ
ঘ) 70
ঙ
ঙ) 80

ব্যাখ্যা

Let number are = 2x, 3x, 4x
given,
LCM of (2×3×2)x = 12x
12x = 240
x = 20
∴ numbers are 2×20 = 40
3×20 = 60
4×20 = 80
∴ Smaller is 40

২৩.

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-

ক
ক) 1500 Tk
খ
খ) 2000 Tk
গ
গ) 2500 Tk
ঘ
ঘ) 3000 Tk

ব্যাখ্যা

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

২৪.

729 ml of a mixture contains milk and water in ratio 7: 2. How much of the water is to be added to get a new mixture containing half milk and half water?

ক
ক) 405ml
খ
খ) 81ml
গ
গ) 72ml
ঘ
ঘ) 91ml
ঙ
ঙ) 95ml

ব্যাখ্যা

Question: 729 ml of a mixture contains milk and water in ratio 7: 2. How much of the water is to be added to get a new mixture containing half milk and half water?

Solution:
The quantity of milk in mixture is (7/9) × 729 ml
= 567 ml
The quantity of water in mixture is (2/9) × 729 ml
= 162 ml

Let, we have to mix y ml water to to get a new mixture containing half milk and half water.

ATQ,
567/(162 + y) = 1/1
⇒ 567 = 162 + y
⇒ y = 567 - 162
∴ y = 405

২৫.

Tk 12000 are to be distributed between B and A such that B gets Tk 4000 less than A. The ratio of the amount received by A to that received by B is -

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

ব্যাখ্যা

Question: Tk 12000 are to be distributed between B and A such that B gets Tk 4000 less than A. The ratio of the amount received by A to that received by B is -

Solution:
A + B = 12000..........(i)
A - B = 4000...............(ii)

Now,
A + B + A - B = 12000 + 4000
⇒ 2A = 16000
⇒ A = 8000

So,
B gets = 12000 - 8000 = 4000

∴ A : B = 8000 : 4000 = 2 : 1

২৬.

In a zoo, there are deer and ducks. If the heads are counted, there are 180, while the legs are 448. What will be the number of ducks in the zoo?

ক
120
খ
136
গ
150
ঘ
160

ব্যাখ্যা

Question: In a zoo, there are deer and ducks. If the heads are counted, there are 180, while the legs are 448. What will be the number of ducks in the zoo?

Solution:
ধরি, হাঁসের সংখ্যা x টি ও হরিণের সংখ্যা y টি

x + y = 180
⇒ 4x + 4y = 720

2x + 4y = 448

4x + 4y - 2x - 4y = 720 - 448
⇒ 2x = 272
∴ x = 136

হাঁসের সংখ্যা ১৩৬ টি

২৭.

Rahim is saving for a new bike which will cost Tk. 48000. Rahim earns Tk. 150000 per month. Rahim spends his money on bills, food and extras in the ratio 8 : 3 : 4. Of the money he spends on extras, he spends 80% and puts 20% into his savings account. How long will it take Rahim to save for his new bike?

ক
1 month
খ
3 months
গ
5 months
ঘ
6 months

ব্যাখ্যা

Question: Rahim is saving for a new bike which will cost Tk. 48000. Rahim earns Tk. 150000 per month. Rahim spends his money on bills, food and extras in the ratio 8 : 3 : 4. Of the money he spends on extras, he spends 80% and puts 20% into his savings account. How long will it take Rahim to save for his new bike?

Solution:
Rahim’s earnings of Tk. 150000 are divided in the ratio of 8 : 3 : 4.

The total number of shares is 8 + 3 + 4 = 15.

Each share is worth Tk. 150000 ÷ 15 = 10000

Rahim spends 4 shares on extras so 4 × 10000 = 40000

20% of 40000 = 8000

The number of months it will take Rahim is 48000 ÷ 8000 = 6

২৮.

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?

ক
ক) 100%
খ
খ) 200%
গ
গ) 300%
ঘ
ঘ) 600%
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%.

২৯.

The salaries of Salman and Parimal are in the ratio of 4:5. If the salary of each is increased by Tk. 3000, the new ratio becomes 25:31. What is Parimal's new salary?

ক
65000 tk
খ
76000 tk
গ
89000 tk
ঘ
93000 tk

ব্যাখ্যা

Question: The salaries of Salman and Parimal are in the ratio of 4:5. If the salary of each is increased by Tk. 3000, the new ratio becomes 25:31. What is Parimal's new salary?

Solution:
Let the original salaries of Salman and Parimal be 4x and 5x respectively.

So,
(4x + 3000)/(5x + 3000) = 25/31
⇒ 124x + 93000 = 125x + 75000
⇒ 125x - 124x = 93000 - 75000
⇒ x = 18000

Parimal's original salary = 5 × 18000 = 90000 tk
So, Parimal's new salary = 90000 + 3000 = 93000 tk

৩০.

Chaman has two big cans of wine and water mixture. Chaman mixes the contents of both the cans in a big container. The new mixture has half water and half wine. In what quantity did Chaman mix contents of Can 1 and 2 if Can 2 has wine to water ratio of 2 : 3 and Can 1 has wine to water ratio 5 : 3?

ক
3 : 4
খ
4 : 5
গ
5 : 6
ঘ
6 : 7

ব্যাখ্যা

Question: Chaman has two big cans of wine and water mixture. Chaman mixes the contents of both the cans in a big container. The new mixture has half water and half wine. In what quantity did Chaman mix contents of Can 1 and 2 if Can 2 has wine to water ratio of 2 : 3 and Can 1 has wine to water ratio 5 : 3?

Solution:
Let,
Amount taken from Can 1 = x parts
Amount taken from Can 2 = y parts

In Can 1:
Wine = 5x/(8x) of total = 5x/8
Water = 3x/(8x) of total = 3x/8

In Can 2:
Wine = 2y/(5y) of total = 2y/5
Water = 3y/(5y) of total = 3y/5

In final mixture (Wine:Water = 1 : 1)
So, Total Wine = Total Water
⇒ (5x/8) + (2y/5) = (3x/8) + (3y/5)
⇒ (25x + 16y)/40 = (15x + 24y)/40
⇒ 25x + 16y = 15x + 24y
⇒ 25x - 15x = 24y - 16y
⇒ 10x = 8y
∴ x : y = 4 : 5

Therefore, Chaman should mix contents of Can 1 and Can 2 in the ratio 4 : 5.

৩১.

A and B together have Tk 2250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?

ক
Tk. 900
খ
Tk. 1660
গ
Tk. 1350
ঘ
Tk. 1050

ব্যাখ্যা

Question: A and B together have Tk 2250. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?

Solution:
ATQ,
4A/15 = 2B/5
⇒ A = (2B × 15)/(5 × 4)
⇒ A = 3B/2
⇒ A/B = 3/2
⇒ A/B = 3/2

∴ A's share = 2250(3/5) = Tk. 1350

৩২.

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:

ক
ক) 1040
খ
খ) 1600
গ
গ) 2560
ঘ
ঘ) 3120
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

৩৩.

In a class composed of x girls and y boys what part of the class is composed of girls?

ক
ক) y/(x + y)
খ
খ) x/(xy)
গ
গ) x/(x + y)
ঘ
ঘ) y/(xy)
ঙ
ঙ) None of these

ব্যাখ্যা

Question: In a class composed of x girls and y boys what part of the class is composed of girls?

Solution:
The part of the class composed of girls can be calculated using the ratio of girls to the total number of students (girls + boys)

Total number of students = x + y

∴ The class is composed of girls = Number of girls / Total number of students
= x/(x + y)

৩৪.

If x/y = 5/3 then (8x - 5y) : (8x + 5y) =

ক
5 : 11
খ
6 : 5
গ
5 : 6
ঘ
3 : 8

ব্যাখ্যা

Question: If x/y = 5/3 then (8x - 5y) : (8x + 5y) =

Solution:
x : y = 5 : 3
⇒ x/y = 5/3
⇒ 8x/5y = (5 × 8)/(3 × 5) [ 8/5 দ্বারা গুণ করে ]
⇒ 8x/5y = 8/3
⇒ (8x - 5y)/(8x + 5y) = (8 - 3)/(8 + 3) [বিয়োজন - যোজন করে]
⇒ (8x - 5y)/(8x + 5y) = (8 - 3)/(8 + 3)
∴ (8x - 5y) : (8x + 5y) = 5 : 11

৩৫.

If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers is :

ক
ক) 3 : 4
খ
খ) 3 : 20
গ
গ) 20 : 3
ঘ
ঘ) 2 : 3

ব্যাখ্যা

.04 of x = .06 of y
⇒ x/y = .06/.4
⇒ x/y = 3/20
⇒ x : y = 3 : 20

৩৬.

A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

ক
2 : 1
খ
3 : 1
গ
3 : 2
ঘ
4 : 3

ব্যাখ্যা

Let man's rate upstream be x km/hr
Then, his rate downstream = 2x km/hr
∴ (speed in still water) : (Speed of stream)
(2x + x)/2 : (2x - x)/2
3x/2 : x/2
3 : 1

৩৭.

A right triangle has sides in the ratio of 5 : 12 : 13. What is in the measure of the smallest angle in a right triangle, in degrees?

ক
ক) 13.34
খ
খ) 22.62
গ
গ) 42.17
ঘ
ঘ) 34.14

ব্যাখ্যা

We know that, sinθ = AB/AC
⇒ sinθ = 5/13
⇒ θ = sin-15/13
∴ θ = 22.62°

৩৮.

The ratio of present age of two brothers is 1 : 2 and 5 years back. the ratio was 1 : 3. What will be the ratio of their age after 5 years?

ক
3 : 5
খ
2 : 5
গ
4 : 5
ঘ
2 : 3

ব্যাখ্যা

Question: The ratio of present age of two brothers is 1 : 2 and 5 years back. the ratio was 1 : 3. What will be the ratio of their age after 5 years?

Solution:
Let, the present age of small brother be = x
and the present age of elder = 2x years

Then,
5 years ago,
(x - 5)/(2x - 5) = 1/3
⇒ 3x - 15 = 2x - 5
∴ x = 10

∴ Age of elder brother = (2 × 10) = 20 years

So, Required ratio = (10 + 5)/(20 + 5)
= 15/25
= 3 : 5

৩৯.

If 3/5 of A = 80% of B = 0.5 of C, then A : B : C is

ক
20 : 15 : 24
খ
4 : 5 : 8
গ
9 : 7 : 6
ঘ
12 : 10 : 23

ব্যাখ্যা

Question : If 3/5 of A = 80% of B = 0.5 of C, then A : B : C is-

Solution :
According to the question,
3/5 of A = 80% of B
⇒ 3A/5 = 80B/100
⇒ 3A/5 = 4B/5
⇒ A/B = 4/3
⇒ A : B = 4 : 3
∴ A : B = 20 : 15 (multiple by 5)

80% of B = 0.5 of C
⇒ 80B/100 = 5C/10
⇒ 4B/5 = C/2
⇒ B/C = 5/8
⇒ B : C = 5 : 8
∴ B : C = 15 : 24 (multiple by 3)

A : B : C = 20 : 15 : 24

৪০.

A 20 liters mixture of acid and water has 5% acid. How much acid must be added to make the solution 20% acid?

ক
3.75 liters
খ
4 liters
গ
5.25 liters
ঘ
3 liters
ঙ
4.50 liters

ব্যাখ্যা

Question: A 20 liters mixture of acid and water has 5% acid. How much acid must be added to make the solution 20% acid?

Solution:
Given that,
Acid = 5% of 20 liters
= (5/100) × 100 = 1 liters
∴ Water = 20 - 1 = 19 liters

Let the amount of acid to be added = x liters
Then,
New total acid = 1 + x
New total mixture = 20 + x

Now,
We want the acid to be 20% of the final mixture is
⇒ (1 + x)/(20 + x) = 20/100
⇒ (1 + x)/(20 + x) = 1/5
⇒ 5 + 5x = 20 + x
⇒ 4x = 15
⇒ x = 15/4
∴ x = 3.75
So 3.75 liters of acid must be added

৪১.

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

ক
1 : 2
খ
2 : 5
গ
1 : 3
ঘ
3 : 2

ব্যাখ্যা

Question: In what ratio must 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:
মনে করি, প্রথম প্রকারের x একক এবং দ্বিতীয় প্রকারের y একক মিশ্রিত করতে হবে।

প্রশ্নমতে,
প্রথম প্রকারের অ্যালকোহলের পরিমাণ = 30% of x = 0.30x
দ্বিতীয় প্রকারের অ্যালকোহলের পরিমাণ = 50% of y = 0.50y

মিশ্রণের মোট পরিমাণ = (x + y)
মিশ্রণে অ্যালকোহলের মোট পরিমাণ = 45% of (x + y) = 0.45(x + y)

শর্তমতে,
0.30x + 0.50y = 0.45(x + y)
⇒ 30x + 50y = 45(x + y) [উভয় পক্ষকে 100 দ্বারা গুণ করে]
⇒ 30x + 50y = 45x + 45y
⇒ 50y - 45y = 45x - 30x
⇒ 5y = 15x
⇒ x/y = 5/15
⇒ x/y = 1/3
∴ x : y = 1 : 3

∴ The ratio is 1 : 3

৪২.

A mixture contains acid and water in the ratio 7 : 5. If 6 liters of water is added to the mixture, the ratio becomes 7 : 8. Find the quantity of acid in the given mixture.

ক
8 liters
খ
10 liters
গ
12 liters
ঘ
14 liters

ব্যাখ্যা

Question: A mixture contains acid and water in the ratio 7 : 5. If 6 liters of water is added to the mixture, the ratio becomes 7 : 8. Find the quantity of acid in the given mixture.

Solution:
Let, the quantity of acid and water be 7x liters and 5x liters respectively

ATQ,
7x/(5x + 6) = 7/8
⇒ 56x = 7(5x + 6)
⇒ 56x = 35x + 42
⇒ 56x - 35x = 42
⇒ 21x = 42
∴ x = 2

So, Quantity of acid = (7 × 2) liters
= 14 liters

৪৩.

A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is :

ক
ক) 45 : 56
খ
খ) 45 : 51
গ
গ) 47 : 56
ঘ
ঘ) 47 : 51

ব্যাখ্যা

According to the question,
Cost Price : Marked Price
(100 - Discount) : (100 + Profit)
100 - 10 : 100 + 12
90 : 112
45 : 56

৪৪.

The capacity of two pots is 12 liters and 48 liters respectively. Find the capacity of a which can exactly measure the content of the two pots.

ক
ক) 10000 cc
খ
খ) 12000 cc
গ
গ) 8000 cc
ঘ
ঘ) 16000 cc

ব্যাখ্যা

Question: The capacity of two pots is 12 liters and 48 liters respectively. Find the capacity of a which can exactly measure the content of the two pots.

Solution:
Required capacity = H.C.F. of 12 liters and 48 liters = 12 liters

1 liter = 1000 cc
12 liters = 12000 cc

৪৫.

A and B together have taka 1,210. If 4/15 of A's amount is equal to 2/5 of B's amount. What is amount B has?

ক
Tk. 484
খ
Tk. 480
গ
Tk. 478
ঘ
Tk. 470

ব্যাখ্যা

Question: A and B together have taka 1,210. If 4/15 of A's amount is equal to 2/5 of B's amount. What is amount B has?

Solution:
4A/15 = 2B/5
⇒ A = (2B × 15)/(5 × 4)
⇒ A = 3B/2
⇒ A/B = 3/2
⇒ A : B = 3 : 2

B's share = 1210 × (2/5) = 484 Tk

৪৬.

The expense of 9 pens and 5 pencils is the same as the expense of 7 pens and 8 pencils. What is the ratio between the price of one pen and one pencil?

ক
3 : 1
খ
2 : 1
গ
1 : 2
ঘ
3 : 2

ব্যাখ্যা

Question: The expense of 9 pens and 5 pencils is the same as the expense of 7 pens and 8 pencils. What is the ratio between the price of one pen and one pencil?

Solution:
Let,
The price of one pen X Tk.
The price of one pencil Y Tk.

ATQ,
9X + 5Y = 7X + 8Y
⇒ 9X - 7X = 8Y - 5Y
⇒ 2X = 3Y
⇒ X/Y = 3/2
∴ X : Y = 3 : 2

৪৭.

A container contain 80 litres of mixture of Honey and water in the ratio 5:3. If 16 liters of this mixture is replaced by Honey, then the ratio of Honey to water in the resulting mixture becomes:

ক
ক) 5 : 2
খ
খ) 4 : 3
গ
গ) 7 : 3
ঘ
ঘ) 8 : 1

ব্যাখ্যা

৮০ লিটার মিশ্রণে মধু ও পানির অনুপাত = ৫ঃ৩
মিশ্রণে,
মধুর পরিমাণ = (৫ × ৮০)/৮ = ৫০ লিটার।
পানির পরিমাণ = (৩ × ৮০)/৮ = ৩০ লিটার।

প্রশ্নে বলা হয়েছে, মধু দ্বারা ১৬ লিটার মিশ্রণ প্রতিস্থাপিত হয়েছে।

১৬ লিটার মিশ্রণেও মধু ও পানির অনুপাত একই থাকবে।
অতএব ১৬ লিটার মিশ্রণে,
মধুর পরিমাণ = (৫ × ১৬)/৮ = ১০ লিটার।
পানির পরিমাণ = ১৬ - ১০ = ৬ লিটার।

সুতরাং, মোট মধুর পরিমাণ = ৫০ - ১০ + ১৬ = ৫৬ লিটার।
মোট পানির পরিমাণ = ৩০ - ৬ = ২৪ লিটার

মধু ও পানির অনুপাত = ৫৬ঃ২৪ = ৭ঃ৩

৪৮.

The ratio of copper and zinc in a 63 kg alloy is 4 : 3. Some amount of copper is extracted from the alloy, and the ratio becomes 10 : 9. How much copper is extracted?

ক
6 kg
খ
8 kg
গ
10 kg
ঘ
12 kg

ব্যাখ্যা

Question: The ratio of copper and zinc in a 63 kg alloy is 4 : 3. Some amount of copper is extracted from the alloy, and the ratio becomes 10 : 9. How much copper is extracted?

Solution:
Amount of copper in alloy = [copper ratio/ sum of ratios] × total quantity of alloy
Copper = (4/7) × 63 = 36 kg
Similarly, the amount of zinc in alloy = (3/7) × 63 = 27 kg
Let the extracted copper from alloy = x kg
Remaining copper in alloy = 36 - x
The new ratio = 10 : 9
i.e., 36 - x : 27 = 10 : 9
⇒ 36 - x : 3 = 10 : 1
⇒ 36 - x = 10 × 3
⇒ 36 - x = 30
∴ x = 36 - 30 = 6 kg.
Hence, the extracted amount of copper is 6 kg.

৪৯.

A container contains 40 liters of milk. From this container 4 liters 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?

ক
26 liters
খ
29.16 liters
গ
28 liters
ঘ
28.2 liters
ঙ
None of these

ব্যাখ্যা

Question: A container contains 40 liters of milk. From this container 4 liters 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?

Solution:
Milk contained by the container now
= 40(1 - 4/40)³
= 40(1 - 1/10)³
= 40 × 0.9 × 0.9 × 0.9
= 29.16

৫০.

A truck covers a distance of 550 meters in 1 minute whereas a bus covers a distance of 44 kms in 60 minutes. The ratio of their speeds is-

ক
ক) 3 ∶ 7
খ
খ) 4 ∶ 5
গ
গ) 3 ∶ 5
ঘ
ঘ) 3 ∶ 4

ব্যাখ্যা

Given that
Distance covered by truck = 550 m
Time taken by truck to cover the distance = 1 min
Distance covered by bus = 44 km = 44,000 m
Time taken by bus to cover the distance = 60 min

Speed of truck = 550/1 = 550 m/min
Speed of bus = 44,000/60 = 2,200/3 m/min
Speed of truck ∶ Speed of bus = 550 ∶ (2,200/3)
= 1 : 4/3
= 3 ∶ 4

∴ The ratio of the speed of the truck to the speed of the bus is 3 ∶ 4.

৫১.

The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond?

ক
ক) 144
খ
খ) 148
গ
গ) 152
ঘ
ঘ) 156

ব্যাখ্যা

Question: The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 152. What is the number of frogs in the pond?

Solution:
The ratio of Ducks and Frogs in the Pond = 37 : 39
Average of Ducks and Frogs in the Pond = 152
So, the total number of Ducks and Frogs in the Pond = 2 × 152 = 304
∴ Number of Frogs = (304 × 39)/76 = 156

৫২.

A and B are in the ratio of 6 : 5 and B and C are in the ratio of 4 : 3. What is the ratio of A : C?

ক
12 : 15
খ
7 : 15
গ
8 : 5
ঘ
13 : 15

ব্যাখ্যা

Question: A and B are in the ratio of 6 : 5 and B and C are in the ratio of 4 : 3. What is the ratio of A : C?

Solution:
Given the ratio of,
A : B = 6 : 5 = (6 × 4) : (5 × 4) = 24 : 20

And,
B : C = 4 : 3 = (4 × 5) : (3 × 5) = 20 : 15

∴ A : C = 24 : 15 = 8 : 5

৫৩.

P and Q started a business investing Tk. 57000 and Tk. 33000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively.

ক
ক) 19 : 33
খ
খ) 17 : 31
গ
গ) 19 : 11
ঘ
ঘ) 12 : 31

ব্যাখ্যা

In this question as time frame for both investors is same as then just get the ratio of their investments.

P : Q
= 57000 : 33000
= 57 : 33
= 19 : 11

৫৪.

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?

ক
ক) 50
খ
খ) 100
গ
গ) 150
ঘ
ঘ) 200
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.

৫৫.

A proficient worker is twice as efficient as an apprentice. After 10 days of joint work, they earn Tk. 45,000 together. What is the apprentice’s wage per day?

ক
Tk. 2000
খ
Tk. 1500
গ
Tk. 1600
ঘ
Tk. 1250

ব্যাখ্যা

Question: A proficient worker is twice as efficient as an apprentice. After 10 days of joint work, they earn Tk. 45,000 together. What is the apprentice’s wage per day?

Solution:
Given that,
A seasoned workers efficiency is twice as much as an apprentice's.
They work together for 10 days
And earn Tk. 45000 together

Here, Efficiency of Seasoned Worker : Apprentice = 2 : 1
Now, earning in 1 day = 45000/10 = Tk. 4500
So, Daily wage of Apprentice = 4500 × (1/3) = Tk. 1500

Thus, the daily wage of the apprentice is Tk. 1500.

৫৬.

If A and B are in the ratio 3 : 4, and B and C are in the ratio 12 : 13. Then A and C will be in the ratio:

ক
3 : 13
খ
9 : 13
গ
36 : 13
ঘ
13 : 9

ব্যাখ্যা

Question: If A and B are in the ratio 3 : 4, and B and C are in the ratio 12 : 13. Then A and C will be in the ratio:

Solution:
দেওয়া আছে,
A : B = 3 : 4
⇒ A/B = 3/4

এবং
B : C = 12 : 13
⇒ B/C = 12/13

∴ (A/B) × (B/C) = (3/4) × (12/13)
⇒ A/C = 9/13
∴ A : C = 9 : 13

Then A and C will be in the ratio is 9 : 13.

৫৭.

Rafi weighs 72 kg. If he reduces his weight in the ratio 6 : 5, find his new weight in kg.

ক
56 Kg
খ
60 Kg
গ
52.5 Kg
ঘ
58.5 Kg

ব্যাখ্যা

Question: Rafi weighs 72 kg. If he reduces his weight in the ratio 6 : 5, find his new weight in kg.

Solution:
ধরি, রাফির পূর্বের ওজন = 6x
রাফির পরের ওজন = 5x

প্রশ্নমতে,
6x = 72
⇒ x = 72 / 6 = 12

∴ ওজন কমে যাওয়ার পর হবে = 5x = 5 × 12 = 60 kg

৫৮.

A jar is filled with liquid, 2 parts of which are water and 4 parts juice. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half juice?

ক
1/2
খ
1/4
গ
2/3
ঘ
5/2
ঙ
7/5

ব্যাখ্যা

Question: A jar is filled with liquid, 2 parts of which are water and 4 parts juice. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half juice?

Solution:
Let the quantity of liquid in the vessel = 6 units.
Out of this liquid, x units are replaced by water.

Amount of water in the new mixture = {2 - (2x/6) + x} unit
= 2 - (x/3) + x
= (6 - x + 3x)/3
= (2x + 6)/3 unit

Amount of juice in the new mixture = 4 - (4x/6) unit
= 4 - (2x/3)
= (12 - 2x)/3 unit

ATQ,
(2x + 6)/3 = (12 - 2x)/3
⇒ 2x + 6 = 12 - 2x
⇒ 4x = 6
⇒ x = 3/2

∴ The fraction of the mixture that is replaced is = (3/2) × (1/6)
= 1/4

৫৯.

If 10% of X is equal to 20% of Y, then find X : Y.

ক
1:2
খ
2:1
গ
4:1
ঘ
1:4
ঙ
1:3

ব্যাখ্যা

10% of X = 20% of Y
or, (10/100) × X = (20/100) × Y
or, X/10 = Y/5
or, 5X = 10Y
or, X = 2Y
or, X/Y = 2/1
So, X : Y = 2 : 1

৬০.

The number of students in 3 classes is in the ratio 2 : 3 : 4. If 12 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
140
খ
148
গ
158
ঘ
162

ব্যাখ্যা

Question: The number of students in 3 classes is in the ratio 2 : 3 : 4. If 12 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 + 12) : (3x + 12) = 8 : 11
⇒ 8(3x + 12) = 11(2x +12)
⇒ 24x + 96 = 22x + 132
⇒ 24x - 22x = 132 - 96
⇒ 2x = 36
⇒ x = 36/2
⇒ x = 18

Hence,
Original number of students,
9x = 9 × 18
= 162

৬১.

If 10% of m is the same as the 20% of n, then m : n is equal to

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

ব্যাখ্যা

10% of m = 20% of n
⇒ (10/100) × m = (20/100) × n
⇒ 10 m = 20 n
⇒ m/n = 20/10
∴ m : n = 2 : 1

৬২.

A mixture is composed of 3 elements. By weight, 3/5 is water, 1/3 of the mixture is sand and the remaining 12 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?

ক
60
খ
120
গ
180
ঘ
None of these

ব্যাখ্যা

Question: A mixture is composed of 3 elements. By weight, 3/5 is water, 1/3 of the mixture is sand and the remaining 12 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?

Solution:
বালু ও পানির পরিমাণ = (1/3) + (3/5) অংশ
= (5 + 9)/15 অংশ
= 14/15 অংশ

অবশিষ্ট কাঁকরের পরিমাণ = 1 - (14/15) অংশ
= 1/15 অংশ

প্রশ্নমতে,
1/15 = 12 পাউন্ড
∴ 1 বা সম্পূর্ণ অংশ = 12 × 15 পাউন্ড
= 180 পাউন্ড

অতএব, সম্পূর্ণ মিশ্রণের পরিমাণ 180 পাউন্ড।

৬৩.

A cask contain 12 litres of mixture of milk and water in the ratio 3:1. How much of the mixture must be drawn off and water substituted so that milk and water in the cask may becomes half and half.

ক
ক) 3 Litres
খ
খ) 4 Litres
গ
গ) 2 Litres
ঘ
ঘ) 5 Litres

ব্যাখ্যা

12 লিটার মিশ্রণে দুধ ও পানির অনুপাত = 3 : 1
দুধের পরিমাণ = 12 × 3/4 = 9 লিটার
পানির পরিমাণ = 12 × 1/4 = 3 লিটার

ধরি, x লিটার মিশ্রণ ফেলে দেওয়া হয়।
তাহলে, x লিটার পানি প্রতিস্থাপিত হবে।

x লিটার মিশ্রণে,
দুধের পরিমাণ = 3x/4 লিটার
পানির পরিমাণ = x/4 লিটার

মোট দুধের পরিমাণ = 9 - 3x/4
মোট পানির পরিমাণ = 3 - x/4 + x

যেহেতু দুধ ও পানির অনুপাত = 1:1 হতে হলে, দুধ ও পানির পরিমাণ সমান হতে হবে।

প্রশ্নমতে,
দুধ = পানি
বা, 9 - 3x/4 = 3 - x/4 + x
বা, 6 = 3x/4 - x/4 + x
বা, 6 = 6x/4
বা, x = 4

৬৪.

Two equal glasses are respectively one-third and one-fourth full of milk. They are then filled up with water and the contents are mixed in a tumbler. Ratio of milk and water in tumbler is-

ক
7 : 5
খ
7 : 17
গ
3 : 7
ঘ
11 : 23

ব্যাখ্যা

Question: Two equal glasses are respectively one-third and one-fourth full of milk. They are then filled up with water and the contents are mixed in a tumbler. Ratio of milk and water in tumbler is-

Solution:
Quantity of milk in tumbler = 1/4 + 1/3 = 7/12

Quantity of water in tumbler
= (1 - 1/4) + (1 -1/3) = 3/4 + 2/3 = 17/12

So, ratio of milk and water = (7/12) : (17/12)
= 7 : 17

৬৫.

A Tk. 30,000 prize is to be divided among three employees in the ratio of 2 : 3 : 5. What is the value of the smallest share?

ক
ক) 9000
খ
খ) 7500
গ
গ) 6000
ঘ
ঘ) 4500

ব্যাখ্যা

Question: A Tk. 30,000 prize is to be divided among three employees in the ratio of 2 : 3 : 5. What is the value of the smallest share?

Solution:
৩০০০০ টাকা ২ : ৩ : ৫ অনুপাতে ভাগ করে দেয়া হয়।

অতএব,
২x + ৩x + ৫x = ৩০০০০
⇒ ১০x = ৩০০০০
∴ x = ৩০০০ টাকা

সর্বনিম্ন শেয়ার = ২ × ৩০০০ টাকা
= ৬০০০ টাকা

৬৬.

If 3 : 27 :: 5 : x, then what is the value of x?

ক
9
খ
36
গ
45
ঘ
63

ব্যাখ্যা

Question: If 3 : 27 :: 5 : x, then what is the value of x?

Solution:
3/27 = 5/x
⇒ x = 5 × 27/3
⇒ x = 45

৬৭.

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

ক
1 : 2
খ
5 : 4
গ
4 : 5
ঘ
3 : 2

ব্যাখ্যা

Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

Solution:
Let the third number be x

Then, first number = 120% of x = 120x/100 = 6x/5
Second number = 150% of x = 150x/100 = 3x/2

∴ Ratio of first two numbers = 6x/5 : 3x/2
= 12x : 15x
= 4 : 5

৬৮.

In a 60-liter mixture, the ratio of juice and water is 5:1. How much water must be added to make the ratio 2:1?

ক
10 liters
খ
12 liters
গ
15 liters
ঘ
18 liters

ব্যাখ্যা

Question: In a 60-liter mixture, the ratio of juice and water is 5:1. How much water must be added to make the ratio 2:1?

সমাধান:
মোট মিশ্রণের পরিমাণ = ৬০ লিটার
জুস : পানি = ৫ : ১
∴ জুসের পরিমাণ = (৫/৬) × ৬০ = ৫০ লিটার
∴ পানির পরিমাণ = (১/৬) × ৬০ = ১০ লিটার

মনে করি,
ক লিটার পানি যোগ করতে হবে।
⇒ নতুন পানির পরিমাণ = ১০ + ক লিটার
জুস অপরিবর্তিত = ৫০ লিটার

প্রশ্নমতে,
৫০/(১০ + ক) = ২/১
⇒ ৫০ = ২ × (১০ + ক)
⇒ ৫০ = ২০ + ২ক
⇒ ২ক = ৩০
⇒ ক = ১৫

∴ ১৫ লিটার পানি যোগ করতে হবে।

৬৯.

If A : B = 3 : 4, and B : C = 12 : 17, then A : C = ?

ক
9 : 17
খ
9 : 12
গ
12 : 17
ঘ
17 : 12

ব্যাখ্যা

A : B = 3 : 4 = (3 × 3) : (4 × 3) = 9 : 12
B : C = 12 : 17
A : B : C = 9 : 12 : 17
Therefore, A : C = 9 : 17

৭০.

Mean proportional of 4 and 36 is x and third proportional of 18 and x is y. Find the value of y.

ক
ক) 9
খ
খ) 12
গ
গ) 8
ঘ
ঘ) 6

ব্যাখ্যা

প্রশ্ন: Mean proportional of 4 and 36 is x and third proportional of 18 and x is y. Find the value of y.

সমাধান:
Given,
Mean proportional of 4 and 36 = x
∴ x² = 4 × 36
⇒ x = 12

Third proportional of 18 and 12 = y
∴ 12² = 18 × y
⇒ 144 = 18 × y
⇒ y = 8

৭১.

A and B together have Tk. 500. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?

ক
ক) 200
খ
খ) 250
গ
গ) 300
ঘ
ঘ) 350

ব্যাখ্যা

Question: A and B together have Tk. 500. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?

Solution:
Here,
(4/15)A = (2/5)B
A/B = 30/20
A : B = 3 : 2

Hence,
The amount of A = (500 × 3/5)
= 1500/5
= 300

৭২.

Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is

ক
ক) 27
খ
খ) 33
গ
গ) 49
ঘ
ঘ) 55

ব্যাখ্যা

Let the numbers be 3x and 5x.
Then, (3x-9)/(5x - 9) = 12/23
⇒ 23(3x - 9) = 12(5x - 9)
⇒ 69x - 207 = 60x - 108
⇒ 9x = 99
⇒ x = 11.
∴ The smaller number = (3×11) = 33

৭৩.

Tea worth Tk. 126 per kg and Tk. 135 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk. 153 per kg, the price of the third variety per kg will be:

ক
Tk. 150.2
খ
Tk. 170.8
গ
Tk. 184.5
ঘ
Tk. 190

ব্যাখ্যা

Question: Tea worth Tk. 126 per kg and Tk. 135 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk. 153 per kg, the price of the third variety per kg will be:

Solution:
let, price of third variety x tk per kg
126y + 135 × 2y + x × 2y = 153 (y + 2y + 2y)
⇒ 126 + 270 + 2x = 765
⇒ 2x = 369
∴ x = 184.5 tk

৭৪.

The ratio between the perimeter and the length of a rectangle is 5 : 2. If the area of the rectangle is 484 sq. cm, what is the length of the rectangle?

ক
11 cm
খ
16 cm
গ
23 cm
ঘ
32 cm
ঙ
44 cm

ব্যাখ্যা

Question: The ratio between the perimeter and the length of a rectangle is 5 : 2. If the area of the rectangle is 484 sq. cm, what is the length of the rectangle?

Solution:
Let Length = l
& Breadth = b
Perimeter of a rectangle = 2(l + b)

Now,
2(l + b)/l = 5/2
⇒ 4(l + b) = 5l
⇒ l = 4b

Area, l × b = 484
⇒ 4b × b = 484
⇒ b² = 121
⇒ b = 11

∴ l = 4 × 11 = 44
The length of the rectangle is 44 cm.

৭৫.

There are peacock and horse in a zoo. The total number of their heads is 50 and the number of legs is 140. How many horses are there?

ক
20
খ
25
গ
15
ঘ
30

ব্যাখ্যা

Question: There are peacock and horse in a zoo. The total number of their heads is 50 and the number of legs is 140. How many horses are there?

Solution:
Let, there are x horses.

ATQ,
4x + (50 - x)2 = 140
4x + 100 - 2x = 140
2x = 40
x = 20

৭৬.

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

ক
ক) 1/3
খ
খ) 1/4
গ
গ) 1/5
ঘ
ঘ) 1/7

ব্যাখ্যা

Let initially vessel have 8 litres of liquid and x litres of this liquid be replaced with water,
Then quantity of water in new mixture = 3 - 3x/8 + x
Quantity of syrup in new mixture = 5 - 5x/8
According to the question,
After replacement, the quantity water and syrup same,
(3 - 3x/8 + x) = (5 - 5x/8)
⇒ -3x/8 + x + 5x/8 = 5 - 3
⇒ (-3x + 8x + 5x)/8 = 2
⇒ 10x/8 = 2
⇒ x = 8/5
So, part of the mixture replaced, 8/5 × 1/8 ⇒ 1/5

∴ 1/5 of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup.

৭৭.

In a school having roll strength 324, the ratio of boys and girls is 8 : 4. If 27 more girls get admitted into the school, the ratio of boys and girls becomes?

ক
8 : 5
খ
3 : 5
গ
7 : 3
ঘ
6 : 5

ব্যাখ্যা

Question: In a school having roll strength 324, the ratio of boys and girls is 8 : 4. If 27 more girls get admitted into the school, the ratio of boys and girls becomes?

Solution:
let the boys = 8x,
and the girls = 4x

ATQ,
8x + 4x = 324
⇒ 12x = 324
⇒ x = 324/12
∴ x = 27

Boys = 8 × 27 = 216
and girls = 4 × 27 = 108
27 more girls get admitted then number of girls become = 108 + 27 = 135
Now, new ratio of boys and girls = 216 : 135
= 8 : 5

৭৮.

An 80L solution of alcohol and water has 45% alcohol in it. If you want the mixture to be 75% alcohol, how much alcohol would you add to it?

ক
ক) 30 litres
খ
খ) 75 litres
গ
গ) 96 litres
ঘ
ঘ) 110 litres

ব্যাখ্যা

Current alcohol quantity = {(45/100) × 80}
= 36 Litres.

Let A be alcohol added.
So, 36 + A = (75/100) × (80 + A)
⇒ 36 + A = (3/4) × (80 + A)
⇒ 144 + 4A = 240 + 3A
∴ A = 96 Litres =

96 Litres is the additional quantity of alcohol to be added.

৭৯.

In what ratio must a grocer mix two varieties of pulses costing Tk. 15 and Tk. 20 per kg respectively so as to get a mixture worth Tk. 16.50 kg?

ক
7 : 3
খ
5 : 7
গ
3 : 7
ঘ
7 : 5

ব্যাখ্যা

Question: In what ratio must a grocer mix two varieties of pulses costing Tk. 15 and Tk. 20 per kg respectively so as to get a mixture worth Tk. 16.50 kg?

Solution:
Let
15 Tk kg pulses = x kg and 20 Tk kg pulses = y kg
ATQ,
15x + 20y = 16.5(x + y)
⇒ 15x + 20y = 16.5x + 16.5y
⇒ 1.5x = 3.5y
⇒ x/y = 3.5/1.5
⇒ x/y = 7/3
⇒ x : y = 7 : 3

৮০.

The ratio of P : Q is 3 : 4 and the ratio of Q : R is 5 : 6. If P is equal to 9, what is the value of R?

ক
14.4
খ
15.4
গ
16.5
ঘ
15.5

ব্যাখ্যা

Question: The ratio of P : Q is 3 : 4 and the ratio of Q : R is 5 : 6. If P is equal to 9, what is the value of R?
Solution:
Given that,
P : Q = 3 : 4
Q : R = 5 : 6
And P = 9

Now,
P : Q = 3 : 4
or, P/Q = 3/4
or, 9/Q = 3/4
or, 3Q = 36
or, Q = 36/3
∴ Q = 12

And,
Q : R = 5 : 6
or, Q/R = 5/6
or, 12/R = 5/6
or, 5R = 72
or, R = 72/5
∴ R = 14.4

so, the value of R is 14.4

৮১.

Tk. 30,000 prize is to be divided among three employees in the ratio of 2 : 3 : 5 . What is the value of the smallest share?

ক
ক) Tk. 9000
খ
খ) Tk. 4000
গ
গ) Tk. 6000
ঘ
ঘ) Tk. 3000

ব্যাখ্যা

Question: Tk. 30,000 prize is to be divided among three employees in the ratio of 2 : 3 : 5 . What is the value of the smallest share?

Solution:
ধরি,
অনুপাতের রাশিগুলোর মান = x

তাহলে,
প্রদত্ত অনুপাত হবে 2x : 3x : 5x

প্রশ্নমতে,
বা, 2x + 3x + 5x = 30000
বা, 10x = 30000
∴ x = 3000

ক্ষুদ্রতম শেয়ার, 2x = 2 × 3000
= 6000

৮২.

A container has 64 liters of milk. From this container, 16 liters of milk was taken out and replaced with water. This process was repeated twice. What is the final ratio of milk and water in the container?

ক
4 : 5
খ
9 : 7
গ
16 : 9
ঘ
25 : 39

ব্যাখ্যা

Question: A container has 64 liters of milk. From this container, 16 liters of milk was taken out and replaced with water. This process was repeated twice. What is the final ratio of milk and water in the container?

Solution:
Initial quantity of milk = 64 liters
Removed quantity = 16 liters
Total quantity = 64 liters
Number of times the process is repeated = 2

Remaining milk = Initial quantity × {1 - (Removed Quantity/Total Quantity)}ⁿ
= 64 × {1 - (16/64)}²
= 64 × (3/4)²
= 36 liters

So, Final quantity of milk = 36 liters
Final quantity of water = (64 - 36) = 28 liters

Therefore, Ratio of milk to water = 36/28 = 9 : 7

৮৩.

A pot contains a mixture of two liquids A and B is the ratio 7 : 5. When 12 litres of mixture are drawn off and the pot is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the pot initially?

ক
4
খ
21
গ
28
ঘ
27
ঙ
36

ব্যাখ্যা

Suppose the pot initially contains 7x and 5x of mixtures A and B respectively.
Quantity of A in mixture left = 7x - 7/12 × 12
= 7x - 7
Quantity of B in mixture left = 5x - 5/12 × 12
= 5x - 5
According to the question,
(7x - 7) / {(5x - 5) + 12} = 7/9
or, x = 4
So, the pot contained (4 × 7) liters or 28 liters of A

৮৪.

If the ratio of speed of doing work of three persons is 1 : 3 : 5, what is the ratio of time taken by these people to do the same amount of work?

ক
ক) 15 : 5 : 3
খ
খ) 15 : 5 : 7
গ
গ) 3 : 15 : 5
ঘ
ঘ) 15 : 3 : 5

ব্যাখ্যা

The ratio of the speed of three persons is 1 : 3 : 5
Let the speed of doing work of the three persons be 1x, 3x, and 5x respectively
Time is taken by each person = amount of work done/speed of doing work
Let the amount of work for each person = y (∵ work done is same)

The time is taken by the first person = y/x
The time is taken by the second person = y/3x
The time is taken by the third person = y/5x

The ratio of time taken= y/x : y/3x : y/5x
= 1/x : 1/3x : y/5x
= 1 : 1/3 : 1/5
= 15 : 5 : 3
The ratio is =15 : 5 : 3

৮৫.

A dairy farmer's can contains 6 litres of milk. His wife adds some water to it such that milk and water are in the ratio 4 ∶ 1. How many litres of milk should the farmer add so that the milk and water are in the ratio 5 ∶ 1?

ক
2.5 litres
খ
0.5 litres
গ
1.5 litres
ঘ
3.5 litres

ব্যাখ্যা

Question: A dairy farmer's can contains 6 litres of milk. His wife adds some water to it such that milk and water are in the ratio 4 ∶ 1. How many litres of milk should the farmer add so that the milk and water are in the ratio 5 ∶ 1?

Solution:
Given that,
Initially, 6 litres of milk (no water yet)
Wife adds water so that milk : water = 4 : 1
After that, farmer adds some milk so that the new ratio is 5 : 1

Now, find the amount of water added by the wife,
Milk : Water = 4 : 1
Milk = 6 litres
Let water = w litres
From the ratio we get,
⇒ 6/w = 4/1
⇒ 4w = 6
⇒ w = 6/4
⇒ w = 1.5
So, after wife adds water, mixture = 6 litres milk + 1.5 litres water.

And,
Let the farmer add x litres of milk
Now, Milk = 6 + x litres
Water = 1.5 litres
After farmer adds milk, new ratio is,
⇒ (6 + x)/1.5 = 5/1
⇒ 6 + x = 7.5
⇒ x = 7.5 - 6
∴ x = 1.5

The farmer should add 1.5 litres of milk.

৮৬.

In a 90-liter mixture of milk and water, the ratio of milk to water is 2 : 1. How many liters of water must be added to make the ratio become 1 : 2?

ক
48 litres
খ
80 litres
গ
90 litres
ঘ
50 litres

ব্যাখ্যা

Question: In a 90-liter mixture of milk and water, the ratio of milk to water is 2 : 1. How many liters of water must be added to make the ratio become 1 : 2?

Solution:
Total mixture = 90 litres
Given ratio (milk : water) = 2 : 1

Milk = 90 × (2/3) = 60 litres
Water = 90 − 60 = 30 litres

To make the ratio 1 : 2, x liters of water need to be added.
milk : water = 60 : (30 + x)

So,
60 / (30 + x) = 1 / 2

Cross-multiplying,
2 × 60 = 30 + x
120 = 30 + x
x = 120 − 30
∴ x = 90

Quantity of water to be added = 90 litres.

৮৭.

A starts a flower shop with an investment Tk. 8000. After 3 months B joins him with an investment of Tk. 16000. C joins them later with an investment of Tk. 40,000/-. The business prospers and makes a profit of Tk. 1,12,000/- at the end of the year. If profits of A, B and C are in the ratio of 6 : 9 : 5, for how many months was C a part of the business?

ক
ক) 2 months
খ
খ) 3 months
গ
গ) 5 months
ঘ
ঘ) 6 months

ব্যাখ্যা

We know that
The ratio of Investment x Time = Ratio of Profit
∴ (A's investment × Time) : (B's investment × Time) = Profit of A : Profit of B

∴ Tk. 8000 × 12 months : Tk. 16000 × 9 months : Tk. 40000 × ? months = 6 : 9 : 5
∴ 96000 : 144000 : 40000 × ? = 6 : 9 : 5
By direct observation we can say, if common factor is K, then
6K = 96000;
∴ K = 16000;
and 5K = 40000 × ?
? = 5k/40000
= (5 × 16000)/40000
= 2 months.

৮৮.

In your wallet, there are Tk 500, Tk 200 and Tk 100. notes in the ratio 5 : 9 : 4, amounting to Tk 18,800. Find the number of each note respectively.

ক
20, 36, 16
খ
37, 1, 1
গ
10, 18, 8
ঘ
25, 10, 7
ঙ
None

ব্যাখ্যা

Question: In your wallet, there are Tk 500, Tk 200 and Tk 100. notes in the ratio 5 : 9 : 4, amounting to Tk 18,800. Find the number of each note respectively.

Solution:
In your wallet, there are Tk 500, Tk 200 and Tk 100. notes in the ratio 5 : 9 : 4
Let,
Number of Tk. 500 note is 5x
Number of Tk. 200 note is 9x
Number of Tk. 100 note is 4x

ATQ,
500 × 5x + 200 × 9x + 100 × 4x = 18800
⇒ 2500x + 1800x + 400x = 18800
⇒ 4700x = 18800
⇒ x = 18800/4700
∴ x = 4

Number of Tk. 500 note is 5x = 5 × 4 = 20
Number of Tk. 200 note is 9x = 9 × 4 = 36
Number of Tk. 100 note is 4x = 4 × 4 = 16

৮৯.

Haris and Sunny share some sweets in the ratio of 7 : 5. Haris has 12 more sweets than Sunny. How many sweets were there altogether?

ক
ক) 42
খ
খ) 72
গ
গ) 30
ঘ
ঘ) 144

ব্যাখ্যা

প্রশ্ন: Haris and Sunny share some sweets in the ratio of 7 : 5. Haris has 12 more sweets than Sunny. How many sweets were there altogether?

সমাধান:
Let,
Haris has 7x sweets
Sunny has 5x sweets
∴ Total sweets 7x + 5x = 12x

ATQ,
7x - 5x = 12
⇒ 2x = 12
∴ x = 6

∴ There were 12 × 6 = 72 sweets altogether.

৯০.

The fourth proportional of the values 2.1, 3.5, 5.4 is

ক
ক) 7.5
খ
খ) 8.6
গ
গ) 9.0
ঘ
ঘ) 6.0

ব্যাখ্যা

Given:
2.1, 3.5, 5.4

Formula Used:
If a : b :: c : d
then a × d = b × c

a : b :: c : d,
⇒ 2.1 : 3.5 :: 5.4 : d
⇒ 2.1 × d = 3.5 × 5.4
⇒ d = 9.0

∴ The required answer is 9.0

৯১.

A specific bank branch serves 256 clients on average every day. The ratio between tellers and clients is 1 : 32, so that every teller serves 32 people on average every day. The management wishes to change this ratio to 1 : 20. How many new tellers should be hired?

ক
4
খ
5
গ
9
ঘ
12

ব্যাখ্যা

Question: A specific bank branch serves 256 clients on average every day. The ratio between tellers and clients is 1 : 32, so that every teller serves 32 people on average every day. The management wishes to change this ratio to 1 : 20. How many new tellers should be hired?

Question:

First, let's determine the approximate number of tellers in the branch. We will term this number X

Clients/tellers = 256/X = 32/1

⇒ 256 = 32X

∴ X = 8

There are currently 8 tellers working in the branch.

Let,
needed teller number be Y

Clients/tellers = 256/Y = 20/1

⇒ 256 = 20Y

∴ Y = 12.8

Since we cannot have a fraction as the number of tellers, we will round this number down to 13.

∴ New tellers should be hired 13 - 8 = 5

৯২.

If 4 years ago the ratio between the ages of Nuha and Naba was 5 : 6 and the sum of their ages at present is 52. What is the ratio of their present ages ?

ক
3 : 8
খ
4 : 7
গ
6 : 7
ঘ
5 : 9

ব্যাখ্যা

Question : If 4 years ago the ratio between the ages of Nuha and Naba was 5 : 6 and the sum of their ages at present is 52. What is the ratio of their present ages ?

Solution :
Let
Four years ago, Nuha's age was = 5x
and Naba's age was = 6x

According to the question,
(5x + 4) + (6x + 4) = 52
⇒ 11x + 8 = 52
⇒ 11x = 52 - 8
⇒11x = 44
∴ x = 4

∴ Present age of Nuha = 5x + 4
= 5 × 4 + 4
= 24

∴ Present age of Naba = 6x + 4
= 6 × 4 + 4
= 28

So the ratio of their present ages = 24 : 28
= 6 : 7

৯৩.

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?

ক
ক) 3 litres
খ
খ) 5 litres
গ
গ) 6 litres
ঘ
ঘ) 8 litres

ব্যাখ্যা

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

৯৪.

In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by b -

ক
21 m
খ
26 m
গ
28 m
ঘ
29 m

ব্যাখ্যা

A : B = 100 : 75
B : C = 100 : 96

∴ A : C = A/B × B/C
= (100/75) × (100/96)
= 100/72
100 : 72

∴ A beats C by
100 - 72 = 28 m.

৯৫.

Two numbers are in the ratio 3 : 5. If 8 is added to both the numbers, their ratio becomes 2 : 3. The greater number is

ক
ক) 24
খ
খ) 36
গ
গ) 40
ঘ
ঘ) 45

ব্যাখ্যা

Two numbers are 3y and 5y
(3y + 8)/(5y + 8) = 2/3
10y + 16 = 9y + 24
y = 8
The greater number is 5 × 8 = 40

৯৬.

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:

ক
ক) 150
খ
খ) 160
গ
গ) 170
ঘ
ঘ) 180
ঙ
ঙ) 200

ব্যাখ্যা

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

৯৭.

In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by -

ক
ক) 18m
খ
খ) 20m
গ
গ) 25m
ঘ
ঘ) 27m

ব্যাখ্যা

Question: In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by -

Solution:
A : B = 200 : 169
A : C = 200 : 182

B/C = (B/A) × (A/C)
= 169/182

So, in a 350 race B will pass = (169/182) × 350
= 325m

hence, C will beat B by (350 - 325) or, 25 metres

৯৮.

How much coffee, costing Tk. 100 per kg, should be mixed with 20 kg of cocoa priced at Tk. 300 per kg to get a blend worth Tk. 200 per kg?

ক
14
খ
12
গ
20
ঘ
15
ঙ
None

ব্যাখ্যা

Question: How much coffee, costing Tk. 100 per kg, should be mixed with 20 kg of cocoa priced at Tk. 300 per kg to get a blend worth Tk. 200 per kg?

Solution:
Ratio in which cocoa and coffee should be mixed
= 300 - 200 : 200 - 100
= 100 : 100
= 1 : 1

Let x be the quantity of coffee at 100/kg.

∴ 1 : 1 = x : 20
⇒ x = 20

৯৯.

An alloy of gold and copper weights 50 g. It contains 80% gold. How much gold should be added to the alloy so that percentage of gold is increased to 90?

ক
40 gm
খ
50 gm
গ
45 gm
ঘ
60 gm

ব্যাখ্যা

Question: An alloy of gold and copper weights 50 g. It contains 80% gold. How much gold should be added to the alloy so that percentage of gold is increased to 90?

Solution:
Gold in alloy =50 × 80% = 40gm
Copper in alloy =50 × 20% =10gm
Now,
(40 + x)/10 = 90/10
⇒ 40 + x = 90
⇒ x = 90 - 40
∴ x = 50gm

১০০.

Mehedi pays 3 workers P, Q and R a total of Tk. 6000 a week. P is paid 125% of the amount Q is paid and 80% of the amount R is paid. How much does P make in a week?

ক
ক) Tk. 1968.6
খ
খ) Tk. 1978.5
গ
গ) Tk. 1967.2
ঘ
ঘ) Tk. 1975.3

ব্যাখ্যা

Question: Mehedi pays 3 workers P, Q and R a total of Tk. 6000 a week. P is paid 125% of the amount Q is paid and 80% of the amount R is paid. How much does P make in a week?

Solution:
Let,
P is paid Tk. x
Q is paid Tk. (100x)/125 = (4x)/5
R is paid Tk. (100x)/80 = (5x)/4

ATQ,
x + (4x)/5 + (5x)/4 = 6000
⇒ 20x + 16x + 25x = 6000 × 20 [multiply with 20]
⇒ 61x = 120000
⇒ x = 120000/61
∴ x = 1967.2

∴ P makes 1967.2 Tk. in a week.